easel3d/fractional/src/geometry.rs

//
// 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;
use std::ops::{Add,Sub,Neg,Mul,Div};
use std::fmt::Debug;

use crate::easel::{Canvas,Coordinate,Coordinates,Polygon};
use crate::transform::TMatrix;
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)]
pub struct Polyeder<T>
where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
    points :Vec<Vector<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, u32)>;
}

pub struct Camera<T>
where T: Add + Sub + Neg + Mul + Div + Debug + Copy + Trig + From<i32> {
    width   :T,
    height  :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>
       + 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 = (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 get_projection(&self) -> TMatrix<T> {
        self.project
    }

    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> 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>
       + Debug + Copy + Trig + From<i32> {
    fn new(corners :Vec<usize>, ps :&[Vector<T>]) -> Self {
        let mut f = Face{ corners: corners, normal: None };
        f.update_normal(ps);
        f
    }

    fn update_normal(&mut self, ps :&[Vector<T>]) {
        let edge10 = ps[self.corners[1]] - ps[self.corners[0]];
        let edge12 = ps[self.corners[1]] - ps[self.corners[2]];
        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>
       + Debug + Copy + Trig + From<i32> {
    fn update_normals(&mut self) {
        for f in self.faces.iter_mut() {
            f.update_normal(&self.points);
        }
    }

    // https://rechneronline.de/pi/tetrahedron.php
    pub fn tetrahedron(a :T) -> Polyeder<T> {
        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 / 2.into();

        // half the height in y
        let _yh :T = a /  f6 * T::sqrt(f6).unwrap();
        // half the deeps in z
        let _zh :T = T::sqrt(f3).unwrap() / f4 * a;

        let ps = vec!( Vector( f0,  yc,  f0)
                     , Vector(-ah, -yi, -zi)
                     , Vector( ah, -yi, -zi)
                     , Vector( f0, -yi,  zc) );

        let fs = vec!( Face::new(vec!(1, 2, 3), &ps)
                     , Face::new(vec!(1, 0, 2), &ps)
                     , Face::new(vec!(3, 0, 1), &ps)
                     , Face::new(vec!(2, 0, 3), &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!( Vector(-ah, f0, -zi)
                     , Vector( f0, f0,  zc)
                     , Vector( ah, f0, -zi) );

        let fs = vec!(Face::new(vec!(0, 1, 2), &ps));

        println!("== {:?}", fs);

        Polyeder{ points: ps, faces: fs }
    }

    pub fn cube(a :T) -> Polyeder<T> {
        let ah :T = a / From::<i32>::from(2);

        let ps = vec!( Vector(-ah,  ah, -ah)    // 0 => front 1
                     , Vector(-ah, -ah, -ah)    // 1 => front 2
                     , Vector( ah, -ah, -ah)    // 2 => front 3
                     , Vector( ah,  ah, -ah)    // 3 => front 4
                     , Vector(-ah,  ah,  ah)    // 4 => back 1
                     , Vector(-ah, -ah,  ah)    // 5 => back 2
                     , Vector( ah, -ah,  ah)    // 6 => back 3
                     , Vector( 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 {
    fn transform(&self, m :&TMatrix<T>) -> Self {
        let Polyeder{ points: ps, faces: fs } = self;

        let mut p = Polyeder{ points: ps.iter().map(|p| m.apply(p)).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
    }

    // 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>
              , light :&DirectLight<T>
              , color :u32 ) -> Vec<(Polygon, u32)> {
        // Helper to create a Polygon from Coordinates…
        // TODO probably there needs to be a Polygon constructor for this.
        fn polygon<I>(c :I) -> Polygon
        where I: Iterator<Item = Coordinate> {
            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| camera.project(self.points[*p]);
        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()),
                       };

                       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
                       }};

        let mut ps :Vec<(Polygon, u32)> = self.faces.iter().filter_map(to_poly).collect();
        ps.sort_by(|a, b| a.1.cmp(&b.1));
        ps
    }
}