Start implement 3d from fractional as html5 canvas

tutorial/wasm-game-of-life/Cargo.toml

@@ -12,6 +12,7 @@ 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

tutorial/wasm-game-of-life/src/easel.rs

@@ -0,0 +1,520 @@
+//
+// 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)
+    }
+}

tutorial/wasm-game-of-life/src/geometry.rs

@@ -0,0 +1,377 @@
+//
+// 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()
+    }
+}

tutorial/wasm-game-of-life/src/lib.rs

@@ -1,6 +1,24 @@
+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::ptr;
+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
@@ -9,6 +27,117 @@ use wasm_bindgen::prelude::*;
 #[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
+                  , 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
+                              , 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, 0); size) };
+
+        view3d.camera = Some(Camera::<f64>::new(&view3d, 45));
+        view3d
+    }
+
+    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(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!( (self.tetrahedron.transform(&rot1), 0xFFFF00)
+                          , (       self.cube.transform(&rot2), 0x0000FF) );
+
+        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(&mut 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);
+        unsafe {
+            let ptr  = self.image.as_mut_ptr();
+            ptr::write_bytes(ptr, 0, 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)]

tutorial/wasm-game-of-life/src/transform.rs

@@ -0,0 +1,186 @@
+//
+// 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 ) )
+    }
+}

tutorial/wasm-game-of-life/src/trigonometry.rs

@@ -0,0 +1,143 @@
+//
+// 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::ops::Div;
+use std::ops::Neg;
+use std::marker::Sized;
+use crate::Error;
+
+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)
+    }
+}
+
+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()
+    }
+}

tutorial/wasm-game-of-life/src/vector.rs

@@ -0,0 +1,139 @@
+//
+// 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
+    }
+}

tutorial/wasm-game-of-life/www/index.html

@@ -18,6 +18,7 @@
     </style>
   </head>
   <body>
+    <canvas id="view3d"></canvas>
     <canvas id="game-of-life-canvas"></canvas>
     <script src="./bootstrap.js"></script>
   </body>

tutorial/wasm-game-of-life/www/index.js

@@ -1,13 +1,28 @@
-import { Universe, Cell } from "wasm-game-of-life";
+import { Universe, Cell, View3d, Color } from "wasm-game-of-life";
 import { memory } from "wasm-game-of-life/wasm_game_of_life_bg";
 
+// 3D canvas stuff
+const view3d = View3d.new(151, 151);
+
+const view3d_canvas = document.getElementById("view3d");
+view3d_canvas.width = view3d.width();
+view3d_canvas.width = view3d.height();
+
+const view3d_ctx = view3d_canvas.getContext('2d');
+
+const view3d_renderLoop = () => {
+    view3d.update();
+    requestAnimationFrame(view3d_renderLoop);
+}
+
+// game of life stuff
 const CELL_SIZE   = 5; // px
 const GRID_COLOR  = "#CCCCCC";
 const DEAD_COLOR  = "#FFFFFF";
 const ALIVE_COLOR = "#000000";
 
 const universe = Universe.new();
-const    width = universe.height();
+const    width = universe.width();
 const   height = universe.height();
 
 const canvas  = document.getElementById("game-of-life-canvas");
@@ -74,6 +89,8 @@ const drawCells = () => {
     ctx.stroke();
 };
 
+// start everything ...
 drawGrid();
 drawCells();
 requestAnimationFrame(renderLoop);
+requestAnimationFrame(view3d_renderLoop);