user projection matrix

@@ -29,68 +29,76 @@ use crate::vector::Vector;
 
 #[derive(Debug)]
 pub struct Polyeder<T>
-where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
+where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig {
     points :Vec<Vector<T>>,
     faces  :Vec<Vec<usize>>,
 }
 
 pub trait Primitives<T>
-where T: Add + Sub + Neg + Mul + Div + Copy + Trig + From<i32> {
+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>) -> Vec<Polygon>;
 }
 
 pub struct Camera<T>
-where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
-    width  :T,
-    height :T,
-    fovx   :T,
-    fovy   :T,
+where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
+    width   :T,
+    height  :T,
+    project :TMatrix<T>,
 }
 
 impl<T> Camera<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
        + Mul<Output = T> + Div<Output = T>
-       + Copy + Trig + From<i32> {
+       + 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, angle :i32) -> Self {
-        let  width = <T as From<i32>>::from(c.width() as i32);
-        let height = <T as From<i32>>::from(c.height() as i32);
-
-        // The calculations for fovx and fovy are taken from a book, but I
-        // have the impression, coming from my limited algebra knowledge,
-        // that they are always equal…
-        Camera { width:  width
-               , height: height
-               , fovx:   T::cot(angle) * width
-               , fovy:   width / height * T::cot(angle) * height }
+        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
+               , 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 project(&self, v :Vector<T>) -> Coordinate {
-        let f2 = From::<i32>::from(2);
-        let xs = v.x() / v.z() * self.fovx + self.width  / f2;
-        let ys = v.y() / v.z() * self.fovy + self.height / f2;
+    pub fn get_projection(&self) -> TMatrix<T> {
+        self.project
+    }
 
-        Coordinate(T::round(&xs), T::round(&ys))
+    pub fn project(&self, v :Vector<T>) -> Coordinate {
+        let p = self.project.apply(&v);
+        Coordinate(T::round(&p.x()), T::round(&p.y()))
     }
 }
 
 impl<T> Polyeder<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
        + Mul<Output = T> + Div<Output = T>
-       + Copy + Trig + From<i32> {
+       + Debug + Copy + Trig + From<i32> {
     // https://rechneronline.de/pi/tetrahedron.php
     pub fn tetrahedron(a :T) -> Polyeder<T> {
-        let  f0 :T = From::<i32>::from(0);
-        let  f3 :T = From::<i32>::from(3);
-        let  f4 :T = From::<i32>::from(4);
-        let  f6 :T = From::<i32>::from(6);
-        let f12 :T = From::<i32>::from(12);
+        let  f0 :T = 0.into();
+        let  f3 :T = 3.into();
+        let  f4 :T = 4.into();
+        let  f6 :T = 6.into();
+        let f12 :T = 12.into();
 
         let yi :T = a / f12 * T::sqrt(f6).unwrap();
         let yc :T = a /  f4 * T::sqrt(f6).unwrap();
         let zi :T = T::sqrt(f3).unwrap() / f6 * a;
         let zc :T = T::sqrt(f3).unwrap() / f3 * a;
-        let ah :T = a / From::<i32>::from(2);
+        let ah :T = a / 2.into();
 
         // half the height in y
         let _yh :T = a /  f6 * T::sqrt(f6).unwrap();
@@ -130,19 +138,27 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
 impl<T> Primitives<T> for Polyeder<T>
 where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
        + Mul<Output = T> + Div<Output = T>
-       + Copy + Trig + From<i32> + From<i32> {
+       + Debug + Copy + Trig + From<i32> + From<i32> {
     fn transform(&self, m :&TMatrix<T>) -> Self {
         Polyeder{ points: self.points.iter().map(|p| m.apply(p)).collect()
                 , faces:  self.faces.to_vec() }
     }
 
-    fn project(&self, camera :&Camera<T>) -> Vec<Polygon> {
+    // TODO for now we assume already prejected vertices (points)
+    // in future we need to distinguish more clear between vertex and point
+    // and projected_point.
+    fn project(&self, _camera :&Camera<T>) -> Vec<Polygon> {
         fn polygon<I>(c :I) -> Polygon
         where I: Iterator<Item = Coordinate> {
             Polygon(Coordinates(c.collect()))
         }
 
-        let to_coord = |p :&usize| camera.project(self.points[*p]);
+        // 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| _camera.project(self.points[*p]);
+        let to_coord = |p :&usize| {
+            let v = self.points[*p];
+            Coordinate(v.x().round(), v.y().round()) };
         let to_poly  = |f :&Vec<usize>| polygon(f.iter().map(to_coord));
 
         self.faces.iter().map(to_poly).collect()

@@ -20,7 +20,7 @@
 //
 use std::convert::{TryFrom, TryInto, Into};
 use std::f64::consts::PI as FPI;
-use std::fmt::Display;
+use std::fmt::{Debug, Display};
 use std::marker::Send;
 use std::num::TryFromIntError;
 use std::ops::{Add,Sub,Neg,Mul,Div};
@@ -201,7 +201,7 @@ fn _transform2() {
 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
-           + From<i32> + Copy + Display {
+           + Debug + From<i32> + Copy + Display {
 
     println!("{:>14} : {}", "Vector v1", v1);
     println!("{:>14} : {}", "translate v1", translate(v).apply(&v1));
@@ -211,7 +211,7 @@ fn _transform<T>(v :Vector<T>, v1 :Vector<T>, v2 :Vector<T>, v3 :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
-               + From<i32> + Copy + Display {
+               + Debug + From<i32> + Copy + Display {
 
         for d in [ 30, 45, 60, 90, 120, 135, 150, 180
                  , 210, 225, 240, 270, 300, 315, 330 ].iter() {
@@ -317,7 +317,7 @@ fn _democanvas<T>( xcb         :&XcbEasel
                  , cube        :Polyeder<T> )
     where T: 'static + Add<Output = T> + Sub<Output = T> + Neg<Output = T>
            + Mul<Output = T> + Div<Output = T>
-           + Copy + Trig + Send + From<i32> {
+           + Debug + Copy + Trig + Send + From<i32> {
 
     let mut canvas = xcb.canvas(151, 151).unwrap();
     let camera = Camera::<T>::new(&canvas, 45); // the orig. view angle
@@ -333,14 +333,15 @@ fn _democanvas<T>( xcb         :&XcbEasel
         let mut last  = Instant::now();
 
         let t :TMatrix<T> = translate(Vector(0.into(), 0.into(), 150.into()));
+        let p :TMatrix<T> = camera.get_projection();
 
         loop {
             let deg = ((start.elapsed() / 25).as_millis() % 360) as i32;
 
             let  rz :TMatrix<T> = rotate_z(deg);
 
-            let rot1 = TMatrix::combine(vec!(rz, rotate_x(-deg*2), t));
-            let rot2 = TMatrix::combine(vec!(rz, rotate_y(-deg*2), t));
+            let rot1 = TMatrix::combine(vec!(rz, rotate_x(-deg*2), t, p));
+            let rot2 = TMatrix::combine(vec!(rz, rotate_y(-deg*2), t, p));
 
             let objects = vec!( (tetrahedron.transform(&rot1), 0xFFFF00)
                               , (       cube.transform(&rot2), 0x0000FF) );