Add Drawable primitives

+//
+// This is an abstraction over a drawing environment.
+//
+// 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, Display, Result};
+
+pub trait Easel {
+    fn canvas(self) -> dyn Canvas;
+}
+
+pub trait Canvas {
+    fn draw(self, c :&dyn Drawable, ofs :Coordinate);
+}
+
+pub trait Drawable {
+    fn plot(&self) -> Coordinates;
+}
+
+#[derive(Debug, Clone, Copy)]
+pub struct Coordinate(pub i32, pub i32);
+
+#[derive(Debug, Clone)]
+pub struct Coordinates(pub Vec<Coordinate>);
+
+impl Coordinate {
+    // Tail recursive Bresenham line with integer incremental error.
+    fn line(self, b :&Self) -> Vec<Self> {
+        fn inner( v :&mut [Coordinate]
+                  , bx :i32, by :i32
+                  , dx :i32, dy :i32
+                  , sx :i32, sy :i32
+                  , err :i32) {
+            let Coordinate(x, y) = v[0];
+
+            if x != bx || y != by {
+                let doinc = (2*err >= dy, 2*err <= dx);
+                let (x, y, err) = match doinc {
+                    (true, false) => (x + sx,      y, err + dy),
+                    (false, true) => (     x, y + sy, err + dx),
+                    _             => (x + sx, y + sy, err + dx + dy ),
+                };
+                v[1] = Coordinate(x, y);
+                inner(&mut v[1..], bx, by, dx, dy, sx, sy, err);
+            }
+        }
+
+        let Coordinate(ax, ay) = self;
+        let Coordinate(bx, by) = *b;
+
+        let dx      = (bx - ax).abs();
+        let sx :i32 = if ax < bx { 1 } else { -1 };
+        let dy      = -(by - ay).abs();
+        let sy :i32 = if ay < by { 1 } else { -1 };
+
+        let mut v :Vec<Self> = vec!( Coordinate(0, 0)
+                                   ; cmp::max(dx, -dy) as usize + 1);
+        v[0] = Coordinate(ax, ay);
+        inner(&mut v, bx, by, dx, dy, sx, sy, dx + dy);
+        v
+    }
+}
+
+impl Display for Coordinate {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        write!(f, "<{},{}>", self.0, self.1)
+    }
+}
+
+impl Display for Coordinates {
+    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(pub Coordinate);
+
+impl Drawable for Point{
+    fn plot(&self) -> Coordinates {
+        let Point(c) = *self;
+        Coordinates(vec!(c))
+    }
+}
+
+impl Display for Point {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        let Point(p) = self;
+        write!(f, "Point[{}]", p)
+    }
+}
+
+#[derive(Debug, Clone, Copy)]
+pub struct Line(pub Coordinate, pub Coordinate);
+
+impl Drawable for Line {
+    fn plot(&self) -> Coordinates {
+        let Line(a, b) = *self;
+        Coordinates(a.line(&b))
+    }
+}
+
+impl Display for Line {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        let Line(a, b) = self;
+        write!(f, "Line[{},{}]", a, b)
+    }
+}
+
+#[derive(Debug, Clone, Copy)]
+pub struct Rectangle(pub Coordinate, pub Coordinate);
+
+impl Drawable for Rectangle {
+    fn plot(&self) -> Coordinates {
+        let Rectangle(a, c)    = *self;
+        let Coordinate(ax, ay) = a;
+        let Coordinate(cx, cy) = c;
+        let b = Coordinate(cx, ay);
+        let d = Coordinate(ax, cy);
+
+        let mut r = a.line(&b);
+        r.append(&mut b.line(&c)[1..].to_vec());
+        r.append(&mut c.line(&d)[1..].to_vec());
+        let mut i = d.line(&a);
+        let     l = i.len();
+        r.append(&mut i[1..l-1].to_vec());
+
+        Coordinates(r)
+    }
+}
+
+impl Display for Rectangle {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        let Rectangle(a, b) = self;
+        write!(f, "Rec[{},{}]", a, b)
+    }
+}
+
+#[derive(Debug, Clone)]
+pub struct Polyline(pub Coordinates);
+
+impl Drawable for Polyline {
+    fn plot(&self) -> Coordinates {
+        let Polyline(Coordinates(cs)) = self;
+
+        match cs[..] {
+            []     => Coordinates(Vec::<Coordinate>::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 Display for Polyline {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        let Polyline(a) = self;
+        write!(f, "PLine[{}]", a)
+    }
+}
+
+#[derive(Debug, Clone)]
+pub struct Polygon(pub Coordinates);
+
+impl Drawable for Polygon {
+    fn plot(&self) -> Coordinates {
+        let Polygon(Coordinates(cs)) = self;
+
+        match cs[..] {
+            []     => Coordinates(Vec::<Coordinate>::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 = i.line(&a);
+                let     l = j.len();
+                r.append(&mut j[1..l-1].to_vec());
+                Coordinates(r)
+            },
+        }
+    }
+}
+
+impl Display for Polygon {
+    fn fmt(&self, f: &mut Formatter<'_>) -> Result {
+        let Polygon(a) = self;
+        write!(f, "Poly[{}]", a)
+    }
+}

