reduce to easel3d-xcb demo program

 [package]
-name = "xcb-test"
+name = "easel3d-xcb"
 version = "0.1.0"
 authors = ["Georg Hopp <georg@steffers.org>"]
 edition = "2018"
 
 [dependencies]
+easel3d = { path = "../easel3d" }
 libc = "0.2"
-gl = "0.5.2"
-x11 = { version = "2.3", features = ["glx"] }
 xcb = { version = "0.8", features = ["dri2", "randr", "thread", "xlib_xcb", "shm"] }

-# Rust playground
+# Easel3D-XCB
 
-Things I have recently done while learning the Rust programming language.
+X windows demo application using Easel3D...
 
 ## Synopsis
 
-Change in one of the toplevel subdirectories and try `cargo build` or
-`cargo run`. Maybe not everything is working oob. Feel free to fix whatever
-you want.
+Checkout this repository as well as the _easel3d_ repository to the same
+destination directory.
 
-## Description
-
-Various small examples I have tried while learning rust. The biggest and
-currently most active project is **fractional** which started as an
-implamentation of a rational number data type and then switched to a 3D
-math playground visualizing using **XCB** (in future it might also use
-a **HTML5 Canvas** for drawing as WebAssembly application.
-Using fractions with 3D math has several drawbacks:
+In the root of this repository call `cargo run`.
 
-1. A huge part of 3D math is non rational, like sin, cos, tan and sqrt.
-2. The numerator and denominator tend to become very huge while nearing to non
-   rational numbers and reduction is difficult and time consuming.
-3. Because of 2 it is way slower than the floating point calculation (at least
-   with a decent coprocessor).
+## Description
 
-Anyway, implementing the vector math stuff for both fractions and floating
-point was a nice playground for generics and traits. In future I might add
-another data type which implements the math as done by David Braben for the
-elite computer game.
+A demo application using easel3d to draw in an X-Window.
 
 ## Requirements
 
-### Always
-
 - A recent version of the Rust programming language as well as tooling.
   Currently I use Rust 1.39.0.
+- X11 (xcb, x11-shm)
 
-### For fractional
+## Dependencies
 
-- A running X Server with **XCB** and **X11-SHM** extentions
+### Rust crates.
 
-## Dependencies
+- easel3d (from parent directory)
+- libc >=0.2
+- xcb >=0.8
 
-...
+Along with the dependencies of the xcb crate. `cargo build` should take care
+of having them available.
 
 ## Contributing
 

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "branches"
-version = "0.1.0"
-

-[package]
-name = "branches"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Control Flow Examples
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-fn main() {
-    let condition = true;
-    let number = if condition {
-        5
-    } else {
-        6
-    };
-
-    println!("The value of number is: {}", number);
-}

-[package]
-name = "fractional"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-[dependencies]
-lazy_static = "1.4.0"
-libc = "0.2"
-gl = "0.5.2"
-x11 = { version = "2.3", features = ["glx"] }
-xcb = { version = "0.8", features = ["dri2", "randr", "thread", "xlib_xcb", "shm"] }

-http://www.jongware.com/galaxy1.html

-I really would like to see a HTML5 canvas as canvas for the 3D code.
-
-Some URLs:
-- https://stackoverflow.com/questions/42806037/modify-canvas-from-wasm
-- https://rustwasm.github.io/wasm-bindgen/api/web_sys/struct.HtmlCanvasElement.html
-- https://rustwasm.github.io/wasm-bindgen/api/web_sys/struct.CanvasRenderingContext2d.html
-- https://stackoverflow.com/questions/49935207/editing-canvas-pixel-data-in-webassembly-rust

-https://www.themathpage.com/Alg/reciprocals.htm

-https://en.wikipedia.org/wiki/Texture_mapping
-http://www.gamers.org/dEngine/quake/papers/checker_texmap.html
-https://www.cs.uic.edu/~jbell/CourseNotes/ComputerGraphics/TextureMapping.html
-http://www.decew.net/OSS/References/chapter_2_texture_mapping.pdf
-
-# example affine texture mapping
-http://archive.gamedev.net/archive/reference/articles/article852.html
-
-
-http://www.lysator.liu.se/~mikaelk/doc/perspectivetexture/
-
-# Shader... This also describes z-Buffer... :)
-https://people.ece.cornell.edu/land/OldStudentProjects/cs490-95to96/GUO/report.html
-https://software.intel.com/en-us/articles/the-basics-of-the-art-of-lighting-part-3-lighting-and-shaders/
-https://docs.unity3d.com/Manual/Lighting.html

-//
-// A «continued fraction» is a representation of a fraction as a vector
-// of integrals… Irrational fractions will result in infinite most of the
-// time repetitive vectors. They can be used to get a resonable approximation
-// for sqrt on fractionals.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use crate::Fractional;
-
-#[derive(Debug)]
-pub struct Continuous (Vec<i64>);
-
-impl Continuous {
-    // calculate a sqrt as continued fraction sequence. Taken from:
-    // https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#
-    //  Continued_fraction_expansion
-    pub fn sqrt(x :i64, a0 :i64) -> Self {
-        fn inner(v :&mut [i64], x :i64, a0 :i64, mn :i64, dn :i64, an :i64) {
-            let mn_1 = dn * an - mn;
-            let dn_1 = (x - mn_1 * mn_1) / dn;
-            let an_1 = (a0 + mn_1) / dn_1;
-
-            v[0] = an;
-            // The convergence criteria „an_1 == 2 * a0“ is not good for
-            // very small x thus I decided to break the iteration at constant
-            // time. Which is the 5 below.
-            if v.len() > 1 {
-                inner(&mut v[1..], x, a0, mn_1, dn_1, an_1);
-            }
-        }
-
-        let mut v :Vec<i64> = vec!(0; 5);
-        inner(&mut v, x, a0, 0, 1, a0);
-        Continuous(v)
-    }
-
-    // general continous fraction form of a fractional...
-    pub fn from_prec(f :&Fractional, prec :Option<usize>) -> Self {
-        fn inner(v :&mut Vec<i64>, f :Fractional, prec :Option<usize>) {
-            let mut process = |prec :Option<usize>| {
-                let Fractional(n, d)   = f;
-                let a                  = n / d;
-                let Fractional(_n, _d) = f.noreduce_sub(a.into());
-
-                v.push(a);
-                match _n {
-                    1 => v.push(_d),
-                    0 => {},
-                    _ => inner(v, Fractional(_d, _n), prec),
-                }
-            };
-
-            match prec {
-                Some(0) => {},
-                None    => process(None),
-                Some(p) => process(Some(p - 1)),
-            }
-        }
-
-        let mut v = match prec {
-            None    => Vec::with_capacity(100),
-            Some(p) => Vec::with_capacity(p + 1),
-        };
-
-        inner(&mut v, *f, prec);
-        Continuous(v)
-    }
-
-    pub fn into_prec(&self, prec :Option<usize>) -> Fractional {
-        let Continuous(c) = self;
-        let             p = match prec {
-            Some(p) => if p <= c.len() { p } else { c.len() },
-            None    => c.len(),
-        };
-
-        let to_frac = |acc :Fractional, x :&i64| {
-            let Fractional(an, ad) = acc.noreduce_add((*x).into());
-            Fractional(ad, an)
-        };
-
-        let Fractional(n, d) = c[..p]
-                             . into_iter()
-                             . rev()
-                             . fold(Fractional(0, 1), to_frac);
-        Fractional(d, n)
-    }
-}
-
-impl From<&Fractional> for Continuous {
-    fn from(x :&Fractional) -> Self {
-        Self::from_prec(x, None)
-    }
-}
-
-impl Into<Fractional> for &Continuous {
-    fn into(self) -> Fractional {
-        (&self).into_prec(None)
-    }
-}

-//
-// This is an abstraction over a drawing environment.
-// Future note: z-Buffer is described here:
-// https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/perspective-correct-interpolation-vertex-attributes
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::cmp;
-use std::fmt::{Formatter, Debug, Display, Result};
-use std::ops::{Add, Sub, Div};
-use std::sync::mpsc;
-
-pub trait Easel {
-    //fn canvas(&mut self, width :u16, height :u16) -> Option<&dyn Canvas>;
-}
-
-pub trait Canvas<T> {
-    fn init_events(&self);
-    fn start_events(&self, tx :mpsc::Sender<i32>);
-
-    fn width(&self) -> u16;
-    fn height(&self) -> u16;
-
-    fn clear(&mut self);
-    fn draw(&mut self, c :&dyn Drawable<T>, ofs :Coordinate<T>, color :u32);
-    fn put_text(&self, ofs :Coordinate<T>, s :&str);
-    fn set_pixel(&mut self, c :Coordinate<T>, color :u32);
-    fn show(&self);
-}
-
-pub trait Drawable<T> {
-    fn plot(&self) -> Coordinates<T>;
-}
-
-pub trait Fillable<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    fn fill(&self, canvas :&mut dyn Canvas<T>, color :u32);
-}
-
-#[derive(Debug, Clone, Copy)]
-pub struct Coordinate<T>(pub i32, pub i32, pub T);
-
-#[derive(Debug, Clone)]
-pub struct Coordinates<T>(pub Vec<Coordinate<T>>);
-
-#[derive(Debug, Clone, Copy)]
-pub struct LineIterator<T> where T: Debug {
-               a :Option<Coordinate<T>>
-    ,          b :Coordinate<T>
-    ,         dx :i32
-    ,         dy :i32
-    ,         dz :T
-    ,         sx :i32
-    ,         sy :i32
-    ,        err :i32
-    , only_edges :bool
-}
-
-impl<T> Iterator for LineIterator<T>
-where T: Add<Output = T> + Debug + Copy + From<i32> {
-    type Item = Coordinate<T>;
-
-    fn next(&mut self) -> Option<Self::Item> {
-        match self.a {
-            None    => None,
-            Some(a) => {
-                let Coordinate(ax, ay, az) = a;
-                let Coordinate(bx, by,  _) = self.b;
-
-                if ax != bx || ay != by {
-                    match (2 * self.err >= self.dy, 2 * self.err <= self.dx ) {
-                        (true, false) => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax + self.sx
-                                                      , ay
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dy;
-                            if self.only_edges { self.next() } else { r }
-                        },
-                        (false, true) => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax
-                                                      , ay + self.sy
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dx;
-                            r
-                        },
-                        _             => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax + self.sx
-                                                      , ay + self.sy
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dx + self.dy;
-                            r
-                        },
-                    }
-                } else {
-                    self.a = None;
-                    Some(self.b)
-                }
-            }
-        }
-    }
-}
-
-impl<T> Coordinate<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn iter(self, b :&Self, only_edges :bool) -> LineIterator<T> {
-        let Coordinate(ax, ay, az) = self;
-        let Coordinate(bx, by, bz) = *b;
-
-        let dx = (bx - ax).abs();
-        let dy = -(by - ay).abs();
-
-        LineIterator {    a: Some(self)
-                     ,    b: *b
-                     ,   dx: dx
-                     ,   dy: dy
-                     ,   dz: (bz - az) / cmp::max(dx, -dy).into()
-                     ,   sx: if ax < bx { 1 } else { -1 }
-                     ,   sy: if ay < by { 1 } else { -1 }
-                     , err: dx + dy
-                     , only_edges: only_edges
-        }
-    }
-
-    fn line_iter(self, b :&Self) -> LineIterator<T> {
-        self.iter(b, false)
-    }
-
-    fn line(self, b :&Self) -> Vec<Self> {
-        self.line_iter(b).collect()
-    }
-
-    fn edge_iter(self, b :&Self) -> LineIterator<T> {
-        self.iter(b, true)
-    }
-
-    fn edge(self, b :&Self) -> Vec<Self> {
-        self.edge_iter(b).collect()
-    }
-
-    fn face(edges :&[Self]) -> Vec<Self> {
-        edges.to_vec()
-    }
-}
-
-impl<T> Display for Coordinate<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        write!(f, "<{},{}>", self.0, self.1)
-    }
-}
-
-impl<T> Display for Coordinates<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Coordinates(is) = self;
-
-        let c = match is[..] {
-            []  => String::from(""),
-            [a] => format!("{}", a),
-            _   => {
-                let mut a = format!("{}", is[0]);
-                for i in is[1..].iter() {
-                    a = a + &format!(",{}", i);
-                }
-                a
-            }
-        };
-
-        write!(f, "Coordinates[{}]", c)
-    }
-}
-
-
-#[derive(Debug, Clone, Copy)]
-pub struct Point<T>(pub Coordinate<T>);
-
-impl<T> Drawable<T> for Point<T> where T: Copy {
-    fn plot(&self) -> Coordinates<T> {
-        let Point(c) = *self;
-        Coordinates(vec!(c))
-    }
-}
-
-impl<T> Display for Point<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Point(p) = self;
-        write!(f, "Point[{}]", p)
-    }
-}
-
-#[derive(Debug, Clone, Copy)]
-pub struct Line<T>(pub Coordinate<T>, pub Coordinate<T>);
-
-impl<T> Drawable<T> for Line<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Line(a, b) = *self;
-        Coordinates(a.line(&b))
-    }
-}
-
-impl<T> Display for Line<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Line(a, b) = self;
-        write!(f, "Line[{},{}]", a, b)
-    }
-}
-
-#[derive(Debug, Clone)]
-pub struct Polyline<T>(pub Coordinates<T>);
-
-impl<T> Drawable<T> for Polyline<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Polyline(Coordinates(cs)) = self;
-
-        match cs[..] {
-            []     => Coordinates(Vec::<Coordinate<T>>::new()),
-            [a]    => Coordinates(vec!(a)),
-            [a, b] => Coordinates(a.line(&b)),
-            _      => {
-                let (a, b) = (cs[0], cs[1]);
-                let mut r = a.line(&b);
-                let mut i = b;
-                for j in cs[2..].iter() {
-                    r.append(&mut i.line(j)[1..].to_vec());
-                    i = *j;
-                }
-                Coordinates(r)
-            },
-        }
-    }
-}
-
-impl<T> Display for Polyline<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Polyline(a) = self;
-        write!(f, "PLine[{}]", a)
-    }
-}
-
-#[derive(Debug, Clone, Copy)]
-enum Direction { Left, Right }
-
-#[derive(Debug, Clone)]
-pub struct Polygon<T>(pub Coordinates<T>);
-
-#[derive(Debug, Clone)]
-enum VertexIteratorMode { Vertex, Edge }
-#[derive(Debug, Clone)]
-pub struct VertexIterator<'a,T> where T: Debug {
-    p         :&'a Polygon<T>,
-    top       :usize,
-    current   :Option<usize>,
-    edge      :Option<LineIterator<T>>,
-    mode      :VertexIteratorMode,
-    direction :Direction,
-}
-
-impl<'a,T> VertexIterator<'a,T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    fn edge(p :&'a Polygon<T>, direction :Direction) -> Self {
-        let top  = p.vert_min(direction);
-        let next = p.next_y(top, direction);
-        let edge = match next {
-            None       => None,
-            Some(next) => Some(p.vertex(top).edge_iter(&p.vertex(next))),
-        };
-
-        VertexIterator { p:         p
-                       , top:       top
-                       , current:   next
-                       , edge:      edge
-                       , mode:      VertexIteratorMode::Edge
-                       , direction: direction }
-    }
-
-    fn vertex(p :&'a Polygon<T>, direction :Direction) -> Self {
-        let top  = p.vert_min(direction);
-        let next = p.next_y(top, direction);
-
-        VertexIterator { p:         p
-                       , top:       top
-                       , current:   next
-                       , edge:      None
-                       , mode:      VertexIteratorMode::Vertex
-                       , direction: direction }
-    }
-
-    // if this yields "None" we are finished.
-    fn next_edge(&mut self) -> Option<LineIterator<T>> {
-        let current  = self.current?;
-        let next     = self.p.next_y(current, self.direction)?;
-        let mut edge = self.p.vertex(current).edge_iter(&self.p.vertex(next));
-
-        match edge.next() {
-            // It should be impossible that a new edge iterator has no values
-            // at all… anyway, just in case I handle it here.
-            None    => self.next_edge(),
-            Some(_) => {
-                self.current = Some(next);
-                self.edge    = Some(edge);
-                self.edge
-            },
-        }
-    }
-}
-
-impl<'a,T> Iterator for VertexIterator<'a,T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    type Item = Coordinate<T>;
-
-    fn next(&mut self) -> Option<Self::Item> {
-        match self.mode {
-            VertexIteratorMode::Edge => {
-                // if for whatever reason edge is "None" finish this iterator.
-                let next = self.edge.as_mut()?.next();
-
-                match next {
-                    Some(_) => next,
-                    None    => {
-                        self.next_edge()?;
-                        self.next()
-                    },
-                }
-            },
-            VertexIteratorMode::Vertex => {
-                let current  = self.current?;
-                self.current = self.p.next_y(current, self.direction);
-                Some(self.p.vertex(current))
-            },
-        }
-    }
-}
-
-impl<T> Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Copy + Debug + From<i32> {
-    #[inline]
-    fn vertex(&self, v :usize) -> Coordinate<T> {
-        let Polygon(Coordinates(cs)) = self;
-        cs[v]
-    }
-
-    fn vert_min<'a>(&'a self, d :Direction) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        type ICoord<'a,T> = (usize, &'a Coordinate<T>);
-
-        // TODO I guess the problem here is that it does not account for the
-        //      same y vertex on the beggining and the end. So i guess correct
-        //      would be finding the first one and then dependings on the
-        //      given direction either search left or right for same y's.
-        let fold = |acc :Option<ICoord<'a,T>>, x :ICoord<'a,T>|
-            match acc {
-                None    => Some(x),
-                Some(a) => {
-                    let Coordinate(_, ay, _) = a.1;
-                    let Coordinate(_, xy, _) = x.1;
-                    if xy < ay {Some(x)} else {Some(a)}
-                },
-            };
-
-        let mut  min = cs.iter().enumerate().fold(None, fold).unwrap().0;
-        let mut next = self.step(min, d);
-
-        while self.vertex(min).1 == self.vertex(next).1 {
-            min = next;
-            next = self.step(min, d);
-        }
-
-        min
-    }
-
-    fn left_edge(&self) -> VertexIterator<T> {
-        VertexIterator::edge(self, Direction::Left)
-    }
-
-    fn right_edge(&self) -> VertexIterator<T> {
-        VertexIterator::edge(self, Direction::Right)
-    }
-
-    fn left_vertices(&self) -> VertexIterator<T> {
-        VertexIterator::vertex(self, Direction::Left)
-    }
-
-    fn right_vertices(&self) -> VertexIterator<T> {
-        VertexIterator::vertex(self, Direction::Right)
-    }
-
-    fn left(&self, v :usize) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        match v {
-            0 => cs.len() - 1,
-            _ => v - 1,
-        }
-    }
-
-    fn right(&self, v :usize) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        (v + 1) % cs.len()
-    }
-
-    fn step(&self, v :usize, d :Direction) -> usize {
-        match d {
-            Direction::Left  => self.left(v),
-            Direction::Right => self.right(v),
-        }
-    }
-
-    fn next_y(&self, c :usize, d :Direction) -> Option<usize> {
-        fn inner<T>( p :&Polygon<T>
-                   , c :usize
-                   , n :usize
-                   , d :Direction) -> Option<usize>
-        where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-               + Copy + Debug + From<i32> {
-            if c == n {
-                None
-            } else {
-                let Coordinate(_, cy, _) = p.vertex(c);
-                let Coordinate(_, ny, _) = p.vertex(n);
-
-                if ny < cy { None } else { Some(n) }
-            }
-        }
-
-        inner(self, c, self.step(c, d), d)
-    }
-
-    pub fn debug(&self) {
-        let mut left  = self.left_vertices();
-        let mut right = self.right_vertices();
-
-        if left.find(|l| right.find(|r| l.0 == r.0).is_some()).is_some() {
-            let left  :Vec<Coordinate<T>> = self.left_vertices().collect();
-            let right :Vec<Coordinate<T>> = self.right_vertices().collect();
-
-            println!("===");
-            println!("==  poly : {:?}", self);
-            println!("==  ltop : {:?}", self.vert_min(Direction::Left));
-            println!("==  rtop : {:?}", self.vert_min(Direction::Right));
-            println!("==  left : {:?}", left);
-            println!("== right : {:?}", right);
-            println!("===");
-        }
-    }
-}
-
-impl<T> Drawable<T> for Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Polygon(Coordinates(cs)) = self;
-
-        match cs[..] {
-            []     => Coordinates(Vec::<Coordinate<T>>::new()),
-            [a]    => Coordinates(vec!(a)),
-            [a, b] => Coordinates(a.line(&b)),
-            _      => {
-                let (a, b) = (cs[0], cs[1]);
-                let mut r = a.line(&b);
-                let mut i = b;
-                for j in cs[2..].iter() {
-                    r.append(&mut i.line(j)[1..].to_vec());
-                    i = *j;
-                }
-                let mut j = a.line(&i);
-                let     l = j.len();
-                if l > 1 {
-                    r.append(&mut j[1..l-1].to_vec());
-                }
-                Coordinates(r)
-            },
-        }
-    }
-}
-
-impl<T> Fillable<T> for Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn fill(&self, canvas :&mut dyn Canvas<T>, color :u32) {
-        let scanlines = self.left_edge().zip(self.right_edge());
-
-        for l in scanlines.flat_map(|(l, r)| l.line_iter(&r)) {
-            canvas.set_pixel(l, color);
-        }
-    }
-}
-
-impl<T> Display for Polygon<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Polygon(a) = self;
-        write!(f, "Poly[{}]", a)
-    }
-}

