4 changed files with 188 additions and 121 deletions
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150fractional/src/geometry.rs
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1fractional/src/lib.rs
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132fractional/src/main.rs
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26fractional/src/trigonometry.rs
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//
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// Basic geometric things...
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//
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// Georg Hopp <georg@steffers.org>
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//
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// Copyright © 2019 Georg Hopp
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//
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// This program is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// This program is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <http://www.gnu.org/licenses/>.
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//
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use std::convert::From;
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use std::ops::{Add,Sub,Neg,Mul,Div};
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use std::fmt::Debug;
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use crate::easel::{Canvas,Coordinate,Coordinates,Polygon};
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use crate::transform::TMatrix;
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use crate::trigonometry::Trig;
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use crate::vector::Vector;
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#[derive(Debug)]
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pub struct Polyeder<T>
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where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
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points :Vec<Vector<T>>,
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faces :Vec<Vec<usize>>,
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}
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pub trait Primitives<T>
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where T: Add + Sub + Neg + Mul + Div + Copy + Trig + From<i32> {
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fn transform(&self, m :&TMatrix<T>) -> Self;
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fn project(&self, camera :&Camera<T>) -> Vec<Polygon>;
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}
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pub struct Camera<T>
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where T: Add + Sub + Neg + Mul + Div + Copy + Trig {
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width :T,
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height :T,
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fovx :T,
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fovy :T,
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}
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impl<T> Camera<T>
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where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
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+ Mul<Output = T> + Div<Output = T>
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+ Copy + Trig + From<i32> {
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pub fn new(c :&dyn Canvas, angle :i32) -> Self {
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let width = <T as From<i32>>::from(c.width() as i32);
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let height = <T as From<i32>>::from(c.height() as i32);
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// The calculations for fovx and fovy are taken from a book, but I
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// have the impression, coming from my limited algebra knowledge,
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// that they are always equal…
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Camera { width: width
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, height: height
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, fovx: T::cot(angle) * width
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, fovy: width / height * T::cot(angle) * height }
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}
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pub fn project(&self, v :Vector<T>) -> Coordinate {
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let f2 = From::<i32>::from(2);
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let xs = v.x() / v.z() * self.fovx + self.width / f2;
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let ys = v.y() / v.z() * self.fovy + self.height / f2;
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Coordinate(T::round(&xs), T::round(&ys))
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}
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}
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impl<T> Polyeder<T>
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where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
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+ Mul<Output = T> + Div<Output = T>
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+ Copy + Trig + From<i32> {
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// https://rechneronline.de/pi/tetrahedron.php
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pub fn tetrahedron(a :T) -> Polyeder<T> {
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let f0 :T = From::<i32>::from(0);
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let f3 :T = From::<i32>::from(3);
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let f4 :T = From::<i32>::from(4);
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let f6 :T = From::<i32>::from(6);
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let f12 :T = From::<i32>::from(12);
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let yi :T = a / f12 * T::sqrt(f6).unwrap();
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let yc :T = a / f4 * T::sqrt(f6).unwrap();
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let zi :T = T::sqrt(f3).unwrap() / f6 * a;
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let zc :T = T::sqrt(f3).unwrap() / f3 * a;
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let ah :T = a / From::<i32>::from(2);
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// half the height in y
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let _yh :T = a / f6 * T::sqrt(f6).unwrap();
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// half the deeps in z
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let _zh :T = T::sqrt(f3).unwrap() / f4 * a;
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Polyeder{ points: vec!( Vector( f0, yc, f0)
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, Vector(-ah, -yi, -zi)
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, Vector( ah, -yi, -zi)
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, Vector( f0, -yi, zc) )
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, faces: vec!( vec!(1, 2, 3)
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, vec!(1, 0, 2)
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, vec!(3, 0, 1)
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, vec!(2, 0, 3) )}
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}
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pub fn cube(a :T) -> Polyeder<T> {
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let ah :T = a / From::<i32>::from(2);
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Polyeder{ points: vec!( Vector(-ah, ah, -ah) // 0 => front 1
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, Vector(-ah, -ah, -ah) // 1 => front 2
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, Vector( ah, -ah, -ah) // 2 => front 3
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, Vector( ah, ah, -ah) // 3 => front 4
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, Vector(-ah, ah, ah) // 4 => back 1
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, Vector(-ah, -ah, ah) // 5 => back 2
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, Vector( ah, -ah, ah) // 6 => back 3
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, Vector( ah, ah, ah) ) // 7 => back 4
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, faces: vec!( vec!(0, 1, 2, 3) // front
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, vec!(7, 6, 5, 4) // back
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, vec!(1, 5, 6, 2) // top
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, vec!(0, 3, 7, 4) // bottom
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, vec!(0, 4, 5, 1) // left
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, vec!(2, 6, 7, 3) )} // right
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}
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}
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impl<T> Primitives<T> for Polyeder<T>
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where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
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+ Mul<Output = T> + Div<Output = T>
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+ Copy + Trig + From<i32> + From<i32> {
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fn transform(&self, m :&TMatrix<T>) -> Self {
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Polyeder{ points: self.points.iter().map(|p| m.apply(p)).collect()
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, faces: self.faces.to_vec() }
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}
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fn project(&self, camera :&Camera<T>) -> Vec<Polygon> {
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fn polygon<I>(c :I) -> Polygon
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where I: Iterator<Item = Coordinate> {
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Polygon(Coordinates(c.collect()))
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}
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let to_coord = |p :&usize| camera.project(self.points[*p]);
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let to_poly = |f :&Vec<usize>| polygon(f.iter().map(to_coord));
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self.faces.iter().map(to_poly).collect()
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}
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}
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