@@ -23,6 +23,7 @@ extern crate lazy_static;
 pub type Error = &'static str;
 
 pub mod continuous;
+pub mod easel;
 pub mod fractional;
 pub mod transform;
 pub mod trigonometry;

@@ -18,7 +18,6 @@
 // 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::convert::{TryFrom, TryInto, Into};
 use std::f64::consts::PI as FPI;
 use std::fmt::Display;
@@ -26,47 +25,13 @@ use std::num::TryFromIntError;
 use std::ops::{Add,Sub,Neg,Mul,Div};
 
 use fractional::continuous::Continuous;
+use fractional::easel::{ Coordinate, Coordinates, Drawable, Line, Polyline
+                       , Polygon, Rectangle};
 use fractional::fractional::{Fractional, from_vector};
 use fractional::trigonometry::Trig;
 use fractional::vector::{Vector};
 use fractional::transform::{TMatrix, translate, rotate_x, rotate_y, rotate_z, rotate_v};
 
-// Tail recursive Bresenham line with integer incremental error.
-fn line(a :(u32, u32), b :(u32, u32)) -> Vec<(u32, u32)>{
-    fn inner( v :&mut [(u32, u32)]
-            , bx :u32, by :u32
-            , dx :i32, dy :i32
-            , sx :i32, sy :i32
-            , err :i32) {
-        let (x, y) = v[0];
-
-        if x != bx || y != by {
-            let (x, y, err) = match (2*err as i32 >= dy, 2*err as i32 <= dx) {
-                (true, false) => ((x as i32 + sx) as u32, y, err + dy),
-                (false, true) => (x, (y as i32 + sy) as u32, err + dx),
-                _             => ( (x as i32 + sx) as u32
-                                 , (y as i32 + sy) as u32
-                                 , err + dx + dy ),
-            };
-            v[1] = (x, y);
-            inner(&mut v[1..], bx, by, dx, dy, sx, sy, err);
-        }
-    }
-
-    let (ax, ay) = a;
-    let (bx, by) = b;
-
-    let dx      = (bx as i32 - ax as i32).abs();
-    let sx :i32 = if ax < bx { 1 } else { -1 };
-    let dy      = -(by as i32 - ay as i32).abs();
-    let sy :i32 = if ay < by { 1 } else { -1 };
-
-    let mut v :Vec<(u32, u32)> = vec!((0, 0); cmp::max(dx, -dy) as usize + 1);
-    v[0] = (ax, ay);
-    inner(&mut v, bx, by, dx, dy, sx, sy, dx + dy);
-    v
-}
-
 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())?;
@@ -268,14 +233,31 @@ fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :Vector<T>)
 }
 
 fn _line() {
-    println!("{:>14} : {:?}", "Line", line((0,1), (6,4)));
-    println!("{:>14} : {:?}", "Line", line((0,4), (6,1)));
-    println!("{:>14} : {:?}", "Line", line((6,1), (0,4)));
-    println!("{:>14} : {:?}", "Line", line((6,4), (0,1)));
-    println!("{:>14} : {:?}", "Line", line((0,1), (6,8)));
-    println!("{:>14} : {:?}", "Line", line((0,8), (6,1)));
-    println!("{:>14} : {:?}", "Line", line((6,1), (0,8)));
-    println!("{:>14} : {:?}", "Line", line((6,8), (0,1)));
+    let a = (Coordinate(0, 1), Coordinate(6, 4));
+    let b = (Coordinate(0, 4), Coordinate(6, 1));
+    let c = (Coordinate(1, 0), Coordinate(6, 8));
+    let d = (Coordinate(1, 8), Coordinate(6, 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 r = Rectangle(Coordinate(1, 1), Coordinate(10, 5));
+    println!("{:>14} : {}", r, r.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, -20)
+                        , Coordinate( 20,  20)
+                        , Coordinate(-20,  20) )));
+    println!("{:>14} : {}", pg, pg.plot());
 }
 
 fn main() {