-//
-// Some code to support fractional numbers for full precision rational number
-// calculations. (At least for the standard operations.)
-// This also implements a sqrt on fractional numbers, which can not be precise
-// because of the irrational nature of most sqare roots.
-// Fractions can only represent rational numbers precise.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::cmp::Ordering;
-use std::convert::{TryFrom, TryInto};
-use std::fmt::{Formatter, Display};
-use std::num::TryFromIntError;
-use std::ops::{Add,Sub,Neg,Mul,Div};
-
-use crate::continuous::Continuous;
-
-#[derive(Debug, Eq, Clone, Copy)]
-pub struct Fractional (pub i64, pub i64);
-
-#[inline]
-fn hcf(x :i64, y :i64) -> i64 {
-    match y {
-        0 => x,
-        _ => hcf(y, x % y),
-    }
-}
-
-pub fn from_vector(xs: &Vec<i64>) -> Vec<Fractional> {
-    xs.iter().map(|x| Fractional(*x, 1)).collect()
-}
-
-impl Fractional {
-    #[inline]
-    pub fn gcd(self, other: Self) -> i64 {
-        let Fractional(_, d1) = self;
-        let Fractional(_, d2) = other;
-        (d1 * d2) / hcf(d1, d2)
-    }
-
-    #[inline]
-    pub fn reduce(self) -> Self {
-        let Fractional(n, d) = self;
-        let (_n, _d) = if n > d { (n, d) } else { (d, n) };
-
-        // if the difference from _n % _d to _n is very big we are close to
-        // a whole number and can ignore the fractional part... this reduces
-        // the precision but ensures smaller numbers for numerator and
-        // denominator.
-        if _d > 1 && (_n % _d) * 10000000 < _n {
-            if n == _n {
-                Self(_n / _d, 1)
-            } else {
-                Self(1, _n / _d)
-            }
-        } else {
-            // Self(n / hcf(n, d), d / hcf(n, d))
-            // The above reduces prcisely but results in very large numerator
-            // or denominator occasionally. The below is less precise but
-            // keeps the numbers small… the bad point is, that it is not very
-            // fast.
-            let cont = Continuous::from_prec(&self, Some(5));
-            (&cont).into()
-        }
-    }
-
-    pub fn noreduce_add(self, other: Self) -> Self {
-        let Fractional(n1, d1) = self;
-        let Fractional(n2, d2) = other;
-        let n = n1 * (self.gcd(other) / d1) + n2 * (self.gcd(other) / d2);
-        Self(n, self.gcd(other))
-    }
-
-    pub fn noreduce_sub(self, other: Self) -> Self {
-        self.noreduce_add(other.noreduce_neg())
-    }
-
-    pub fn noreduce_neg(self) -> Self {
-        let Fractional(n, d) = self;
-        Self(-n, d)
-    }
-}
-
-impl From<i64> for Fractional {
-    fn from(x: i64) -> Self {
-        Self(x, 1)
-    }
-}
-
-impl From<i32> for Fractional {
-    fn from(x: i32) -> Self {
-        Self(x as i64, 1)
-    }
-}
-
-impl TryFrom<usize> for Fractional {
-    type Error = &'static str;
-
-    fn try_from(x: usize) -> Result<Self, Self::Error> {
-        let v = i64::try_from(x);
-        match v {
-            Err(_) => Err("Conversion from usize to i32 failed"),
-            Ok(_v) => Ok(Self(_v, 1)),
-        }
-    }
-}
-
-impl TryInto<f64> for Fractional {
-    type Error = TryFromIntError;
-
-    fn try_into(self) -> Result<f64, Self::Error> {
-        let n :i32 = self.0.try_into()?;
-        let d :i32 = self.1.try_into()?;
-        Ok(f64::from(n) / f64::from(d))
-    }
-}
-
-impl TryInto<(i32, i32)> for Fractional {
-    type Error = TryFromIntError;
-
-    fn try_into(self) -> Result<(i32, i32), Self::Error> {
-        let a :i32 = (self.0 / self.1).try_into()?;
-        let b :i32 = (self.0 % self.1).try_into()?;
-        Ok((a, b))
-    }
-}
-
-impl Display for Fractional {
-    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
-        write!(f, "({}/{})", self.0, self.1)
-    }
-}
-
-impl PartialEq for Fractional {
-    fn eq(&self, other: &Self) -> bool {
-        let Fractional(n1, d1) = self;
-        let Fractional(n2, d2) = other;
-        n1 * (self.gcd(*other) / d1) == n2 * (self.gcd(*other) / d2)
-    }
-}
-
-impl PartialOrd for Fractional {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        Some(self.cmp(other))
-    }
-}
-
-impl Ord for Fractional {
-    fn cmp(&self, other: &Self) -> Ordering {
-        let Fractional(n1, d1) = self;
-        let Fractional(n2, d2) = other;
-        let x = n1 * (self.gcd(*other) / d1);
-        let y = n2 * (self.gcd(*other) / d2);
-        x.cmp(&y)
-    }
-}
-
-impl Add for Fractional {
-    type Output = Self;
-
-    fn add(self, other: Self) -> Self {
-        self.noreduce_add(other).reduce()
-    }
-}
-
-impl Sub for Fractional {
-    type Output = Self;
-
-    fn sub(self, other: Self) -> Self {
-        self + -other
-    }
-}
-
-impl Neg for Fractional {
-    type Output = Self;
-
-    fn neg(self) -> Self {
-        let Fractional(n, d) = self;
-        Self(-n, d)
-    }
-}
-
-impl Mul for Fractional {
-    type Output = Self;
-
-    fn mul(self, other :Self) -> Self {
-        let Fractional(n1, d1) = self;
-        let Fractional(n2, d2) = other;
-        Self(n1 * n2, d1 * d2).reduce()
-    }
-}
-
-impl Div for Fractional {
-    type Output = Self;
-
-    fn div(self, other: Self) -> Self {
-        let Fractional(n, d) = other;
-        self * Fractional(d, n)
-    }
-}
-
-    /* some stuff that could be tested...
-    let x = Fractional(1, 3);
-    let y = Fractional(1, 6);
-
-    println!(
-        "Greatest common denominator of {} and {}: {}", x, y, x.gcd(y));
-    println!("Numerator of {}: {}", x, x.numerator());
-    println!("Denominator of {}: {}", x, x.denominator());
-    assert_eq!(Fractional(1, 3), Fractional(2, 6));
-    assert_eq!(Fractional(1, 3), Fractional(1, 3));
-    assert_eq!(y < x, true);
-    assert_eq!(y > x, false);
-    assert_eq!(x == y, false);
-    assert_eq!(x == x, true);
-    assert_eq!(x + y, Fractional(1, 2));
-    println!("{} + {} = {}", x, y, x + y);
-    assert_eq!(x - y, Fractional(1, 6));
-    println!("{} - {} = {}", x, y, x - y);
-    assert_eq!(y - x, Fractional(-1, 6));
-    println!("{} - {} = {}", y, x, y - x);
-    assert_eq!(-x, Fractional(-1, 3));
-    println!("-{} = {}", x, -x);
-    assert_eq!(x * y, Fractional(1, 18));
-    println!("{} * {} = {}", x, y, x * y);
-    assert_eq!(x / y, Fractional(2, 1));
-    println!("{} / {} = {}", x, y, x / y);
-    assert_eq!(y / x, Fractional(1, 2));
-    println!("{} / {} = {}", y, x, y / x);
-
-    println!("Fractional from 3: {}", Fractional::from(3));
-    let z :f64 = Fractional::into(x);
-    println!("Floating point of {}: {}", x, z);
-    let (d, r) = Fractional::into(x);
-    println!("(div, rest) of {}: ({}, {})", x, d, r);
-    */
-

-//
-// Basic geometric things...
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::convert::{From, Into};
-use std::ops::{Add,Sub,Neg,Mul,Div};
-use std::fmt::Debug;
-
-use crate::easel::{Canvas, Coordinate, Coordinates, Polygon};
-use crate::transform::{TMatrix, Transformable};
-use crate::trigonometry::Trig;
-use crate::vector::Vector;
-
-#[derive(Debug, Clone)]
-pub struct Face<T>
-where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
-    corners :Vec<usize>,
-    normal  :Option<Vector<T>>,
-}
-
-#[derive(Debug, PartialEq, Eq, Clone, Copy)]
-pub struct Point<T>(pub Vector<T>, T)
-    where T: Add + Sub + Neg + Mul + Div + PartialEq + Copy + Trig;
-
-impl<T> Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    pub fn new(x :T, y :T, z :T) -> Self {
-        Self(Vector(x, y, z), 1.into())
-    }
-}
-
-impl<T> Add for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn add(self, other :Self) -> Self {
-        let Point(v1, w1) = self;
-        let Point(v2, w2) = other;
-        Self(v1 + v2, w1 + w2)
-    }
-}
-
-impl<T> Neg for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn neg(self) -> Self {
-        let Point(v, w) = self;
-        Self(-v, -w)
-    }
-}
-
-impl<T> Sub for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn sub(self, other :Self) -> Self {
-        self + -other
-    }
-}
-
-impl<T> Mul for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    type Output = Self;
-
-    fn mul(self, other :Self) -> Self {
-        let a :Vector<T> = self.into();
-        let b :Vector<T> = other.into();
-
-        Point(a * b, 1.into())
-    }
-}
-
-impl<T> From<Vector<T>> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    fn from(v :Vector<T>) -> Self {
-        Point(v, 1.into())
-    }
-}
-
-impl<T> Into<Vector<T>> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    fn into(self) -> Vector<T> {
-        let Point(v, w) = self;
-
-        if w == 0.into() {
-            v
-        } else {
-            v.mul(&w.recip())
-        }
-    }
-}
-
-impl<T> Transformable<T> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Trig + Copy + From<i32> {
-    fn transform(&self, m :&TMatrix<T>) -> Self {
-        let Point(v, w) = *self;
-        let (v, w)      = m.apply(&v, w);
-
-        if w == 0.into() {
-            v.into()
-        } else {
-            v.mul(&w.recip()).into()
-        }
-    }
-}
-
-#[derive(Debug)]
-pub struct Polyeder<T>
-where T: Add + Sub + Neg + Mul + Div + PartialEq + Copy + Trig {
-    points :Vec<Point<T>>,
-    faces  :Vec<Face<T>>,
-}
-
-pub trait Primitives<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    fn transform(&self, m :&TMatrix<T>) -> Self;
-    fn project( &self
-              , camera :&Camera<T>
-              , light :&DirectLight<T>
-              , col :u32 ) -> Vec<(Polygon<T>, u32)>;
-}
-
-pub struct Camera<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    width    :T,
-    height   :T,
-    distance :T,
-    project  :TMatrix<T>,
-}
-
-pub struct DirectLight<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    direction: Vector<T>,
-}
-
-impl<T> Camera<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    // This code assumes that the size of the viewport is always
-    // equal to the size of the physical screen… e.g. window/canvas thus some
-    // effects can't be done. See book for examples with different viewport
-    // and screen sizes.
-    pub fn new(c :&dyn Canvas<T>, angle :i32) -> Self {
-        let  width :T = (c.width() as i32).into();
-        let height :T = (c.height() as i32).into();
-        let      d :T = 1.into();
-        let    fov    = T::cot(angle) * width;
-        let     wh    = width / 2.into();
-        let     hh    = height / 2.into();
-
-        Camera { width:    width
-               , height:   height
-               , distance: d
-               , project:  TMatrix::new(
-                     (     fov, 0.into(),       wh, 0.into())
-                   , (0.into(),      fov,       hh, 0.into())
-                   , (0.into(), 0.into(),        d, 1.into())
-                   , (0.into(), 0.into(), 1.into(), 0.into()) ) }
-    }
-
-    pub fn get_distance(&self) -> T {
-        self.distance
-    }
-
-    pub fn get_projection(&self) -> TMatrix<T> {
-        self.project
-    }
-
-    pub fn project(&self, p :Point<T>) -> Point<T> {
-        p.transform(&self.project)
-    }
-}
-
-impl<T> DirectLight<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Copy + Trig + From<i32> {
-    pub fn new(v :Vector<T>) -> Self {
-        DirectLight{ direction: v }
-    }
-
-    pub fn dir(&self) -> Vector<T> {
-        self.direction
-    }
-}
-
-impl<T> Face<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    fn new(corners :Vec<usize>, ps :&[Point<T>]) -> Self {
-        let mut f = Face{ corners: corners, normal: None };
-        f.update_normal(ps);
-        f
-    }
-
-    fn update_normal(&mut self, ps :&[Point<T>]) {
-        let edge10 :Vector<T> = (ps[self.corners[1]] - ps[self.corners[0]]).into();
-        let edge12 :Vector<T> = (ps[self.corners[1]] - ps[self.corners[2]]).into();
-        self.normal = Some(edge10 * edge12);
-    }
-}
-
-impl<T> Polyeder<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    fn update_normals(&mut self) {
-        for f in self.faces.iter_mut() {
-            f.update_normal(&self.points);
-        }
-    }
-
-    // construct via cube, see polyhedra.pdf
-    pub fn tetrahedron(a :T) -> Polyeder<T> {
-        let f2 :T = 2.into();
-        let ch    = a / (f2 * T::sqrt(f2).unwrap());
-
-        let ps = vec!( Point::new(-ch, -ch,  ch)    // A
-                     , Point::new(-ch,  ch, -ch)    // C
-                     , Point::new( ch, -ch, -ch)    // E
-                     , Point::new( ch,  ch,  ch) ); // G
-
-        // bottom: 1, 2, 3
-        let fs = vec!( Face::new(vec!(2, 1, 0), &ps) // bottom
-                     , Face::new(vec!(3, 2, 0), &ps)
-                     , Face::new(vec!(0, 1, 3), &ps)
-                     , Face::new(vec!(1, 2, 3), &ps) );
-        //let fs = vec!( Face::new(vec!(0, 1, 2), &ps) // bottom
-        //             , Face::new(vec!(0, 2, 3), &ps)
-        //             , Face::new(vec!(3, 1, 0), &ps)
-        //             , Face::new(vec!(3, 2, 1), &ps) );
-
-        Polyeder{ points: ps, faces: fs }
-    }
-
-    pub fn triangle(a :T) -> Polyeder<T> {
-        let f0 :T = 0.into();
-        let f3 :T = 3.into();
-        let f6 :T = 6.into();
-        let zi :T = T::sqrt(f3).unwrap() / f6 * a;
-        let zc :T = T::sqrt(f3).unwrap() / f3 * a;
-        let ah :T = a / 2.into();
-
-        let ps = vec!( Point::new(-ah, f0, -zi)
-                     , Point::new( f0, f0,  zc)
-                     , Point::new( ah, f0, -zi) );
-
-        let fs = vec!(Face::new(vec!(0, 1, 2), &ps));
-
-        Polyeder{ points: ps, faces: fs }
-    }
-
-    pub fn cube(a :T) -> Polyeder<T> {
-        let ah :T = a / From::<i32>::from(2);
-
-        let ps = vec!( Point::new(-ah,  ah, -ah)    // 0 => front 1
-                     , Point::new(-ah, -ah, -ah)    // 1 => front 2
-                     , Point::new( ah, -ah, -ah)    // 2 => front 3
-                     , Point::new( ah,  ah, -ah)    // 3 => front 4
-                     , Point::new(-ah,  ah,  ah)    // 4 => back 1
-                     , Point::new(-ah, -ah,  ah)    // 5 => back 2
-                     , Point::new( ah, -ah,  ah)    // 6 => back 3
-                     , Point::new( ah,  ah,  ah) );  // 7 => back 4
-
-        let fs = vec!( Face::new(vec!(0, 1, 2, 3), &ps)    // front
-                     , Face::new(vec!(7, 6, 5, 4), &ps)    // back
-                     , Face::new(vec!(1, 5, 6, 2), &ps)    // top
-                     , Face::new(vec!(0, 3, 7, 4), &ps)    // bottom
-                     , Face::new(vec!(0, 4, 5, 1), &ps)    // left
-                     , Face::new(vec!(2, 6, 7, 3), &ps) ); // right
-
-        Polyeder{ points: ps, faces: fs }
-    }
-}
-
-impl<T> Primitives<T> for Polyeder<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Copy + Trig + From<i32> + PartialOrd {
-    // TODO Maybe this should also be an instance of Transformable…
-    fn transform(&self, m :&TMatrix<T>) -> Self {
-        let Polyeder{ points: ps, faces: fs } = self;
-
-        let mut p = Polyeder{
-              points: ps.iter().map(|p| p.transform(m)).collect()
-            , faces:  fs.to_vec()
-        };
-
-        // TODO alternatively we could rotate the normals too, but this cannot
-        // done with the original matrix… the question is, what is faster.
-        p.update_normals();
-        p
-    }
-
-    fn project( &self
-              , camera :&Camera<T>
-              , light :&DirectLight<T>
-              , color :u32 ) -> Vec<(Polygon<T>, u32)> {
-        // Helper to create a Polygon from Coordinates…
-        // TODO probably there needs to be a Polygon constructor for this.
-        fn polygon<I, T>(c :I) -> Polygon<T>
-        where I: Iterator<Item = Coordinate<T>> {
-            Polygon(Coordinates(c.collect()))
-        }
-
-        // this one does the projection... as the projection was the last
-        // matrix we do not need to do it here.
-        let to_coord = |p :&usize| {
-            let Point(v, _) = camera.project(self.points[*p]);
-            Coordinate(T::round(&v.x()), T::round(&v.y()), v.z() - 1.into())
-        };
-        let to_poly  = |f :&Face<T>| {
-                       let     pg    = polygon(f.corners.iter().map(to_coord));
-                       let mut  r :T = (((color >> 16) & 0xFF) as i32).into();
-                       let mut  g :T = (((color >>  8) & 0xFF) as i32).into();
-                       let mut  b :T = (((color      ) & 0xFF) as i32).into();
-                       let     lf :T = match f.normal {
-                           None    => 1.into(),
-                           Some(n) => n.dot(light.dir())
-                                    / (n.mag() * light.dir().mag()),
-                       };
-
-                       // this "if" represents a first simple backface culling
-                       // approach. We only return face that face towards us.
-                       if lf < 0.into() {
-                           r = r * -lf;
-                           g = g * -lf;
-                           b = b * -lf;
-
-                           let c :u32 = (r.round() as u32) << 16
-                                      | (g.round() as u32) << 8
-                                      | (b.round() as u32);
-
-                           Some((pg, c))
-                       } else {
-                           None
-                       }};
-
-        self.faces.iter().filter_map(to_poly).collect()
-    }
-}

-//
-// Lib for fractional calculations.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-extern crate lazy_static;
-
-pub type Error = &'static str;
-
-pub mod continuous;
-pub mod easel;
-pub mod fractional;
-pub mod transform;
-pub mod trigonometry;
-pub mod vector;
-pub mod xcb;
-pub mod geometry;
-
-use fractional::Fractional;
-use vector::Vector;

-//
-// Test our fractional crate / module...
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::convert::{TryFrom, TryInto, Into};
-use std::f64::consts::PI as FPI;
-use std::fmt::{Debug, Display};
-use std::marker::Send;
-use std::num::TryFromIntError;
-use std::ops::{Add,Sub,Neg,Mul,Div};
-use std::sync::mpsc;
-use std::thread;
-use std::time::{Duration, Instant};
-
-use fractional::continuous::Continuous;
-use fractional::easel::{ Coordinate, Coordinates, Drawable, Line, Polyline
-                       , Polygon, Canvas, Fillable };
-use fractional::fractional::{Fractional, from_vector};
-use fractional::trigonometry::Trig;
-use fractional::vector::Vector;
-use fractional::transform::{TMatrix, Transformable};
-use fractional::xcb::XcbEasel;
-use fractional::geometry::{Camera, DirectLight, Polyeder, Primitives};
-
-fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> {
-    let r = v.iter().fold(0, |acc, x| acc + x);
-    let l = i64::try_from(v.len())?;
-    Ok(Fractional(r, l))
-}
-
-fn common_fractional() {
-    let a = vec![3, 6, 1, 9];
-    let b = from_vector(&a);
-    let c = mean(&a).unwrap(); // This might fail if the len of the
-                               // vector (usize) does not fit into i32.
-    let cr :f64 = c.try_into().unwrap();
-
-    println!("         [i32] : {:?}", a);
-    println!("  [Fractional] : {:?}", b);
-    println!(" mean of [i32] : {}"  , c);
-    println!("        as f64 : {}"  , cr);
-    println!("  again as f64 : {}"  , TryInto::<f64>::try_into(c).unwrap());
-}
-
-fn continuous() {
-    let d = Fractional(45, 16);
-    let e = Fractional(16, 45);
-
-    let dc :Continuous = (&d).into();
-    let ec :Continuous = (&e).into();
-
-    println!("cont frac of d : {} => {:?}", d, dc);
-    println!("cont frac of e : {} => {:?}", e, ec);
-    println!("   reverted dc : {:?} {}", dc, Into::<Fractional>::into(&dc));
-    println!("   reverted ec : {:?} {}", ec, Into::<Fractional>::into(&ec));
-}
-
-fn sqrt() {
-    let f       = Fractional(-9, 4);
-    let fr :f64 = f.try_into().unwrap();
-    let sq      = f.sqrt();
-    let _sq     = fr.sqrt();
-
-    println!("{:>14} : {:?} / {}", format!("sqrt {}", f), sq, _sq);
-
-    for f in [ Fractional(9, 4)
-             , Fractional(45, 16)
-             , Fractional(16, 45)
-             , Fractional(9, 3) ].iter() {
-        let fr  :f64 = (*f).try_into().unwrap();
-        let sq       = f.sqrt().unwrap();
-        let sqr :f64 = sq.try_into().unwrap();
-        let _sqr     = fr.sqrt();
-
-        println!("{:>14} : {} {} / {}", format!("sqrt {}", f), sq, sqr, _sqr);
-    }
-}
-
-fn pi() {
-    let pi              = Fractional::pi();
-    let pir :f64        = pi.try_into().unwrap();
-    let pit :(i32, i32) = pi.try_into().unwrap();
-    let pi2r :f64       = (pi * pi).try_into().unwrap();
-
-    println!("        Rust π : {}"     , FPI);
-    println!("             π : {} {}"  , pi, pir);
-    println!("    π as tuple : {:?}"   , pit);
-    println!("       Rust π² : {}"     , FPI * FPI);
-    println!("            π² : {} {}"  , pi * pi, pi2r);
-}
-
-fn _sin() {
-    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
-             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
-        let s       = Fractional::sin(*d as i32);
-        let sr :f64 = s.try_into().unwrap();
-        let _s      = f64::sin(*d as f64 * FPI / 180.0);
-
-        println!("{:>14} : {} {} / {}", format!("sin {}", d), s, sr, _s);
-    }
-}
-
-fn _tan() {
-    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
-             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
-        let t       = Fractional::tan(*d as i32);
-        let tr :f64 = t.try_into().unwrap();
-        let _t      = f64::tan(*d as f64 * FPI / 180.0);
-
-        println!("{:>14} : {} {} / {}", format!("tan {}", d), t, tr, _t);
-    }
-}
-
-fn _cos() {
-    for d in [ 0, 30, 45, 90, 135, 180, 225, 270, 315
-             , 9, 17, 31, 73, 89, 123, 213, 312, 876 ].iter() {
-        let c       = Fractional::cos(*d as i32);
-        let cr :f64 = c.try_into().unwrap();
-        let _c      = f64::cos(*d as f64 * FPI / 180.0);
-
-        println!("{:>14} : {} {} / {}", format!("cos {}", d), c, cr, _c);
-    }
-}
-
-fn _vector1() {
-    let v1 = Vector(1.into(), 2.into(), 3.into());
-    let v2 = Vector(2.into(), 2.into(), 3.into());
-    let s :Fractional = 3.into();
-
-    _vector(v1, v2, s);
-}
-
-fn _vector2() {
-    let v1 = Vector(1.0, 2.0, 3.0);
-    let v2 = Vector(2.0, 2.0, 3.0);
-    let s = 3.0;
-
-    _vector(v1, v2, s);
-}
-
-fn _vector<T>(v1 :Vector<T>, v2 :Vector<T>, s :T)
-    where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-           + Mul<Output = T> + Div<Output = T> + Trig + Copy + Display {
-    println!("{:>14} : {}", "Vector v1", v1);
-    println!("{:>14} : {}", "Vector v2", v2);
-    println!("{:>14} : {}", "magnitude v1", v1.mag());
-    println!("{:>14} : {}", "-v1", -v1);
-    println!("{:>14} : {}", "v1 + v1", v1 + v1);
-    println!("{:>14} : {}", "v1 - v1", v1 - v1);
-    println!("{:>14} : {}", "v2 - v1", v2 - v1);
-    println!("{:>14} : {}", format!("v1 * {}", s), v1.mul(&s));
-    println!("{:>14} : {}", "norm v1", v1.norm());
-    println!("{:>14} : {}", "magnitude norm v1", v1.norm().mag());
-    println!("{:>14} : {}", "magnitude v1", v1.mag());
-    println!("{:>14} : {}", "norm * magnitude", v1.norm().mul(&v1.mag()));
-    println!("{:>14} : {}", "distance v1 v2", v1.distance(v2));
-    println!("{:>14} : {}", "distance v2 v1", v2.distance(v1));
-    println!("{:>14} : {}", "v1 dot v2", v1.dot(v2));
-    println!("{:>14} : {}", "v2 dot v1", v2.dot(v1));
-    println!("{:>14} : {}", "v1 * v2", v1 * v2);
-    println!("{:>14} : {}", "v2 * v1", v2 * v1);
-}
-
-fn _transform1() {
-    let v  = Vector(Fractional(1,1), Fractional(1,1), Fractional(1,1));
-    let v1 = Vector(Fractional(1,1), Fractional(2,1), Fractional(3,1));
-    let v2 = Vector(Fractional(1,1), Fractional(1,1), Fractional(0,1));
-    let v3 = Vector(Fractional(1,1), Fractional(0,1), Fractional(1,1));
-
-    _transform(v, v1, v2, v3);
-}
-
-fn _transform2() {
-    let v  = Vector(1.0, 1.0, 1.0);
-    let v1 = Vector(1.0, 2.0, 3.0);
-    let v2 = Vector(1.0, 1.0, 0.0);
-    let v3 = Vector(1.0, 0.0, 1.0);
-
-    _transform(v, v1, v2, v3);
-}
-
-fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :Vector<T>)
-    where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-           + Mul<Output = T> + Div<Output = T> + Trig
-           + Debug + From<i32> + Copy + Display {
-
-    println!("{:>14} : {}", "Vector v1", v1);
-    println!( "{:>14} : {}", "translate v1"
-            , v.transform(&TMatrix::translate(v)));
-    println!();
-
-    fn _rot<T>( o :&str , n :&str , v :&Vector<T>
-              , fs :&[&dyn Fn(i32) -> TMatrix<T>] )
-        where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-               + Mul<Output = T> + Div<Output = T> + Trig
-               + Debug + From<i32> + Copy + Display {
-
-        for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-                 , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-            let mi = fs.iter().map(|f| f(*d as i32));
-            println!( "{:>14} : {}"
-                    , format!("{} {} {}", o, d, n)
-                    , v.transform(&TMatrix::combine(mi)) );
-        }
-    }
-
-    println!("{:>14} : {}", "Vector v2", v2);
-    _rot("rot_x", "v2", &v2, &[&TMatrix::rotate_x]);
-    println!();
-    _rot("rot_y", "v2", &v2, &[&TMatrix::rotate_y]);
-    println!();
-    _rot("rot_xy", "v2", &v2, &[&TMatrix::rotate_x, &TMatrix::rotate_y]);
-    println!();
-    println!("{:>14} : {}", "Vector v3", v3);
-    _rot("rot_z", "v3", &v3, &[&TMatrix::rotate_z]);
-    println!();
-
-    for d in [ 30, 45, 60, 90, 120, 135, 150, 180
-             , 210, 225, 240, 270, 300, 315, 330 ].iter() {
-        println!( "{:>14} : {}"
-                , format!("rot_v {} v2", d)
-                , v2.transform(&TMatrix::rotate_v(&v, *d as i32)) );
-    }
-}
-
-fn _line() {
-    let a = (Coordinate(0, 1, 0.0), Coordinate(6, 4, 0.0));
-    let b = (Coordinate(0, 4, 0.0), Coordinate(6, 1, 0.0));
-    let c = (Coordinate(1, 0, 0.0), Coordinate(6, 8, 0.0));
-    let d = (Coordinate(1, 8, 0.0), Coordinate(6, 0, 0.0));
-
-    for i in [a, b, c, d].iter() {
-        println!("{:>14} : {}", Line(i.0, i.1), Line(i.0, i.1).plot());
-        println!("{:>14} : {}", Line(i.1, i.0), Line(i.1, i.0).plot());
-    }
-
-    println!();
-    let pl = Polyline(
-        Coordinates(vec!(a.0, a.1, b.0, b.1, c.0, c.1, d.0, d.1)));
-    println!("{:>14} : {}", pl, pl.plot());
-
-    println!();
-    let pg = Polygon(
-        Coordinates(vec!( Coordinate(  0, -10, 0.0)
-                        , Coordinate( 10,  10, 0.0)
-                        , Coordinate(-10,  10, 0.0) )));
-    println!("{:>14} : {}", pg, pg.plot());
-
-    let i = Vector(Fractional(  0,1), Fractional(-30,1), Fractional(0,1));
-    let j = Vector(Fractional( 30,1), Fractional( 30,1), Fractional(0,1));
-    let k = Vector(Fractional(-30,1), Fractional( 30,1), Fractional(0,1));
-
-    let rot :TMatrix<Fractional> = TMatrix::rotate_z(20);
-    let Vector(ix, iy, _) = i.transform(&rot);
-    let Vector(jx, jy, _) = j.transform(&rot);
-    let Vector(kx, ky, _) = k.transform(&rot);
-
-    fn to_i32(x :Fractional) -> i32 {
-        let Fractional(n, d) = x;
-        (n / d + if (n % d).abs() < (n / 2).abs() { 0 } else { 1 }) as i32
-    }
-
-    println!();
-    let pg = Polygon(
-        Coordinates(vec!( Coordinate(to_i32(ix) + 100, to_i32(iy) + 100, 0.0)
-                        , Coordinate(to_i32(jx) + 100, to_i32(jy) + 100, 0.0)
-                        , Coordinate(to_i32(kx) + 100, to_i32(ky) + 100, 0.0) )));
-    println!("{:>14} : {}", pg, pg.plot());
-
-    let i = Vector(  0.0, -30.0, 0.0);
-    let j = Vector( 30.0,  30.0, 0.0);
-    let k = Vector(-30.0,  30.0, 0.0);
-
-    let rot :TMatrix<f64> = TMatrix::rotate_z(20);
-    let Vector(ix, iy, _) = i.transform(&rot);
-    let Vector(jx, jy, _) = j.transform(&rot);
-    let Vector(kx, ky, _) = k.transform(&rot);
-
-    fn to_i32_2(x :f64) -> i32 {
-        x.round() as i32
-    }
-
-    println!();
-    let pg = Polygon(
-        Coordinates(vec!( Coordinate(to_i32_2(ix) + 100, to_i32_2(iy) + 100, 0.0)
-                        , Coordinate(to_i32_2(jx) + 100, to_i32_2(jy) + 100, 0.0)
-                        , Coordinate(to_i32_2(kx) + 100, to_i32_2(ky) + 100, 0.0) )));
-    println!("{:>14} : {}", pg, pg.plot());
-}
-
-fn _democanvas<T>( xcb         :&XcbEasel
-                 , title       :&'static str
-                 , tx          :mpsc::Sender<i32>
-                 , _triangle   :Polyeder<T>
-                 , tetrahedron :Polyeder<T>
-                 , cube        :Polyeder<T>
-                 , light       :DirectLight<T> )
-    where T: 'static + Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-           + Mul<Output = T> + Div<Output = T>
-           + Debug + Copy + Trig + Send + From<i32> + PartialOrd {
-
-    let mut canvas = xcb.canvas(151, 151).unwrap();
-    let camera     = Camera::<T>::new(&canvas, 45); // the orig. view angle
-                                                    // was 50.
-
-    canvas.set_title(title);
-    canvas.init_events();
-    canvas.start_events(tx.clone());
-
-    thread::spawn(move || {
-        let     start = Instant::now();
-        let     step  = Duration::from_millis(25);
-        let mut last  = Instant::now();
-
-        let t = TMatrix::translate(Vector(0.into() , 0.into() , 150.into()));
-
-        loop {
-            let deg = ((start.elapsed() / 25).as_millis() % 360) as i32;
-
-            let rz = TMatrix::rotate_z(deg);
-            let rx = TMatrix::rotate_x(-deg*2);
-            let ry = TMatrix::rotate_y(-deg*2);
-
-            let rot1 = TMatrix::combine(vec!(rz, rx, t));
-            let rot2 = TMatrix::combine(vec!(rz, ry, t));
-
-            let objects = vec!( (tetrahedron.transform(&rot1), 0xFFFF00)
-                              , (       cube.transform(&rot2), 0x0000FF) );
-            //let objects = vec!( (       cube.transform(&rot2), 0x0000FF) );
-            //let objects = vec!( (tetrahedron.transform(&rot1), 0xFFFF00) );
-            //let objects = vec!( (triangle.transform(&rot1), 0xFFFF00) );
-
-            canvas.clear();
-
-            for (o, color) in objects {
-                for (pg, c) in o.project(&camera, &light, color) {
-                    //canvas.draw(&pg, Coordinate(0, 0, 0.into()), c);
-                    (&pg).fill(&mut canvas, c);
-                    //(&pg).debug();
-                    //println!("\n");
-                }
-            }
-
-            let passed = Instant::now() - last;
-            let f      = (passed.as_nanos() / step.as_nanos()) as u32;
-
-            if f > 1 {
-                println!("{} !!! Detected frame drop", title);
-            }
-
-            last = last + step*(f + 1);
-            canvas.put_text( Coordinate(10, 15, 0.into())
-                           , &format!( "sleep: {:?}"
-                           , last - Instant::now() ));
-            canvas.show();
-            thread::sleep(last - Instant::now());
-        }
-    });
-}
-
-fn main() {
-    common_fractional();
-    println!();
-    continuous();
-    println!();
-    sqrt();
-    println!();
-    pi();
-    println!();
-    _sin();
-    println!();
-    _cos();
-    println!();
-    _tan();
-    println!();
-    _vector1();
-    println!();
-    _vector2();
-    println!();
-    _transform1();
-    println!();
-    _transform2();
-    println!();
-    _line();
-
-    let xcb = XcbEasel::new().unwrap();
-    let (tx, rx) = mpsc::channel();
-
-
-    _democanvas( &xcb, "Something...(f64)", tx.clone()
-               , Polyeder::triangle(60.0)
-               , Polyeder::tetrahedron(100.0)
-               , Polyeder::cube(56.25)
-               , DirectLight::new(Vector(0.0, 0.0, 1.0)) );
-    /*
-    _democanvas( &xcb, "Something...(Fractional)", tx.clone()
-               , Polyeder::triangle(Fractional(60,1))
-               , Polyeder::tetrahedron(Fractional(80,1))
-               , Polyeder::cube(Fractional(55,1))
-               , DirectLight::new(Vector( Fractional(0,1)
-                                        , Fractional(0,1)
-                                        , Fractional(1,1) )) );
-    */
-
-    for x in rx {
-        match x {
-            1 => break,
-            _ => {},
-        }
-    }
-}

-//
-// Transformation of vectors in a given coordinate system...
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::ops::{Add, Sub, Neg, Mul, Div};
-use std::fmt::Debug;
-
-use crate::Vector;
-use crate::trigonometry::Trig;
-
-#[derive(Debug, Clone, Copy)]
-pub struct TMatrix<T>( (T, T, T, T)
-                     , (T, T, T, T)
-                     , (T, T, T, T)
-                     , (T, T, T, T) )
-    where T: Add + Sub + Neg + Mul + Div + Debug + Trig + From<i32> + Copy;
-
-pub trait Transformable<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Trig + From<i32> + Copy {
-    fn transform(&self, m :&TMatrix<T>) -> Self;
-}
-
-impl<T> TMatrix<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Trig + From<i32> + Copy {
-    pub fn new( r1 :(T, T, T, T)
-              , r2 :(T, T, T, T)
-              , r3 :(T, T, T, T)
-              , r4 :(T, T, T, T) ) -> Self {
-        TMatrix(r1, r2, r3, r4)
-    }
-
-    pub fn unit() -> Self {
-        Self::new( (1.into(), 0.into(), 0.into(), 0.into())
-                 , (0.into(), 1.into(), 0.into(), 0.into())
-                 , (0.into(), 0.into(), 1.into(), 0.into())
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn translate(v :Vector<T>) -> Self {
-        let Vector(x, y, z) = v;
-
-        Self::new( (1.into(), 0.into(), 0.into(),        x)
-                 , (0.into(), 1.into(), 0.into(),        y)
-                 , (0.into(), 0.into(), 1.into(),        z)
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn rotate_x(a :i32) -> Self {
-        let sin :T = Trig::sin(a);
-        let cos :T = Trig::cos(a);
-
-        Self::new( (1.into(), 0.into(), 0.into(), 0.into())
-                 , (0.into(), cos     , -sin    , 0.into())
-                 , (0.into(), sin     , cos     , 0.into())
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn rotate_y(a :i32) -> Self {
-        let sin :T = Trig::sin(a);
-        let cos :T = Trig::cos(a);
-
-        Self::new( (cos     , 0.into(), sin     , 0.into())
-                 , (0.into(), 1.into(), 0.into(), 0.into())
-                 , (-sin    , 0.into(), cos     , 0.into())
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn rotate_z(a :i32) -> Self {
-        let sin :T = Trig::sin(a);
-        let cos :T = Trig::cos(a);
-
-        Self::new( (cos     , -sin    , 0.into(), 0.into())
-                 , (sin     , cos     , 0.into(), 0.into())
-                 , (0.into(), 0.into(), 1.into(), 0.into())
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn rotate_v(v :&Vector<T>, a :i32) -> Self {
-        let Vector(x, y, z) = *v;
-
-        let sin :T = Trig::sin(a);
-        let cos :T = Trig::cos(a);
-
-        let zero :T = 0.into();
-        let one  :T = 1.into();
-
-        Self::new( ( (one - cos) * x * x + cos
-                   , (one - cos) * x * y - sin * z
-                   , (one - cos) * x * z + sin * y
-                   , zero )
-                 , ( (one - cos) * x * y + sin * z
-                   , (one - cos) * y * y + cos
-                   , (one - cos) * y * z - sin * x
-                   , zero )
-                 , ( (one - cos) * x * z - sin * y
-                   , (one - cos) * y * z + sin * x
-                   , (one - cos) * z * z + cos
-                   , zero )
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn scale(v :Vector<T>) -> Self {
-        let Vector(x, y, z) = v;
-
-        Self::new( (       x, 0.into(), 0.into(), 0.into())
-                 , (0.into(),        y, 0.into(), 0.into())
-                 , (0.into(), 0.into(),        z, 0.into())
-                 , (0.into(), 0.into(), 0.into(), 1.into()) )
-    }
-
-    pub fn combine<I>(mi :I) -> TMatrix<T>
-        where I: IntoIterator<Item = TMatrix<T>> {
-
-        mi.into_iter().fold(Self::unit(), |acc, x| x * acc)
-    }
-
-    pub fn apply(&self, v :&Vector<T>, w :T) -> (Vector<T>, T) {
-        let TMatrix( (a11, a12, a13, a14)
-                   , (a21, a22, a23, a24)
-                   , (a31, a32, a33, a34)
-                   , (a41, a42, a43, a44) ) = *self;
-        let Vector(x, y, z) = *v;
-
-        let v = Vector( a11 * x + a12 * y + a13 * z + a14 * w
-                      , a21 * x + a22 * y + a23 * z + a24 * w
-                      , a31 * x + a32 * y + a33 * z + a34 * w );
-        let w = a41 * x + a42 * y + a43 * z + a44 * w;
-
-        //v.mul(&w.recip())
-        (v, w)
-    }
-}
-
-impl<T> Mul for TMatrix<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Trig + From<i32> + Copy {
-    type Output = Self;
-
-    // ATTENTION: This is not commutative, nor assoziative.
-    fn mul(self, other :Self) -> Self {
-        let TMatrix( (a11, a12, a13, a14)
-                   , (a21, a22, a23, a24)
-                   , (a31, a32, a33, a34)
-                   , (a41, a42, a43, a44) ) = self;
-        let TMatrix( (b11, b12, b13, b14)
-                   , (b21, b22, b23, b24)
-                   , (b31, b32, b33, b34)
-                   , (b41, b42, b43, b44) ) = other;
-
-        TMatrix( ( a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41
-                 , a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42
-                 , a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43
-                 , a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44 )
-               , ( a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41
-                 , a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42
-                 , a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43
-                 , a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44 )
-               , ( a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41
-                 , a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42
-                 , a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43
-                 , a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44 )
-               , ( a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41
-                 , a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42
-                 , a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43
-                 , a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44 ) )
-    }
-}

-//
-// Some trigonometic functions with Fractions results.
-// Currently only sin, cos and tan are implemented.
-//  As I was unable to find a really good integral approximation for them I
-// implement them as a table which is predefined using the floating point
-// function f64::sin and then transformed into a fraction of a given
-// PRECISION.
-//  These approximations are quite good and for a few edge cases
-// even better than the floating point implementations.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::cmp::Ordering;
-use std::ops::Div;
-use std::ops::Neg;
-use std::marker::Sized;
-use crate::{Fractional, Error};
-use crate::continuous::Continuous;
-
-pub trait Trig {
-    fn pi()         -> Self;
-    fn recip(self)  -> Self;
-    fn round(&self) -> i32;
-    fn sqrt(self)   -> Result<Self, Error> where Self: Sized;
-    fn sintab()     -> Vec<Self> where Self: Sized;
-    fn tantab()     -> Vec<Self> where Self: Sized;
-
-    fn sin(d :i32) -> Self
-        where Self: Sized + Neg<Output = Self> + Copy {
-        match d {
-            0  ..=90  => Self::sintab()[d as usize],
-            91 ..=180 => Self::sintab()[180 - d as usize],
-            181..=270 => -Self::sintab()[d as usize - 180],
-            271..=359 => -Self::sintab()[360 - d as usize],
-            _         => {
-                Self::sin(if d < 0 { d % 360 + 360 } else { d % 360 })
-            },
-        }
-    }
-
-    fn cos(d :i32) -> Self
-        where Self: Sized + Neg<Output = Self> + Copy {
-        match d {
-            0  ..=90  => Self::sintab()[90 - d as usize],
-            91 ..=180 => -Self::sintab()[90 - (180 - d as usize)],
-            181..=270 => -Self::sintab()[90 - (d as usize - 180)],
-            271..=359 => Self::sintab()[90 - (360 - d as usize)],
-            _         => {
-                Self::cos(if d < 0 { d % 360 + 360 } else { d % 360 })
-            },
-        }
-    }
-
-    fn tan(d :i32) -> Self where Self: Sized + Copy {
-        match d {
-            0  ..=179 => Self::tantab()[d as usize],
-            180..=359 => Self::tantab()[d as usize - 180],
-            _         => {
-                Self::tan(if d < 0 { d % 360 + 360 } else { d % 360 })
-            },
-        }
-    }
-
-    fn cot(d :i32) -> Self
-        where Self: Sized + Copy + From<i32> + Div<Output = Self> {
-        Into::<Self>::into(1) / Self::tan(d)
-    }
-}
-
-// Try to keep precision as high as possible while having a denominator
-// as small as possible. The values are taken by try and error.
-const PRECISION       :i64 = 1000000;
-const MAX_DENOMINATOR :i64 = 7000;
-
-// This is a really close fractional approximation for pi.
-impl Trig for Fractional {
-    fn pi() -> Self {
-        Fractional(355, 113)
-    }
-
-    fn recip(self) -> Self {
-        let Fractional(n, d) = self;
-        Fractional(d, n)
-    }
-
-    fn round(&self) -> i32 {
-        let Fractional(n, d) = self;
-        (n / d) as i32
-    }
-
-    // This is a really bad approximation of sqrt for a fractional...
-    // for (9/3) it will result 3 which if way to far from the truth,
-    // which is ~1.7320508075
-    // BUT we can use this value as starting guess for creating a 
-    // continous fraction for the sqrt... and create a much better
-    // fractional representation of the sqrt.
-    // So, if inner converges, but is not a perfect square (does not
-    // end up in an Ordering::Equal - which is the l > h case)
-    // we use the l - 1 as starting guess for sqrt_cfrac.
-    // taken from:
-    // https://www.geeksforgeeks.org/square-root-of-an-integer/
-    fn sqrt(self) -> Result<Self, Error> {
-        // find the sqrt of x in O(log x/2).
-        // This stops if a perfect sqare was found. Else it passes
-        // the found value as starting guess to the continous fraction
-        // sqrt function.
-        fn floor_sqrt(x :i64) -> Fractional {
-            fn inner(l :i64, h :i64, x :i64) -> Fractional {
-                if l > h {
-                    (&Continuous::sqrt(x, l - 1)).into()
-                } else {
-                    let m = (l + h) / 2;
-                    match x.cmp(&(m * m)) {
-                        Ordering::Equal   => m.into(),
-                        Ordering::Less    => inner(l, m - 1, x),
-                        Ordering::Greater => inner(m + 1, h, x),
-                    }
-                }
-            }
-
-            match x {
-                0 => 0.into(),
-                1 => 1.into(),
-                _ => inner(1, x / 2, x),
-            }
-        }
-
-        let Fractional(n, d) = self;
-
-        let n = match n.cmp(&0) {
-            Ordering::Equal   => 0.into(),
-            Ordering::Less    => return Err("sqrt on negative undefined"),
-            Ordering::Greater => floor_sqrt(n),
-        };
-
-        let d = match d.cmp(&0) {
-            Ordering::Equal   => 0.into(),
-            Ordering::Less    => return Err("sqrt on negative undefined"),
-            Ordering::Greater => floor_sqrt(d),
-        };
-
-        Ok(n / d)
-    }
-
-    fn sintab() -> Vec<Self> {
-        // hold sin Fractionals from 0 to 89 ...
-        // luckily with a bit of index tweeking this can also be used for
-        // cosine values.
-        lazy_static::lazy_static! {
-            static ref SINTAB :Vec<Fractional> =
-                (0..=90).map(|x| _sin(x)).collect();
-        }
-
-        // fractional sin from f64 sin. (From 0° to 90°)
-        fn _sin(d: u32) -> Fractional {
-            match d {
-                0  => Fractional(0, 1),
-                90 => Fractional(1, 1),
-                _  => generate(d, PRECISION, &f64::sin),
-            }
-        }
-
-        SINTAB.to_vec()
-    }
-
-    fn tantab() -> Vec<Self> {
-        // This table exists only because the sin(α) / cos(α) method
-        // yields very large unreducable denominators in a lot of cases.
-        lazy_static::lazy_static! {
-            static ref TANTAB :Vec<Fractional> =
-                (0..180).map(|x| _tan(x)).collect();
-        }
-
-        // fractional tan from f64 tan. (From 0° to 179°)
-        fn _tan(d: u32) -> Fractional {
-            match d {
-                0   => Fractional(0, 1),
-                45  => Fractional(1, 1),
-                90  => Fractional(1, 0), // although they are both inf and -inf.
-                135 => -Fractional(1, 1),
-                _   => generate(d, PRECISION, &f64::tan),
-            }
-        }
-
-        TANTAB.to_vec()
-    }
-}
-
-// search for a fraction with a denominator less than MAX_DENOMINATOR that
-// provides the minimal PRECISION criteria.
-// !! With f = &f64::tan and d close to the inf boundarys of tan
-//    we get very large numerators because the numerator becomes a
-//    multiple of the denominator.
-fn generate(d :u32, p :i64, f :&dyn Fn(f64) -> f64) -> Fractional {
-    // This is undefined behaviour for very large f64, but our f64
-    // is always between 0.0 and 1000000.0 which should be fine.
-    let s = (f((d as f64).to_radians()) * p as f64).round() as i64;
-    let Fractional(n, dn) = Fractional(s, p).reduce();
-    match dn.abs().cmp(&MAX_DENOMINATOR) {
-        Ordering::Less => Fractional(n, dn),
-        _              => generate(d, p + 1, f),
-    }
-}
-
-impl Trig for f64 {
-    fn pi() -> Self {
-        std::f64::consts::PI
-    }
-
-    fn recip(self) -> Self {
-        self.recip()
-    }
-
-    fn round(&self) -> i32 {
-        f64::round(*self) as i32
-    }
-
-    fn sqrt(self) -> Result<Self, Error> {
-        let x = self.sqrt();
-        match x.is_nan() {
-            true  => Err("sqrt on negative undefined"),
-            false => Ok(x),
-        }
-    }
-
-    fn sintab() -> Vec<Self> {
-        lazy_static::lazy_static! {
-            static ref SINTAB :Vec<f64> =
-                (0..=90).map(|x| _sin(x)).collect();
-        }
-
-        // f64 sin. (From 0° to 90°)
-        fn _sin(d: u32) -> f64 {
-            match d {
-                0  => 0.0,
-                90 => 1.0,
-                _  => (d as f64).to_radians().sin(),
-            }
-        }
-
-        SINTAB.to_vec()
-    }
-
-    fn tantab() -> Vec<Self> {
-        // This table exists only because the sin(α) / cos(α) method
-        // yields very large unreducable denominators in a lot of cases.
-        lazy_static::lazy_static! {
-            static ref TANTAB :Vec<f64> =
-                (0..180).map(|x| _tan(x)).collect();
-        }
-
-        // fractional tan from f64 tan. (From 0° to 179°)
-        fn _tan(d: u32) -> f64 {
-            match d {
-                0   => 0.0,
-                45  => 1.0,
-                90  => std::f64::INFINITY,
-                135 => -1.0,
-                _   => (d as f64).to_radians().tan(),
-            }
-        }
-
-        TANTAB.to_vec()
-    }
-}

-//
-// Stuff for manipulating 3 dimensional vectors.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::fmt::{Debug, Display, Formatter, Result};
-use std::ops::{Add, Sub, Neg, Mul, Div};
-
-use crate::trigonometry::Trig;
-use crate::transform::{TMatrix, Transformable};
-
-#[derive(Debug, Eq, Clone, Copy)]
-pub struct Vector<T>(pub T, pub T, pub T)
-    where T: Add + Sub + Neg + Mul + Div + Trig + Copy;
-
-impl<T> Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + Copy {
-    pub fn x(self) -> T { self.0 }
-    pub fn y(self) -> T { self.1 }
-    pub fn z(self) -> T { self.2 }
-
-    pub fn mag(self) -> T {
-        let Vector(x, y, z) = self;
-        (x * x + y * y + z * z).sqrt().unwrap()
-    }
-
-    pub fn mul(self, s :&T) -> Self {
-        let Vector(x, y, z) = self;
-        Vector(x * *s, y * *s, z * *s)
-    }
-
-    pub fn dot(self, other :Self) -> T {
-        let Vector(x1, y1, z1) = self;
-        let Vector(x2, y2, z2) = other;
-
-        x1 * x2 + y1 * y2 + z1 * z2
-    }
-
-    pub fn norm(self) -> Self {
-        // TODO This can result in 0 or inf Vectors…
-        //      Maybe we need to handle zero and inf magnitude here…
-        self.mul(&self.mag().recip())
-    }
-
-    pub fn distance(self, other :Self) -> T {
-        (self - other).mag()
-    }
-}
-
-impl<T> Display for Vector<T>
-where T: Add + Sub + Neg + Mul + Div + Trig + Display + Copy {
-    fn fmt(&self, f :&mut Formatter<'_>) -> Result {
-        let Vector(x, y, z) = self;
-        write!(f, "({}, {}, {})", x, y, z)
-    }
-}
-
-impl<T> PartialEq for Vector<T>
-where T: Add + Sub + Neg + Mul + Div + Trig + PartialEq + Copy {
-    fn eq(&self, other :&Self) -> bool {
-        let Vector(x1, y1, z1) = self;
-        let Vector(x2, y2, z2) = other;
-        x1 == x2 && y1 == y2 && z1 == z2
-    }
-}
-
-impl<T> Add for Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + Copy {
-    type Output = Self;
-
-    fn add(self, other :Self) -> Self {
-        let Vector(x1, y1, z1) = self;
-        let Vector(x2, y2, z2) = other;
-        Vector(x1 + x2, y1 + y2, z1 + z2)
-    }
-}
-
-impl<T> Sub for Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + Copy {
-    type Output = Self;
-
-    fn sub(self, other :Self) -> Self {
-        self + -other
-    }
-}
-
-impl<T> Neg for Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + Copy {
-    type Output = Self;
-
-    fn neg(self) -> Self {
-        let Vector(x, y, z) = self;
-        Self(-x, -y, -z)
-    }
-}
-
-impl<T> Mul for Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T> + Trig + Copy {
-    type Output = Self;
-
-    fn mul(self, other :Self) -> Self {
-        let Vector(ax, ay, az) = self;
-        let Vector(bx, by, bz) = other;
-
-        Vector( ay * bz - az * by
-              , az * bx - ax * bz
-              , ax * by - ay * bx )
-    }
-}
-
-impl<T> Transformable<T> for Vector<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Trig + Copy + Debug + From<i32> {
-    fn transform(&self, m :&TMatrix<T>) -> Self {
-        let (v, _) = m.apply(self, 0.into());
-        v
-    }
-}

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "functions"
-version = "0.1.0"
-

-[package]
-name = "functions"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-fn main() {
-    another_function(5, add_five(6));
-}
-
-fn another_function(x: i32, y: i32) {
-    println!("The value of x id: {}", x);
-    println!("The value of y id: {}", y);
-}
-
-fn add_five(x: i32) -> i32 {
-    x + 5
-}

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "fuchsia-cprng"
-version = "0.1.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
-[[package]]
-name = "guessing_game"
-version = "0.1.0"
-dependencies = [
- "rand 0.3.23 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "libc"
-version = "0.2.65"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
-[[package]]
-name = "rand"
-version = "0.3.23"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-dependencies = [
- "libc 0.2.65 (registry+https://github.com/rust-lang/crates.io-index)",
- "rand 0.4.6 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "rand"
-version = "0.4.6"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-dependencies = [
- "fuchsia-cprng 0.1.1 (registry+https://github.com/rust-lang/crates.io-index)",
- "libc 0.2.65 (registry+https://github.com/rust-lang/crates.io-index)",
- "rand_core 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
- "rdrand 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)",
- "winapi 0.3.8 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "rand_core"
-version = "0.3.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-dependencies = [
- "rand_core 0.4.2 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "rand_core"
-version = "0.4.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
-[[package]]
-name = "rdrand"
-version = "0.4.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-dependencies = [
- "rand_core 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "winapi"
-version = "0.3.8"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-dependencies = [
- "winapi-i686-pc-windows-gnu 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)",
- "winapi-x86_64-pc-windows-gnu 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)",
-]
-
-[[package]]
-name = "winapi-i686-pc-windows-gnu"
-version = "0.4.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
-[[package]]
-name = "winapi-x86_64-pc-windows-gnu"
-version = "0.4.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
-[metadata]
-"checksum fuchsia-cprng 0.1.1 (registry+https://github.com/rust-lang/crates.io-index)" = "a06f77d526c1a601b7c4cdd98f54b5eaabffc14d5f2f0296febdc7f357c6d3ba"
-"checksum libc 0.2.65 (registry+https://github.com/rust-lang/crates.io-index)" = "1a31a0627fdf1f6a39ec0dd577e101440b7db22672c0901fe00a9a6fbb5c24e8"
-"checksum rand 0.3.23 (registry+https://github.com/rust-lang/crates.io-index)" = "64ac302d8f83c0c1974bf758f6b041c6c8ada916fbb44a609158ca8b064cc76c"
-"checksum rand 0.4.6 (registry+https://github.com/rust-lang/crates.io-index)" = "552840b97013b1a26992c11eac34bdd778e464601a4c2054b5f0bff7c6761293"
-"checksum rand_core 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)" = "7a6fdeb83b075e8266dcc8762c22776f6877a63111121f5f8c7411e5be7eed4b"
-"checksum rand_core 0.4.2 (registry+https://github.com/rust-lang/crates.io-index)" = "9c33a3c44ca05fa6f1807d8e6743f3824e8509beca625669633be0acbdf509dc"
-"checksum rdrand 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)" = "678054eb77286b51581ba43620cc911abf02758c91f93f479767aed0f90458b2"
-"checksum winapi 0.3.8 (registry+https://github.com/rust-lang/crates.io-index)" = "8093091eeb260906a183e6ae1abdba2ef5ef2257a21801128899c3fc699229c6"
-"checksum winapi-i686-pc-windows-gnu 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)" = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
-"checksum winapi-x86_64-pc-windows-gnu 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)" = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"

-[package]
-name = "guessing_game"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-[dependencies]
-rand = "0.3.14"

-use std::io;
-use std::cmp::Ordering;
-use rand::Rng;
-
-fn main() {
-    println!("Guess the number!");
-
-    let secret_number = rand::thread_rng()
-        .gen_range(1, 101);
-
-    loop {
-        println!("Please input your guess.");
-
-        let mut guess = String::new();
-
-        io::stdin()
-            .read_line(&mut guess)
-            .expect("Failed to read line");
-
-        let guess: u32 = match guess.trim().parse() {
-            Ok(num) => num,
-            Err(_)  => continue,
-        };
-
-        println!("You guessed: {}", guess);
-
-        match guess.cmp(&secret_number) {
-            Ordering::Less    => println!("Too small!"),
-            Ordering::Greater => println!("Too big!"),
-            Ordering::Equal   => {
-                println!("You win!");
-                break;
-            }
-        }
-    }
-}

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "hello"
-version = "0.1.0"
-

-[package]
-name = "hello"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-[dependencies]

-fn main() {
-    println!("Hello, world!");
-}

-# Here I collect some interesting links.
-
-## cargo environment
-
-Currently I always build all dependencies within th projects own .cargo subdir
-by setting the environment variable CARGO_HOME.
-
-    export CARGO_HOME=./.cargo
-
-Actually I am quite unsure if that is really a good idea because this results
-in a lot of rebuilds for each new project.
-
-## Implement Monads with rust.
-
-Which is currently difficult through impossible, but might be feasible with
-some small additions to the rust type system, namely
-«(generic) associated traits.»
-
-[Read here](https://varkor.github.io/blog/2019/03/28/idiomatic-monads-in-rust.html)
-
-### Is impl Trait what we needed?
-
-A new language feature which sounded a bit like the needed one for above is:
-
-[impl Trait](https://medium.com/@iopguy/impl-trait-in-rust-explanation-efde0d94946a)
-
-Crossreading it a bit seems to indicate that this is not like the above needed
-language feature.
-
-## WASM ... on gentoo ...
-
-Right now rust is not really a first class citizen within the gentoo eco
-system. For that reason at least when compiling rust with the `system-llvm`
-use flag some manual preparations are needed.
-
-### general informations about Wasm from MDN ...
-
-[WebAssembly](https://developer.mozilla.org/en-US/docs/WebAssembly)
-
-### rustwasm tutorial
-
-[rustwasm](https://rustwasm.github.io/book/introduction.html)
-
-### location of rustlib ...
-
-`wasm-pack` expects the wasm runtime under /usr/lib/rustlib/ but a gentoo
-installation puts it under /usr/lib/rust-1.39.0/rustlib/. To come around this
-issue I just created a symlink.
-
-Maybe it would be best to send a patch for also settings this symlink to
-upstream eselect-rust.
-
-### Missing lld
-
-Again `wasm-pack` searches for llvm-lld or rust-lld for the link phase. This
-is currently not a dependency for llvm with WASM support, so I installed it
-manually. Finally you have to tell rustc to use lld as linker via this
-environment variable:
-
-    export RUSTFLAGS="-C linker=lld"
-
-## Traits when, how & why
-
-A slightly old but still worthwhile post about rusts standard traits.
-
-[About traits](https://llogiq.github.io/2015/07/30/traits.html)
-
-# Side note... 3d math
-[3d math primer](https://www.3dgep.com/3d-math-primer-for-game-programmers-vector-operations/)
-[basic 3d math](https://matrix44.net/cms/notes/opengl-3d-graphics/basic-3d-math-vectors/)
-[vector calculator](https://www.mathportal.org/calculators/matrices-calculators/vector-calculator.php)
-[3d vector mathematics](https://vvvv.org/documentation/3d-vector-mathematics)
-[sin appr. with fractions](https://dsp.stackexchange.com/questions/46629/finding-polynomial-approximations-of-a-sine-wave)
-
-# transformations within a coordinate system.
-[migenius](https://www.migenius.com/articles/3d-transformations-part1-matrices)
-[tutorialspoint](https://www.tutorialspoint.com/computer_graphics/3d_transformation.htm)
-
-# more math...
-
-A whole lot of interesting stuff about continued fractions:
-[continues fractions](http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html)
-

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "loops"
-version = "0.1.0"
-

-[package]
-name = "loops"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Loops examples.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-fn main() {
-    // It seams that to use loops this way you absolutely need a mutable.
-    // If I build it with a normal type and try to shadow it within the loop
-    // the outer variable is always used as input for the shadow, thus it is
-    // always the same.... that really sucks.
-    let mut counter = 0;
-
-    let result = loop {
-        counter = counter + 1;
-        if counter == 10 {
-            break counter * 2;
-        }
-    };
-
-    println!("The result is {}", result);
-
-    // The same is true with «while» ... which again sucks.
-    let mut number = 3;
-
-    while number != 0 {
-        println!("{}!", number);
-        number = number - 1;
-    }
-
-    println!("LIFTOFF!!!");
-
-    // apart from beeing frustrated about the above facts... lets continue.
-    let a = [10, 20, 30, 40, 50];
-    let mut index = 0;
-
-    while index < 5 {
-        println!("the value is: {}", a[index]);
-        index = index + 1;
-    }
-
-    for element in a.iter() {
-        println!("the value is still: {}", element);
-    }
-
-    for number in (1..4).rev() {
-        println!("for {}!", number);
-    }
-}

-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "ownership"
-version = "0.1.0"
-

-[package]
-name = "ownership"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Examples related to ownership, also introducing String.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-fn main() {
-    concat();
-    move_variable();
-    clone_variable();
-
-    let s = String::from("hello");  // s comes into scope
-
-    take_ownership(s);              // s's value moves into the function
-                                    // … and so is no longer valid here.
-    let x = 5;                      // x comes into scope
-
-    makes_copy(x);                  // the scalar value has the Copy trait and
-                                    // lives on the stack and thus is still
-                                    // valid here.
-
-    let _s1 = gives_ownership();     // move the return value into _s1
-    let  s2 = String::from("hello"); // s2 comes into scope
-    let _s3 = takes_and_gives(s2);   // s2 is moved into function, which in
-                                     // turn moves the return value into _s3.
-
-    let s1 = String::from("hello");  // s1 comes into scope.
-    let len = calculate_length(&s1); // A reference to s1 is given to a
-                                     // calculate_length which effectively is
-                                     // not s1 itself but another pointer to
-                                     // s1… which is the reason that we still
-                                     // can use it below.
-    let _another_s = &s1;            // again only a reference which does not
-                                     // take ownership, thus s1 can still be
-                                     // used below.
-    println!("The length of '{}' is {}.", s1, len);
-
-    // Passing values as reference to a function is called borrowing. A
-    // borrowed value can't be changed.
-    change(&s1);
-
-    // but we can force this… which is probably not the best of ideas most
-    // of the time…
-    let mut s_mut = String::from("hello");
-    change_mutable(&mut s_mut);
-
-    // but you can have only one mutable reference of a value in a single
-    // scope. The following would fail with:
-    // cannot borrow `s_mut` as mutable more than once at a time second
-    // mutable borrow occurs here
-    // let r1 = &mut s_mut;
-    // let r2 = &mut s_mut;
-    // println!("{}, {}", r1, r2);
-
-    // We also can't have an immutable reference while we have a mutable one.
-    // Look on Page 98 for an explanation.
-
-    // The scope of references is not the whole block they are introduced in
-    // but goes only until their last usage. Thus if you first have an
-    // immutable reference but never use it after a mutable reference is
-    // declared, that would be ok… At all this is kind of confusing and very
-    // Mozzilaish. :D
-
-    // Now we demonstrate string slices…
-    let s4 = String::from("hello world");
-    let s_slice = first_word(&s4);
-
-    // working with an mutable reference like with s4.clear() will not
-    // compile at this point because we already have and use later on an
-    // immutable reference.
-
-    println!("The slice was: {}", s_slice);
-
-    // not that string literals are slices. They are immutable references of
-    // the programs TEXT segment. Thats the reason why they are immutable.
-
-    // Thus try generic_first_word…
-    println!("First word on literal: {}", generic_first_word("hello world"));
-    println!("First word on String: {}", generic_first_word(&s4[..]));
-} // x and s go out of scope but nothing happens for s because this function
-  // has no longer the ownership of s.
-  // s3 goes out of scope and is dropped. s2 was moved and s1 is dropped.
-
-fn concat() {
-    let mut s = String::from("hello");
-    s.push_str(", world!");
-    println!("{}", s);
-}
-
-fn move_variable() {
-    let s1 = String::from("hello");
-    let s2 = s1; // does not copy data but only the String structure.
-    // when using s1 below we get an error that a moved value was borrowed.
-    println!("{}, world!", s2);
-}
-
-fn clone_variable() {
-    let s1 = String::from("hello");
-    let s2 = s1.clone();
-    // this time both are valid.
-    println!("s1 = {}, s2 = {}", s1, s2)
-}
-
-fn take_ownership(some_string: String) { // some_string comes into scope
-    println!("{}", some_string);
-} // some_string goes out of scope and «drop» is called, thus memory freed.
-
-fn makes_copy(some_integer: i32) { // some integer comes into scope
-    println!("{}", some_integer);
-} // Here, some_integer goes out of scope but because it was a copy and on the
-  // stack nothing special happens… beside that stack space is freed.
-
-fn gives_ownership() -> String { // this will move the return value into the
-                                 // calling function.
-    let some_string = String::from("hello"); // some_string comes into scope
-    some_string
-}
-
-fn takes_and_gives(a_string: String) -> String { // a_string comes into scope
-    a_string                                     // and is returned and moved
-                                                 // to the calling function.
-} // a_string goes out of scope but nothing happens as it is moved.
-
-fn calculate_length(s: &String) -> usize { // s comes into scope. It is a
-                                           // reference. References do not
-                                           // take ownership of the underlying
-                                           // value which is the String in
-                                           // main.
-    s.len()
-} // Here s goes out of scope but because it has no ownership of the String
-  // nothing happens.
-
-fn change(_some_string: &String) {
-    // the following would give this error:
-    // `_some_string` is a `&` reference, so the data it refers to cannot be
-    // borrowed as mutable
-    // _some_string.push_str(", world!");
-}
-
-fn change_mutable(some_string: &mut String) {
-    some_string.push_str(", world");
-}
-
-fn first_word(s: &String) -> &str {
-    let bytes = s.as_bytes();
-
-    for (i, &item) in bytes.iter().enumerate() {
-        if item == b' ' {
-            return &s[..i];
-        }
-    }
-
-    &s[..]
-}
-
-// To make first_word work on either string literals (which are in fact string
-// slices, s.o.) one would write first_word like this…
-fn generic_first_word(s: &str) -> &str {
-    let bytes = s.as_bytes();
-
-    for (i, &item) in bytes.iter().enumerate() {
-        if item == b' ' {
-            return &s[..i];
-        }
-    }
-
-    &s[..]
-}

-[package]
-name = "rectangles"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Examples related to structs…
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-#[derive(Debug)]
-struct Rectangle {
-    width:  u32,
-    height: u32,
-}
-
-impl Rectangle {
-    fn area(&self) -> u32 {
-        self.width * self.height
-    }
-
-    fn can_hold(&self, inner: &Rectangle) -> bool {
-        self.width >= inner.width && self.height >= inner.height
-    }
-
-    fn square(size: u32) -> Rectangle {
-        Rectangle { width: size, height: size }
-    }
-}
-
-fn main() {
-    let width1  = 30;
-    let height1 = 50;
-
-    println!(
-        "The area of the rectangle ist {} square pixels.",
-        area(width1, height1));
-
-    let rect1 = (30, 50);
-
-    println!(
-        "The area of the rectangle ist {} square pixels.",
-        _area(rect1));
-
-    let rect1 = Rectangle { width: 30, height: 50 };
-
-    println!(
-        "The area of the rectangle ist {} square pixels.",
-        __area(&rect1));
-
-    println!("_rect1 is {:?}", rect1);
-
-    println!(
-        "The area of the rectangle ist {} square pixels.",
-        rect1.area());
-
-    let rect2 = Rectangle { width: 10, height: 40};
-    let rect3 = Rectangle { width: 60, height: 45};
-
-    println!("Can rect1 hold rect2? {}", rect1.can_hold(&rect2));
-    println!("Can rect1 hold rect3? {}", rect1.can_hold(&rect3));
-
-    let square1 = Rectangle::square(32);
-
-    println!("Got the square rectange: {:?}", square1);
-}
-
-fn area(width: u32, height: u32) -> u32 {
-    width * height
-}
-
-fn _area(dimensions: (u32, u32)) -> u32 {
-    let (width, height) = dimensions;
-    width * height
-}
-
-fn __area(rectangle: &Rectangle) -> u32 {
-    rectangle.width * rectangle.height
-}

-[package]
-name = "recursion"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Try some recursion with pattern matching... especially in
-// conjunction with match to get a similar behavious as in e.g.
-// haskell...
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-// Borrowing rules do not apply here because everything lives on the stack.
-fn faculty(x: u32) -> u32 {
-    match x {
-        0 => 1,
-        _ => x * faculty(x - 1),
-    }
-}
-
-// for a tail recursive version we need to pass the currently calculated
-// faculty to an inner tail recursive function.
-// This will probably be optimized better, because the compiler would be
-// able to unroll the complete recursion.
-fn tail_faculty(x: u32) -> u32 {
-    fn faculty(x: u32, f: u32) -> u32 {
-        match x {
-            0 => f,
-            _ => faculty(x - 1, x * f),
-        }
-    };
-    faculty(x, 1)
-}
-
-fn main() {
-    for i in 0..10 {
-        println!("Fakultät                {} = {}", i, faculty(i));
-        println!("tail recursive Fakultät {} = {}", i, tail_faculty(i));
-    }
-}

-[package]
-name = "restaurant"
-version = "0.1.0"
-authors = ["Georg Hopp <georg@steffers.org>"]
-edition = "2018"
-
-# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
-
-[dependencies]

-//
-// Move some restaurant stuff in a different file....
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-pub mod hosting;
-
-mod serving {
-    fn take_order() {}
-    fn take_payment() {}
-}

-//
-// Now also sepatate hosting....
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-pub fn add_to_waitlist() {}
-fn seat_at_table() {}

-//
-// Restaurant lib for demontrating rust modules.
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-
-mod front_of_house;
-
-fn serve_order() {}
-
-mod back_of_house {
-    pub struct Breakfast {
-        pub toast: String,
-        seasonal_fruit: String,
-    }
-
-    impl Breakfast {
-        pub fn summer(toast: &str) -> Breakfast {
-            Breakfast {
-                toast: String::from(toast),
-                seasonal_fruit: String::from("peaches"),
-            }
-        }
-    }
-
-    pub enum Appetizer {
-        Soup,
-        Salad,
-    }
-
-    fn fix_incorrect_order() {
-        cook_order();
-        super::serve_order();
-    }
-
-    fn cook_order() {}
-}
-
-// Either absolute:
-// use crate::front_of_house::hosting;
-// or relaive:
-use front_of_house::hosting;
-// we can also provide new names...
-use crate::front_of_house::hosting as host;
-// Public definitions braught into scope with use are
-// private in this scope except we use «pub use»
-pub use front_of_house::hosting as pubhost;
-
-pub fn eat_at_restaurant() {
-    // Absolute path
-    crate::front_of_house::hosting::add_to_waitlist();
-
-    // Relative path
-    front_of_house::hosting::add_to_waitlist();
-
-    // With use'd path
-    hosting::add_to_waitlist();
-
-    // With renamed used path
-    host::add_to_waitlist();
-
-    pubhost::add_to_waitlist();
-
-    // Order a breakfast in the summer with Rye toast
-    let mut meal = back_of_house::Breakfast::summer("Rye");
-
-    // Change our mind about what bread we'd like
-    meal.toast = String::from("Wheat");
-
-    println!("I'd like {} toast please", meal.toast);
-
-    // The next line won't compile if we uncomment it; we're not allowed
-    // to see or modify the seasonal fruit that comes with the meal
-    // meal.seasonal_fruit = String::from("blueberries");
-
-    let order1 = back_of_house::Appetizer::Soup;
-    let order2 = back_of_house::Appetizer::Salad;
-}

@@ -20,13 +20,16 @@
 //
 extern crate xcb;
 
+use std::fmt::Debug;
 use std::sync::Arc;
-use std::ptr; //::{null, null_mut};
+use std::ptr;
 use std::thread;
 use std::sync::mpsc;
 use std::ops::{Add, Sub, Div};
 
-use crate::easel::{Easel, Canvas, Drawable, Coordinate, Coordinates};
+use easel3d::easel::Easel;
+use easel3d::easel::canvas::{Canvas, Vertex};
+use easel3d::easel::drawable::Drawable;
 
 #[derive(Clone)]
 pub struct XcbEasel (Arc<xcb::Connection>, i32);
@@ -62,6 +65,7 @@ impl XcbEasel {
                         , height :u16) -> Option<XcbCanvas<'a, T>>
     where T: Clone + From<i32> {
         let Self(conn, _) = self;
+        let size = width as usize * height as usize;
         let conn          = conn.clone();
         let screen        = match self.screen() {
             None         => return None,
@@ -85,8 +89,8 @@ impl XcbEasel {
                       , &[ (xcb::GC_FOREGROUND, screen.white_pixel())
                       , (xcb::GC_GRAPHICS_EXPOSURES, 0) ] );
 
-        let zbuf :Vec<T> = vec!(0.into(); (width * height) as usize);
-        let (shmid, shm) = getshm((width * height) as usize);
+        let zbuf :Vec<T> = vec!(0.into(); size);
+        let (shmid, shm) = getshm(size);
         xcb::shm::attach(&conn, shmseg, shmid as u32, false);
         unsafe { libc::shmctl(shmid, libc::IPC_RMID, ptr::null_mut()); }
 
@@ -138,7 +142,7 @@ impl Easel for XcbEasel {}
 
 impl<'a, T> Canvas<T> for XcbCanvas<'a, T>
 where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Copy + From<i32> + PartialOrd {
+       + Debug + Copy + From<i32> + PartialOrd {
     fn init_events(&self) {
         let mask = [( xcb::CW_EVENT_MASK, xcb::EVENT_MASK_EXPOSURE
                                         | xcb::EVENT_MASK_KEY_PRESS
@@ -233,12 +237,10 @@ where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
         }
     }
 
-    fn draw(&mut self, d :&dyn Drawable<T>, ofs :Coordinate<T>, color: u32) {
-        let Coordinates(c)            = d.plot();
-        let Coordinate(xofs, yofs, _) = ofs;
-
-        for Coordinate(x, y, zr) in c {
-            let idx :usize = ((y+yofs)*(self.width as i32)+x+xofs) as usize;
+    fn draw(&mut self, d :&dyn Drawable<T>, color: u32) {
+        for c in d.plot() {
+            let (x, y, zr) = c.as_tuple();
+            let idx :usize = (y*(self.width as i32)+x) as usize;
             if self.zbuf[idx] < zr {
                 self.zbuf[idx] = zr;
                 self.shm[idx] = color;
@@ -246,15 +248,15 @@ where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
         }
     }
 
-    fn put_text(&self, ofs :Coordinate<T>, s :&str) {
-        let Coordinate(xofs, yofs, _) = ofs;
+    fn put_text(&self, ofs :Vertex<T>, s :&str) {
+        let (xofs, yofs, _) = ofs.as_tuple();
         xcb::xproto::image_text_8( &self.conn, self.pixmap, self.gc
                                  , xofs as i16, yofs as i16, s );
         self.conn.flush();
     }
 
-    fn set_pixel(&mut self, c :Coordinate<T>, color :u32) {
-        let Coordinate(x, y, zr) = c;
+    fn set_pixel(&mut self, c :Vertex<T>, color :u32) {
+        let (x, y, zr) = c.as_tuple();
         let idx :usize = (y * (self.width as i32) + x) as usize;
 
         if self.zbuf[idx] < zr {

+//
+// Test our fractional crate / module...
+//
+// Georg Hopp <georg@steffers.org>
+//
+// Copyright © 2019 Georg Hopp
+//
+// This program is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program.  If not, see <http://www.gnu.org/licenses/>.
+//
+
+use std::fmt::Debug;
+use std::ops::{Add, Div, Mul, Neg, Sub};
+use std::sync::mpsc;
+use std::thread;
+use std::time::{Duration, Instant};
+
+use easel3d::easel::canvas::{Vertex, Canvas};
+use easel3d::easel::fillable::Fillable;
+use easel3d::math::trigonometry::Trig;
+use easel3d::math::vector::Vector;
+use easel3d::math::transform::TMatrix;
+use easel3d::space::camera::Camera;
+use easel3d::space::light::DirectLight;
+use easel3d::space::polyeder::Polyeder;
+use easel3d::space::primitives::Primitives;
+
+mod easel3d_xcb;
+
+use easel3d_xcb::XcbEasel;
+
+fn democanvas<T>( xcb         :&XcbEasel
+                , title       :&'static str
+                , tx          :mpsc::Sender<i32>
+                , _triangle   :Polyeder<T>
+                , tetrahedron :Polyeder<T>
+                , cube        :Polyeder<T>
+                , light       :DirectLight<T> )
+    where T: 'static + Add<Output = T> + Sub<Output = T> + Neg<Output = T>
+           + Mul<Output = T> + Div<Output = T>
+           + Debug + Copy + Trig + Send + From<i32> + From<f64> + PartialOrd {
+
+    let mut canvas = xcb.canvas(301, 301).unwrap();
+    let camera     = Camera::<T>::new(&canvas, 45); // the orig. view angle
+                                                    // was 50.
+
+    canvas.set_title(title);
+    canvas.init_events();
+    canvas.start_events(tx.clone());
+
+    thread::spawn(move || {
+        let     start = Instant::now();
+        let     step  = Duration::from_millis(20);
+        let mut last  = Instant::now();
+
+        let t = TMatrix::translate(Vector(0.into() , 0.into() , 150.into()));
+
+        loop {
+            let deg = ((start.elapsed() / 20).as_millis() % (4*360)) as i32;
+
+            let rz = TMatrix::rotate_z(deg);
+            let rx = TMatrix::rotate_x(-deg*2);
+            let ry = TMatrix::rotate_y(-deg*2);
+
+            let rot1 = TMatrix::combine(vec!(rz, rx, t));
+            let rot2 = TMatrix::combine(vec!(rz, ry, t));
+
+            let objects = vec!( (tetrahedron.transform(&rot1), 0xFFFF00)
+                              , (       cube.transform(&rot2), 0x0000FF) );
+            //let objects = vec!( (       cube.transform(&rot2), 0x0000FF) );
+            //let objects = vec!( (tetrahedron.transform(&rot1), 0xFFFF00) );
+            //let objects = vec!( (triangle.transform(&rot1), 0xFFFF00) );
+
+            let rlx = TMatrix::rotate_x(-deg/4);
+            let rly = TMatrix::rotate_y(-deg/1);
+            let tlight = light.transform(&TMatrix::combine(vec!(rlx, rly)));
+
+            canvas.clear();
+
+            for (o, color) in objects {
+                for (pg, c) in o.project(&camera, &tlight, color) {
+                    (&pg).fill(&mut canvas, c);
+                }
+            }
+
+            let passed = Instant::now() - last;
+            let f      = (passed.as_nanos() / step.as_nanos()) as u32;
+
+            if f > 1 {
+                println!("{} !!! Detected frame drop", title);
+            }
+
+            last = last + step*(f + 1);
+            canvas.put_text( Vertex::new(10, 15, 0.into())
+                           , &format!( "sleep: {:?}"
+                           , last - Instant::now() ));
+            canvas.show();
+            thread::sleep(last - Instant::now());
+        }
+    });
+}
+
+fn main() {
+    let      xcb = XcbEasel::new().unwrap();
+    let (tx, rx) = mpsc::channel();
+
+    democanvas( &xcb, "Something...(f64)", tx.clone()
+              , Polyeder::triangle(60.0)
+              , Polyeder::tetrahedron(100.0)
+              , Polyeder::cube(56.25)
+              , DirectLight::new(Vector(0.0, 0.0, 1.0)) );
+
+    for x in rx {
+        match x {
+            1 => break,
+            _ => {},
+        }
+    }
+}

-/target
-**/*.rs.bk
-Cargo.lock
-bin/
-pkg/
-wasm-pack/
-wasm-pack.log

-[package]
-name = "wasm-game-of-life"
-version = "0.1.0"
-authors = ["hopp@silpion.de"]
-edition = "2018"
-
-[lib]
-crate-type = ["cdylib", "rlib"]
-
-[features]
-default = ["console_error_panic_hook"]
-
-[dependencies]
-wasm-bindgen = "0.2"
-lazy_static = "1.4.0"
-
-# The `console_error_panic_hook` crate provides better debugging of panics by
-# logging them with `console.error`. This is great for development, but requires
-# all the `std::fmt` and `std::panicking` infrastructure, so isn't great for
-# code size when deploying.
-console_error_panic_hook = { version = "0.1.1", optional = true }
-
-# `wee_alloc` is a tiny allocator for wasm that is only ~1K in code size
-# compared to the default allocator's ~10K. It is slower than the default
-# allocator, however.
-#
-# Unfortunately, `wee_alloc` requires nightly Rust when targeting wasm for now.
-wee_alloc = { version = "0.4.2", optional = true }
-
-[dev-dependencies]
-wasm-bindgen-test = "0.2"
-
-[profile.release]
-# Tell `rustc` to optimize for small code size.
-opt-level = "s"

-<div align="center">
-
-  <h1><code>wasm-pack-template</code></h1>
-
-  <strong>A template for kick starting a Rust and WebAssembly project using <a href="https://github.com/rustwasm/wasm-pack">wasm-pack</a>.</strong>
-
-  <p>
-    <a href="https://travis-ci.org/rustwasm/wasm-pack-template"><img src="https://img.shields.io/travis/rustwasm/wasm-pack-template.svg?style=flat-square" alt="Build Status" /></a>
-  </p>
-
-  <h3>
-    <a href="https://rustwasm.github.io/docs/wasm-pack/tutorials/npm-browser-packages/index.html">Tutorial</a>
-    <span> | </span>
-    <a href="https://discordapp.com/channels/442252698964721669/443151097398296587">Chat</a>
-  </h3>
-
-  <sub>Built with 🦀🕸 by <a href="https://rustwasm.github.io/">The Rust and WebAssembly Working Group</a></sub>
-</div>
-
-## About
-
-[**📚 Read this template tutorial! 📚**][template-docs]
-
-This template is designed for compiling Rust libraries into WebAssembly and
-publishing the resulting package to NPM.
-
-Be sure to check out [other `wasm-pack` tutorials online][tutorials] for other
-templates and usages of `wasm-pack`.
-
-[tutorials]: https://rustwasm.github.io/docs/wasm-pack/tutorials/index.html
-[template-docs]: https://rustwasm.github.io/docs/wasm-pack/tutorials/npm-browser-packages/index.html
-
-## 🚴 Usage
-
-### 🐑 Use `cargo generate` to Clone this Template
-
-[Learn more about `cargo generate` here.](https://github.com/ashleygwilliams/cargo-generate)
-
-```
-cargo generate --git https://github.com/rustwasm/wasm-pack-template.git --name my-project
-cd my-project
-```
-
-### 🛠️ Build with `wasm-pack build`
-
-```
-wasm-pack build
-```
-
-### 🔬 Test in Headless Browsers with `wasm-pack test`
-
-```
-wasm-pack test --headless --firefox
-```
-
-### 🎁 Publish to NPM with `wasm-pack publish`
-
-```
-wasm-pack publish
-```
-
-## 🔋 Batteries Included
-
-* [`wasm-bindgen`](https://github.com/rustwasm/wasm-bindgen) for communicating
-  between WebAssembly and JavaScript.
-* [`console_error_panic_hook`](https://github.com/rustwasm/console_error_panic_hook)
-  for logging panic messages to the developer console.
-* [`wee_alloc`](https://github.com/rustwasm/wee_alloc), an allocator optimized
-  for small code size.

-{
-  "lockfileVersion": 1
-}

-//
-// This is an abstraction over a drawing environment.
-// Future note: z-Buffer is described here:
-// https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/perspective-correct-interpolation-vertex-attributes
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::cmp;
-use std::fmt::{Formatter, Debug, Display, Result};
-use std::ops::{Add, Sub, Div};
-use std::sync::mpsc;
-
-pub trait Easel {
-    //fn canvas(&mut self, width :u16, height :u16) -> Option<&dyn Canvas>;
-}
-
-pub trait Canvas<T> {
-    fn init_events(&self);
-    fn start_events(&self, tx :mpsc::Sender<i32>);
-
-    fn width(&self) -> u16;
-    fn height(&self) -> u16;
-
-    fn clear(&mut self);
-    fn draw(&mut self, c :&dyn Drawable<T>, ofs :Coordinate<T>, color :u32);
-    fn put_text(&self, ofs :Coordinate<T>, s :&str);
-    fn set_pixel(&mut self, c :Coordinate<T>, color :u32);
-    fn show(&self);
-}
-
-pub trait Drawable<T> {
-    fn plot(&self) -> Coordinates<T>;
-}
-
-pub trait Fillable<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    fn fill(&self, canvas :&mut dyn Canvas<T>, color :u32);
-}
-
-#[derive(Debug, Clone, Copy)]
-pub struct Coordinate<T>(pub i32, pub i32, pub T);
-
-#[derive(Debug, Clone)]
-pub struct Coordinates<T>(pub Vec<Coordinate<T>>);
-
-#[derive(Debug, Clone, Copy)]
-pub struct LineIterator<T> where T: Debug {
-               a :Option<Coordinate<T>>
-    ,          b :Coordinate<T>
-    ,         dx :i32
-    ,         dy :i32
-    ,         dz :T
-    ,         sx :i32
-    ,         sy :i32
-    ,        err :i32
-    , only_edges :bool
-}
-
-impl<T> Iterator for LineIterator<T>
-where T: Add<Output = T> + Debug + Copy + From<i32> {
-    type Item = Coordinate<T>;
-
-    fn next(&mut self) -> Option<Self::Item> {
-        match self.a {
-            None    => None,
-            Some(a) => {
-                let Coordinate(ax, ay, az) = a;
-                let Coordinate(bx, by,  _) = self.b;
-
-                if ax != bx || ay != by {
-                    match (2 * self.err >= self.dy, 2 * self.err <= self.dx ) {
-                        (true, false) => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax + self.sx
-                                                      , ay
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dy;
-                            if self.only_edges { self.next() } else { r }
-                        },
-                        (false, true) => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax
-                                                      , ay + self.sy
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dx;
-                            r
-                        },
-                        _             => {
-                            let r    = self.a;
-                            self.a   = Some(Coordinate( ax + self.sx
-                                                      , ay + self.sy
-                                                      , az + self.dz ));
-                            self.err = self.err + self.dx + self.dy;
-                            r
-                        },
-                    }
-                } else {
-                    self.a = None;
-                    Some(self.b)
-                }
-            }
-        }
-    }
-}
-
-impl<T> Coordinate<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn iter(self, b :&Self, only_edges :bool) -> LineIterator<T> {
-        let Coordinate(ax, ay, az) = self;
-        let Coordinate(bx, by, bz) = *b;
-
-        let dx = (bx - ax).abs();
-        let dy = -(by - ay).abs();
-
-        LineIterator {    a: Some(self)
-                     ,    b: *b
-                     ,   dx: dx
-                     ,   dy: dy
-                     ,   dz: (bz - az) / cmp::max(dx, -dy).into()
-                     ,   sx: if ax < bx { 1 } else { -1 }
-                     ,   sy: if ay < by { 1 } else { -1 }
-                     , err: dx + dy
-                     , only_edges: only_edges
-        }
-    }
-
-    fn line_iter(self, b :&Self) -> LineIterator<T> {
-        self.iter(b, false)
-    }
-
-    fn line(self, b :&Self) -> Vec<Self> {
-        self.line_iter(b).collect()
-    }
-
-    fn edge_iter(self, b :&Self) -> LineIterator<T> {
-        self.iter(b, true)
-    }
-
-    fn edge(self, b :&Self) -> Vec<Self> {
-        self.edge_iter(b).collect()
-    }
-
-    fn face(edges :&[Self]) -> Vec<Self> {
-        edges.to_vec()
-    }
-}
-
-impl<T> Display for Coordinate<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        write!(f, "<{},{}>", self.0, self.1)
-    }
-}
-
-impl<T> Display for Coordinates<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Coordinates(is) = self;
-
-        let c = match is[..] {
-            []  => String::from(""),
-            [a] => format!("{}", a),
-            _   => {
-                let mut a = format!("{}", is[0]);
-                for i in is[1..].iter() {
-                    a = a + &format!(",{}", i);
-                }
-                a
-            }
-        };
-
-        write!(f, "Coordinates[{}]", c)
-    }
-}
-
-
-#[derive(Debug, Clone, Copy)]
-pub struct Point<T>(pub Coordinate<T>);
-
-impl<T> Drawable<T> for Point<T> where T: Copy {
-    fn plot(&self) -> Coordinates<T> {
-        let Point(c) = *self;
-        Coordinates(vec!(c))
-    }
-}
-
-impl<T> Display for Point<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Point(p) = self;
-        write!(f, "Point[{}]", p)
-    }
-}
-
-#[derive(Debug, Clone, Copy)]
-pub struct Line<T>(pub Coordinate<T>, pub Coordinate<T>);
-
-impl<T> Drawable<T> for Line<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Line(a, b) = *self;
-        Coordinates(a.line(&b))
-    }
-}
-
-impl<T> Display for Line<T> {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Line(a, b) = self;
-        write!(f, "Line[{},{}]", a, b)
-    }
-}
-
-#[derive(Debug, Clone)]
-pub struct Polyline<T>(pub Coordinates<T>);
-
-impl<T> Drawable<T> for Polyline<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Polyline(Coordinates(cs)) = self;
-
-        match cs[..] {
-            []     => Coordinates(Vec::<Coordinate<T>>::new()),
-            [a]    => Coordinates(vec!(a)),
-            [a, b] => Coordinates(a.line(&b)),
-            _      => {
-                let (a, b) = (cs[0], cs[1]);
-                let mut r = a.line(&b);
-                let mut i = b;
-                for j in cs[2..].iter() {
-                    r.append(&mut i.line(j)[1..].to_vec());
-                    i = *j;
-                }
-                Coordinates(r)
-            },
-        }
-    }
-}
-
-impl<T> Display for Polyline<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Polyline(a) = self;
-        write!(f, "PLine[{}]", a)
-    }
-}
-
-#[derive(Debug, Clone, Copy)]
-enum Direction { Left, Right }
-
-#[derive(Debug, Clone)]
-pub struct Polygon<T>(pub Coordinates<T>);
-
-#[derive(Debug, Clone)]
-enum VertexIteratorMode { Vertex, Edge }
-#[derive(Debug, Clone)]
-pub struct VertexIterator<'a,T> where T: Debug {
-    p         :&'a Polygon<T>,
-    top       :usize,
-    current   :Option<usize>,
-    edge      :Option<LineIterator<T>>,
-    mode      :VertexIteratorMode,
-    direction :Direction,
-}
-
-impl<'a,T> VertexIterator<'a,T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    fn edge(p :&'a Polygon<T>, direction :Direction) -> Self {
-        let top  = p.vert_min(direction);
-        let next = p.next_y(top, direction);
-        let edge = match next {
-            None       => None,
-            Some(next) => Some(p.vertex(top).edge_iter(&p.vertex(next))),
-        };
-
-        VertexIterator { p:         p
-                       , top:       top
-                       , current:   next
-                       , edge:      edge
-                       , mode:      VertexIteratorMode::Edge
-                       , direction: direction }
-    }
-
-    fn vertex(p :&'a Polygon<T>, direction :Direction) -> Self {
-        let top  = p.vert_min(direction);
-        let next = p.next_y(top, direction);
-
-        VertexIterator { p:         p
-                       , top:       top
-                       , current:   next
-                       , edge:      None
-                       , mode:      VertexIteratorMode::Vertex
-                       , direction: direction }
-    }
-
-    // if this yields "None" we are finished.
-    fn next_edge(&mut self) -> Option<LineIterator<T>> {
-        let current  = self.current?;
-        let next     = self.p.next_y(current, self.direction)?;
-        let mut edge = self.p.vertex(current).edge_iter(&self.p.vertex(next));
-
-        match edge.next() {
-            // It should be impossible that a new edge iterator has no values
-            // at all… anyway, just in case I handle it here.
-            None    => self.next_edge(),
-            Some(_) => {
-                self.current = Some(next);
-                self.edge    = Some(edge);
-                self.edge
-            },
-        }
-    }
-}
-
-impl<'a,T> Iterator for VertexIterator<'a,T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Copy + From<i32> {
-    type Item = Coordinate<T>;
-
-    fn next(&mut self) -> Option<Self::Item> {
-        match self.mode {
-            VertexIteratorMode::Edge => {
-                // if for whatever reason edge is "None" finish this iterator.
-                let next = self.edge.as_mut()?.next();
-
-                match next {
-                    Some(_) => next,
-                    None    => {
-                        self.next_edge()?;
-                        self.next()
-                    },
-                }
-            },
-            VertexIteratorMode::Vertex => {
-                let current  = self.current?;
-                self.current = self.p.next_y(current, self.direction);
-                Some(self.p.vertex(current))
-            },
-        }
-    }
-}
-
-impl<T> Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Copy + Debug + From<i32> {
-    #[inline]
-    fn vertex(&self, v :usize) -> Coordinate<T> {
-        let Polygon(Coordinates(cs)) = self;
-        cs[v]
-    }
-
-    fn vert_min<'a>(&'a self, d :Direction) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        type ICoord<'a,T> = (usize, &'a Coordinate<T>);
-
-        // TODO I guess the problem here is that it does not account for the
-        //      same y vertex on the beggining and the end. So i guess correct
-        //      would be finding the first one and then dependings on the
-        //      given direction either search left or right for same y's.
-        let fold = |acc :Option<ICoord<'a,T>>, x :ICoord<'a,T>|
-            match acc {
-                None    => Some(x),
-                Some(a) => {
-                    let Coordinate(_, ay, _) = a.1;
-                    let Coordinate(_, xy, _) = x.1;
-                    if xy < ay {Some(x)} else {Some(a)}
-                },
-            };
-
-        let mut  min = cs.iter().enumerate().fold(None, fold).unwrap().0;
-        let mut next = self.step(min, d);
-
-        while self.vertex(min).1 == self.vertex(next).1 {
-            min = next;
-            next = self.step(min, d);
-        }
-
-        min
-    }
-
-    fn left_edge(&self) -> VertexIterator<T> {
-        VertexIterator::edge(self, Direction::Left)
-    }
-
-    fn right_edge(&self) -> VertexIterator<T> {
-        VertexIterator::edge(self, Direction::Right)
-    }
-
-    fn left_vertices(&self) -> VertexIterator<T> {
-        VertexIterator::vertex(self, Direction::Left)
-    }
-
-    fn right_vertices(&self) -> VertexIterator<T> {
-        VertexIterator::vertex(self, Direction::Right)
-    }
-
-    fn left(&self, v :usize) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        match v {
-            0 => cs.len() - 1,
-            _ => v - 1,
-        }
-    }
-
-    fn right(&self, v :usize) -> usize {
-        let Polygon(Coordinates(cs)) = self;
-
-        (v + 1) % cs.len()
-    }
-
-    fn step(&self, v :usize, d :Direction) -> usize {
-        match d {
-            Direction::Left  => self.left(v),
-            Direction::Right => self.right(v),
-        }
-    }
-
-    fn next_y(&self, c :usize, d :Direction) -> Option<usize> {
-        fn inner<T>( p :&Polygon<T>
-                   , c :usize
-                   , n :usize
-                   , d :Direction) -> Option<usize>
-        where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-               + Copy + Debug + From<i32> {
-            if c == n {
-                None
-            } else {
-                let Coordinate(_, cy, _) = p.vertex(c);
-                let Coordinate(_, ny, _) = p.vertex(n);
-
-                if ny < cy { None } else { Some(n) }
-            }
-        }
-
-        inner(self, c, self.step(c, d), d)
-    }
-
-    pub fn debug(&self) {
-        let mut left  = self.left_vertices();
-        let mut right = self.right_vertices();
-
-        if left.find(|l| right.find(|r| l.0 == r.0).is_some()).is_some() {
-            let left  :Vec<Coordinate<T>> = self.left_vertices().collect();
-            let right :Vec<Coordinate<T>> = self.right_vertices().collect();
-
-            println!("===");
-            println!("==  poly : {:?}", self);
-            println!("==  ltop : {:?}", self.vert_min(Direction::Left));
-            println!("==  rtop : {:?}", self.vert_min(Direction::Right));
-            println!("==  left : {:?}", left);
-            println!("== right : {:?}", right);
-            println!("===");
-        }
-    }
-}
-
-impl<T> Drawable<T> for Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn plot(&self) -> Coordinates<T> {
-        let Polygon(Coordinates(cs)) = self;
-
-        match cs[..] {
-            []     => Coordinates(Vec::<Coordinate<T>>::new()),
-            [a]    => Coordinates(vec!(a)),
-            [a, b] => Coordinates(a.line(&b)),
-            _      => {
-                let (a, b) = (cs[0], cs[1]);
-                let mut r = a.line(&b);
-                let mut i = b;
-                for j in cs[2..].iter() {
-                    r.append(&mut i.line(j)[1..].to_vec());
-                    i = *j;
-                }
-                let mut j = a.line(&i);
-                let     l = j.len();
-                if l > 1 {
-                    r.append(&mut j[1..l-1].to_vec());
-                }
-                Coordinates(r)
-            },
-        }
-    }
-}
-
-impl<T> Fillable<T> for Polygon<T>
-where T: Add<Output = T> + Sub<Output = T> + Div<Output = T>
-       + Debug + Clone + Copy + From<i32> {
-    fn fill(&self, canvas :&mut dyn Canvas<T>, color :u32) {
-        let scanlines = self.left_edge().zip(self.right_edge());
-
-        for l in scanlines.flat_map(|(l, r)| l.line_iter(&r)) {
-            canvas.set_pixel(l, color);
-        }
-    }
-}
-
-impl<T> Display for Polygon<T> where T: Copy {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
-        let Polygon(a) = self;
-        write!(f, "Poly[{}]", a)
-    }
-}

-//
-// Basic geometric things...
-//
-// Georg Hopp <georg@steffers.org>
-//
-// Copyright © 2019 Georg Hopp
-//
-// This program is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// This program is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-//
-// You should have received a copy of the GNU General Public License
-// along with this program.  If not, see <http://www.gnu.org/licenses/>.
-//
-use std::convert::{From, Into};
-use std::ops::{Add,Sub,Neg,Mul,Div};
-use std::fmt::Debug;
-
-use crate::easel::{Canvas, Coordinate, Coordinates, Polygon};
-use crate::transform::{TMatrix, Transformable};
-use crate::trigonometry::Trig;
-use crate::vector::Vector;
-
-#[derive(Debug, Clone)]
-pub struct Face<T>
-where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
-    corners :Vec<usize>,
-    normal  :Option<Vector<T>>,
-}
-
-#[derive(Debug, PartialEq, Eq, Clone, Copy)]
-pub struct Point<T>(pub Vector<T>, T)
-    where T: Add + Sub + Neg + Mul + Div + PartialEq + Copy + Trig;
-
-impl<T> Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    pub fn new(x :T, y :T, z :T) -> Self {
-        Self(Vector(x, y, z), 1.into())
-    }
-}
-
-impl<T> Add for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn add(self, other :Self) -> Self {
-        let Point(v1, w1) = self;
-        let Point(v2, w2) = other;
-        Self(v1 + v2, w1 + w2)
-    }
-}
-
-impl<T> Neg for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn neg(self) -> Self {
-        let Point(v, w) = self;
-        Self(-v, -w)
-    }
-}
-
-impl<T> Sub for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy {
-    type Output = Self;
-
-    fn sub(self, other :Self) -> Self {
-        self + -other
-    }
-}
-
-impl<T> Mul for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    type Output = Self;
-
-    fn mul(self, other :Self) -> Self {
-        let a :Vector<T> = self.into();
-        let b :Vector<T> = other.into();
-
-        Point(a * b, 1.into())
-    }
-}
-
-impl<T> From<Vector<T>> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    fn from(v :Vector<T>) -> Self {
-        Point(v, 1.into())
-    }
-}
-
-impl<T> Into<Vector<T>> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Trig + Copy + From<i32> {
-    fn into(self) -> Vector<T> {
-        let Point(v, w) = self;
-
-        if w == 0.into() {
-            v
-        } else {
-            v.mul(&w.recip())
-        }
-    }
-}
-
-impl<T> Transformable<T> for Point<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Trig + Copy + From<i32> {
-    fn transform(&self, m :&TMatrix<T>) -> Self {
-        let Point(v, w) = *self;
-        let (v, w)      = m.apply(&v, w);
-
-        if w == 0.into() {
-            v.into()
-        } else {
-            v.mul(&w.recip()).into()
-        }
-    }
-}
-
-#[derive(Debug)]
-pub struct Polyeder<T>
-where T: Add + Sub + Neg + Mul + Div + PartialEq + Copy + Trig {
-    points :Vec<Point<T>>,
-    faces  :Vec<Face<T>>,
-}
-
-pub trait Primitives<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    fn transform(&self, m :&TMatrix<T>) -> Self;
-    fn project( &self
-              , camera :&Camera<T>
-              , light :&DirectLight<T>
-              , col :u32 ) -> Vec<(Polygon<T>, u32)>;
-}
-
-#[derive(Debug, Clone, Copy)]
-pub struct Camera<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    width    :T,
-    height   :T,
-    distance :T,
-    project  :TMatrix<T>,
-}
-
-pub struct DirectLight<T>
-where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
-    direction: Vector<T>,
-}
-
-impl<T> Camera<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    // This code assumes that the size of the viewport is always
-    // equal to the size of the physical screen… e.g. window/canvas thus some
-    // effects can't be done. See book for examples with different viewport
-    // and screen sizes.
-    pub fn new(c :&dyn Canvas<T>, angle :i32) -> Self {
-        let  width :T = (c.width() as i32).into();
-        let height :T = (c.height() as i32).into();
-        let      d :T = 1.into();
-        let    fov    = T::cot(angle) * width;
-        let     wh    = width / 2.into();
-        let     hh    = height / 2.into();
-
-        Camera { width:    width
-               , height:   height
-               , distance: d
-               , project:  TMatrix::new(
-                     (     fov, 0.into(),       wh, 0.into())
-                   , (0.into(),      fov,       hh, 0.into())
-                   , (0.into(), 0.into(),        d, 1.into())
-                   , (0.into(), 0.into(), 1.into(), 0.into()) ) }
-    }
-
-    pub fn get_distance(&self) -> T {
-        self.distance
-    }
-
-    pub fn get_projection(&self) -> TMatrix<T> {
-        self.project
-    }
-
-    pub fn project(&self, p :Point<T>) -> Point<T> {
-        p.transform(&self.project)
-    }
-}
-
-impl<T> DirectLight<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Copy + Trig + From<i32> {
-    pub fn new(v :Vector<T>) -> Self {
-        DirectLight{ direction: v }
-    }
-
-    pub fn dir(&self) -> Vector<T> {
-        self.direction
-    }
-}
-
-impl<T> Face<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    fn new(corners :Vec<usize>, ps :&[Point<T>]) -> Self {
-        let mut f = Face{ corners: corners, normal: None };
-        f.update_normal(ps);
-        f
-    }
-
-    fn update_normal(&mut self, ps :&[Point<T>]) {
-        let edge10 :Vector<T> = (ps[self.corners[1]] - ps[self.corners[0]]).into();
-        let edge12 :Vector<T> = (ps[self.corners[1]] - ps[self.corners[2]]).into();
-        self.normal = Some(edge10 * edge12);
-    }
-}
-
-impl<T> Polyeder<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + PartialEq + Debug + Copy + Trig + From<i32> {
-    fn update_normals(&mut self) {
-        for f in self.faces.iter_mut() {
-            f.update_normal(&self.points);
-        }
-    }
-
-    // construct via cube, see polyhedra.pdf
-    pub fn tetrahedron(a :T) -> Polyeder<T> {
-        let f2 :T = 2.into();
-        let ch    = a / (f2 * T::sqrt(f2).unwrap());
-
-        let ps = vec!( Point::new(-ch, -ch,  ch)    // A
-                     , Point::new(-ch,  ch, -ch)    // C
-                     , Point::new( ch, -ch, -ch)    // E
-                     , Point::new( ch,  ch,  ch) ); // G
-
-        // bottom: 1, 2, 3
-        let fs = vec!( Face::new(vec!(2, 1, 0), &ps) // bottom
-                     , Face::new(vec!(3, 2, 0), &ps)
-                     , Face::new(vec!(0, 1, 3), &ps)
-                     , Face::new(vec!(1, 2, 3), &ps) );
-        //let fs = vec!( Face::new(vec!(0, 1, 2), &ps) // bottom
-        //             , Face::new(vec!(0, 2, 3), &ps)
-        //             , Face::new(vec!(3, 1, 0), &ps)
-        //             , Face::new(vec!(3, 2, 1), &ps) );
-
-        Polyeder{ points: ps, faces: fs }
-    }
-
-    pub fn triangle(a :T) -> Polyeder<T> {
-        let f0 :T = 0.into();
-        let f3 :T = 3.into();
-        let f6 :T = 6.into();
-        let zi :T = T::sqrt(f3).unwrap() / f6 * a;
-        let zc :T = T::sqrt(f3).unwrap() / f3 * a;
-        let ah :T = a / 2.into();
-
-        let ps = vec!( Point::new(-ah, f0, -zi)
-                     , Point::new( f0, f0,  zc)
-                     , Point::new( ah, f0, -zi) );
-
-        let fs = vec!(Face::new(vec!(0, 1, 2), &ps));
-
-        Polyeder{ points: ps, faces: fs }
-    }
-
-    pub fn cube(a :T) -> Polyeder<T> {
-        let ah :T = a / From::<i32>::from(2);
-
-        let ps = vec!( Point::new(-ah,  ah, -ah)    // 0 => front 1
-                     , Point::new(-ah, -ah, -ah)    // 1 => front 2
-                     , Point::new( ah, -ah, -ah)    // 2 => front 3
-                     , Point::new( ah,  ah, -ah)    // 3 => front 4
-                     , Point::new(-ah,  ah,  ah)    // 4 => back 1
-                     , Point::new(-ah, -ah,  ah)    // 5 => back 2
-                     , Point::new( ah, -ah,  ah)    // 6 => back 3
-                     , Point::new( ah,  ah,  ah) );  // 7 => back 4
-
-        let fs = vec!( Face::new(vec!(0, 1, 2, 3), &ps)    // front
-                     , Face::new(vec!(7, 6, 5, 4), &ps)    // back
-                     , Face::new(vec!(1, 5, 6, 2), &ps)    // top
-                     , Face::new(vec!(0, 3, 7, 4), &ps)    // bottom
-                     , Face::new(vec!(0, 4, 5, 1), &ps)    // left
-                     , Face::new(vec!(2, 6, 7, 3), &ps) ); // right
-
-        Polyeder{ points: ps, faces: fs }
-    }
-}
-
-impl<T> Primitives<T> for Polyeder<T>
-where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
-       + Mul<Output = T> + Div<Output = T>
-       + Debug + Copy + Trig + From<i32> + PartialOrd {
-    // TODO Maybe this should also be an instance of Transformable…
-    fn transform(&self, m :&TMatrix<T>) -> Self {
-        let Polyeder{ points: ps, faces: fs } = self;
-
-        let mut p = Polyeder{
-              points: ps.iter().map(|p| p.transform(m)).collect()
-            , faces:  fs.to_vec()
-        };
-
-        // TODO alternatively we could rotate the normals too, but this cannot
-        // done with the original matrix… the question is, what is faster.
-        p.update_normals();
-        p
-    }
-
-    fn project( &self
-              , camera :&Camera<T>
-              , light :&DirectLight<T>
-              , color :u32 ) -> Vec<(Polygon<T>, u32)> {
-        // Helper to create a Polygon from Coordinates…
-        // TODO probably there needs to be a Polygon constructor for this.
-        fn polygon<I, T>(c :I) -> Polygon<T>
-        where I: Iterator<Item = Coordinate<T>> {
-            Polygon(Coordinates(c.collect()))
-        }
-
-        // this one does the projection... as the projection was the last
-        // matrix we do not need to do it here.
-        let to_coord = |p :&usize| {
-            let Point(v, _) = camera.project(self.points[*p]);
-            Coordinate(T::round(&v.x()), T::round(&v.y()), v.z() - 1.into())
-        };
-        let to_poly  = |f :&Face<T>| {
-                       let     pg    = polygon(f.corners.iter().map(to_coord));
-                       let mut  r :T = (((color >> 16) & 0xFF) as i32).into();
-                       let mut  g :T = (((color >>  8) & 0xFF) as i32).into();
-                       let mut  b :T = (((color      ) & 0xFF) as i32).into();
-                       let     lf :T = match f.normal {
-                           None    => 1.into(),
-                           Some(n) => n.dot(light.dir())
-                                    / (n.mag() * light.dir().mag()),
-                       };
-
-                       // this "if" represents a first simple backface culling
-                       // approach. We only return face that face towards us.
-                       if lf < 0.into() {
-                           r = r * -lf;
-                           g = g * -lf;
-                           b = b * -lf;
-
-                           let c :u32 = (r.round() as u32) << 16
-                                      | (g.round() as u32) << 8
-                                      | (b.round() as u32);
-
-                           Some((pg, c))
-                       } else {
-                           None
-                       }};
-
-        self.faces.iter().filter_map(to_poly).collect()
-    }
-}

-extern crate lazy_static;
-
-pub type Error = &'static str;
-
-pub mod easel;
-pub mod transform;
-pub mod trigonometry;
-pub mod vector;
-pub mod geometry;
-
-mod utils;
-
-use vector::Vector;
-use easel::{Canvas, Coordinate, Drawable, Fillable};
-use geometry::{Camera, DirectLight, Polyeder, Primitives};
-use transform::{TMatrix};
-
-use std::fmt::{Display, Formatter, Result};
-use std::sync::mpsc;
-use std::time::Instant;
-use wasm_bindgen::prelude::*;
-
-// When the `wee_alloc` feature is enabled, use `wee_alloc` as the global
-// allocator.
-#[cfg(feature = "wee_alloc")]
-#[global_allocator]
-static ALLOC: wee_alloc::WeeAlloc = wee_alloc::WeeAlloc::INIT;
-
-#[wasm_bindgen]
-#[derive(Clone, Copy, Debug, PartialEq, Eq)]
-pub struct Color(u8, u8, u8, u8);
-
-#[wasm_bindgen]
-pub struct View3d { width       :u16
-                  , height      :u16
-                  , size        :usize
-                  , degree      :i32
-                  //, start       :Instant
-                  , tetrahedron :Polyeder<f64>
-                  , cube        :Polyeder<f64>
-                  , camera      :Option<Camera<f64>>
-                  , light       :DirectLight<f64>
-                  , zbuf        :Vec<f64>
-                  , image       :Vec<Color>
-}
-
-#[wasm_bindgen]
-impl View3d {
-    pub fn new(width :u16, height :u16) -> Self {
-        let size = width as usize * height as usize;
-        let light_vector = Vector(0.0, 0.0, 1.0);
-
-        let mut view3d = Self { width:       width
-                              , height:      height
-                              , size:        size
-                              , degree:      0
-                              //, start:       Instant::now()
-                              , tetrahedron: Polyeder::tetrahedron(100.0)
-                              , cube:        Polyeder::cube(56.25)
-                              , camera:      None
-                              , light:       DirectLight::new(light_vector)
-                              , zbuf:        vec!(0.0; size)
-                              , image:       vec!(Color(0, 0, 0, 0xFF); size)
-        };
-
-        view3d.camera = Some(Camera::<f64>::new(&view3d, 45));
-        view3d
-    }
-
-    pub fn width(&self) -> u16 {
-        self.width
-    }
-
-    pub fn height(&self) -> u16 {
-        self.height
-    }
-
-    pub fn update(&mut self) {
-        //let deg = ((self.start.elapsed() / 25).as_millis() % 360) as i32;
-        let  t = TMatrix::translate(Vector(0.0, 0.0, 150.0));
-        let rz = TMatrix::rotate_z(self.degree);
-        let rx = TMatrix::rotate_x(-self.degree*2);
-        let ry = TMatrix::rotate_y(-self.degree*2);
-
-        let rot1 = TMatrix::combine(vec!(rz, rx, t));
-        let rot2 = TMatrix::combine(vec!(rz, ry, t));
-
-        let objects = vec!( (self.tetrahedron.transform(&rot1), 0xFFFF00)
-                          , (       self.cube.transform(&rot2), 0x0000FF) );
-
-        self.degree = (self.degree + 1) % 360;
-
-        self.clear();
-
-        match self.camera {
-            None         => {},
-            Some(camera) => {
-                for (o, color) in objects {
-                    for (pg, c) in o.project(&camera, &self.light, color) {
-                        (&pg).fill(self, c);
-                    }
-                }
-            },
-        }
-    }
-
-    pub fn image(&self) -> *const Color {
-        self.image.as_ptr()
-    }
-}
-
-impl Canvas<f64> for View3d {
-    fn width(&self) -> u16 {
-        self.width
-    }
-
-    fn height(&self) -> u16 {
-        self.height
-    }
-
-    fn clear(&mut self) {
-        self.zbuf  = vec!(0.0; self.size);
-        self.image = vec!(Color(0, 0, 0, 0xFF); self.size);
-    }
-
-    fn set_pixel(&mut self, c :Coordinate<f64>, color :u32) {
-        let Coordinate(x, y, zr) = c;
-        let idx :usize = (y * (self.width as i32) + x) as usize;
-
-        let r = ((color >> 16) & 0xFF) as u8;
-        let g = ((color >>  8) & 0xFF) as u8;
-        let b = (        color & 0xFF) as u8;
-
-        if self.zbuf[idx] < zr {
-            self.zbuf[idx]  = zr;
-            self.image[idx] = Color(r, g, b, 0xFF);
-        }
-    }
-
-    // Empty implementations for now… mostly not needed because it is
-    // done from JavaScript…
-    fn init_events(&self) {}
-    fn start_events(&self, _ :mpsc::Sender<i32>) {}
-    fn draw( &mut self, _ :&dyn Drawable<f64>, _ :Coordinate<f64>, _ :u32 ) {}
-    fn put_text(&self, _ :Coordinate<f64>, _ :&str) {}
-    fn show(&self) {}
-}
-
-#[wasm_bindgen]
-#[repr(u8)]
-#[derive(Clone, Copy, Debug, PartialEq, Eq)]
-pub enum Cell {
-    Dead  = 0,
-    Alive = 1,
-}
-
-#[wasm_bindgen]
-pub struct Universe {
-    width  :u32,
-    height :u32,
-    cells  :Vec<Cell>,
-}
-
-#[wasm_bindgen]
-impl Universe {
-    pub fn new() -> Universe {
-        let width  = 64;
-        let height = 64;
-
-        let init_cells = |i :u32| {
-            if i % 2 == 0 || i % 7 == 0 { Cell::Alive } else { Cell::Dead }
-        };
-
-        let cells = (0..width * height).map(init_cells).collect();
-
-        Universe {
-            width:  width,
-            height: height,
-            cells:  cells,
-        }
-    }
-
-    pub fn width(&self) -> u32 {
-        self.width
-    }
-
-    pub fn height(&self) -> u32 {
-        self.height
-    }
-
-    pub fn cells(&self) -> *const Cell {
-        self.cells.as_ptr()
-    }
-
-    pub fn render(&self) -> String {
-        self.to_string()
-    }
-
-    pub fn tick(&mut self) {
-        let mut next = self.cells.clone();
-
-        for row in 0..self.height {
-            for col in 0..self.width {
-                let idx            = self.get_index(row, col);
-                let cell           = self.cells[idx];
-                let live_neighbors = self.live_neighbor_count(row, col);
-
-                // Game of life rules....
-                let next_cell = match (cell, live_neighbors) {
-                    (Cell::Alive, 2) |
-                    (Cell::Alive, 3) => Cell::Alive,
-                    (Cell::Alive, _) => Cell::Dead,
-                    ( Cell::Dead, 3) => Cell::Alive,
-                    (  otherwise, _) => otherwise,
-                };
-
-                next[idx] = next_cell;
-            }
-        }
-
-        self.cells = next;
-    }
-
-    fn get_index(&self, row :u32, col :u32) -> usize {
-        (row * self.width + col) as usize
-    }
-
-    fn live_neighbor_count(&self, row :u32, col :u32) -> u8 {
-        let mut count = 0;
-
-        for delta_row in [self.height - 1, 0, 1].iter().cloned() {
-            for delta_col in [self.width - 1, 0, 1].iter().cloned() {
-                if delta_row == 0 && delta_col == 0 {
-                    continue;
-                }
-
-                let neighbor_row = (row + delta_row) % self.height;
-                let neighbor_col = (col + delta_col) % self.width;
-                let idx = self.get_index(neighbor_row, neighbor_col);
-                count += self.cells[idx] as u8;
-            }
-        }
-
-        count
-    }
-}
-
-impl Display for Universe {
-    fn fmt(&self, f :&mut Formatter) -> Result {
-        for line in self.cells.as_slice().chunks(self.width as usize) {
-            for &cell in line {
-                let symbol = match cell {
-                    Cell::Dead  => ' ',
-                    Cell::Alive => '*',
-                };
-                write!(f, "{}", symbol)?;
-            }
-            write!(f, "\n")?;
-        }
-
-        Ok(())
-    }
-}