188 lines
6.8 KiB
Rust
188 lines
6.8 KiB
Rust
use glam::{bool, f32, Mat2, Vec2, vec2};
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use coords::{FlatCoordinateSystem, InnerCS, OuterCS};
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use metric::Tube;
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use Subspace::{Boundary, Inner, Outer};
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use crate::riemann;
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use crate::tube::coords::FlatRegion;
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use crate::types::{FlatTraceResult, Hit, Location, Object, Ray};
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pub mod metric;
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mod coords;
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pub struct Space {
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pub tube: Tube,
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pub objs: Vec<Object>,
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}
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#[derive(PartialEq, Eq, Debug)]
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pub enum Subspace {
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Outer,
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Boundary,
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Inner,
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}
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impl Space {
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pub fn which_subspace(&self, pt: Vec2) -> Subspace {
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if pt.y.abs() > self.tube.external_halflength {
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Outer
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} else if pt.x.abs() > self.tube.outer_radius {
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Outer
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} else if pt.x.abs() > self.tube.inner_radius {
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Boundary
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} else {
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Inner
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}
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}
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/// Выполняет один шаг трассировки. Работает в любой части пространства, но вне Boundary доступны более эффективные методы.
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/// ray задаётся в основной СК.
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pub fn trace_step(&self, ray: Ray) -> Ray {
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let a: Vec2 = -riemann::contract2(riemann::krist(&self.tube, ray.pos), ray.dir);
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let v = ray.dir + a;
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let p = ray.pos + v;
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Ray { pos: p, dir: v }
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}
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/// Выполняет один шаг перемещения. Работает в любой части пространства.
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/// off задаётся в локальной СК. Рекомендуется считать небольшими шагами.
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pub fn move_step(&self, loc: Location, off: Vec2) -> Location {
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let corr = Mat2::IDENTITY - riemann::contract(riemann::krist(&self.tube, loc.pos), loc.rot * off);
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let p = loc.pos + corr * loc.rot * off;
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Location { pos: p, rot: corr * loc.rot }
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}
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pub fn trace_iter(&self, ray: Ray) -> impl Iterator<Item=Ray> + '_ {
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std::iter::successors(Some(ray), |&ray| Some(self.trace_step(ray)))
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}
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pub fn trace_inner(&self, ray: Ray) -> FlatTraceResult {
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assert_eq!(self.which_subspace(ray.pos), Inner);
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self.trace_flat(InnerCS(self.tube), ray)
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}
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pub fn trace_outer(&self, ray: Ray) -> FlatTraceResult {
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assert_eq!(self.which_subspace(ray.pos), Outer);
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self.trace_flat(OuterCS(self.tube), ray)
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}
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fn trace_flat(&self, cs: impl FlatRegion, ray: Ray) -> FlatTraceResult {
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let ray = cs.global_to_flat(ray);
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let dist = cs.distance_to_boundary(ray);
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let objs = self.list_objects(|loc| cs.global_to_flat(loc));
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FlatTraceResult {
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end: dist.map(|dist| cs.flat_to_global(ray.forward(dist))),
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objects: Self::hit_objects(objs.as_slice(), ray, dist, |pos| cs.flat_to_global(pos)),
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}
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}
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fn trace_boundary(&self, ray: Ray) -> Ray {
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assert_eq!(self.which_subspace(ray.pos), Boundary);
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self.trace_iter(ray)
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.find(|&ray| self.which_subspace(ray.pos) != Boundary)
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.expect("Can't get outta the wall!")
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}
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fn list_objects(&self, tfm: impl Fn(Location) -> Location) -> Vec<Object> {
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self.objs.iter().map(|&Object { id, loc, r }| Object { id, loc: tfm(loc), r }).collect()
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}
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fn hit_objects(objs: &[Object], ray: Ray, limit: Option<f32>, globalize: impl Fn(Vec2) -> Vec2) -> Vec<Hit> {
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let limit = limit.unwrap_or(f32::INFINITY);
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objs.iter()
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.filter_map(|obj| {
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let rel = ray.pos - obj.loc.pos;
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let diff = rel.dot(ray.dir).powi(2) - ray.dir.length_squared() * (rel.length_squared() - obj.r.powi(2));
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if diff > 0.0 {
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let t = (-rel.dot(ray.dir) - diff.sqrt()) / ray.dir.length_squared();
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Some((obj, t))
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} else {
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None
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}
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})
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.filter(|&(_, t)| t >= 0.0 && t < limit)
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.map(|(obj, t)| {
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let pos = ray.forward(t).pos;
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let rel = obj.loc.rot.inverse() * Ray { pos: pos - obj.loc.pos, dir: ray.dir };
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Hit { id: obj.id, distance: t, pos: globalize(pos), rel }
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})
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.collect()
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}
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pub fn line(&self, a: Vec2, b: Vec2, step: f32) -> Vec<Vec2> {
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match self.which_subspace(a) {
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Outer => vec![b],
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Inner => {
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let cs = InnerCS(self.tube);
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let n = ((b - a).length() / step) as usize + 1;
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let a = cs.global_to_flat(a);
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let b = cs.global_to_flat(b);
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(1..=n).map(|k| cs.flat_to_global(a.lerp(b, k as f32 / n as f32))).collect()
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}
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Boundary => panic!("Can't draw a line here!"),
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}
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}
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}
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struct Rect {
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pub size: Vec2,
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}
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impl Rect {
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/// Отражает луч, чтобы все координаты направления были положительны (допустимо благодаря симметрии Rect).
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fn flip_ray(ray: Ray) -> Ray {
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Ray { pos: ray.pos * ray.dir.signum(), dir: ray.dir.abs() }
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}
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fn is_inside(&self, pt: Vec2) -> bool {
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pt.abs().cmplt(self.size).all()
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}
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fn trace_into(&self, ray: Ray) -> Option<f32> {
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let ray = Self::flip_ray(ray);
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// ray.pos.x + t * ray.dir.x = −size.x
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let ts = (-self.size - ray.pos) / ray.dir;
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let t = ts.max_element();
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let pt = ray.pos + t * ray.dir;
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if t < 0.0 { return None; }
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if pt.cmpgt(self.size).any() { return None; }
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Some(t)
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}
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fn trace_out_of(&self, ray: Ray) -> Option<f32> {
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let ray = Self::flip_ray(ray);
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// ray.pos.x + t * ray.dir.x = +size.x
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let ts = (self.size - ray.pos) / ray.dir;
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let t = ts.min_element();
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Some(t)
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}
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}
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#[test]
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fn test_rect() {
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assert_eq!(Rect::flip_ray(Ray { pos: vec2(2.0, 3.0), dir: vec2(4.0, 5.0) }), Ray { pos: vec2(2.0, 3.0), dir: vec2(4.0, 5.0) });
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assert_eq!(Rect::flip_ray(Ray { pos: vec2(2.0, 3.0), dir: vec2(-4.0, 5.0) }), Ray { pos: vec2(-2.0, 3.0), dir: vec2(4.0, 5.0) });
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assert_eq!(Rect::flip_ray(Ray { pos: vec2(2.0, 3.0), dir: vec2(4.0, -5.0) }), Ray { pos: vec2(2.0, -3.0), dir: vec2(4.0, 5.0) });
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assert_eq!(Rect::flip_ray(Ray { pos: vec2(2.0, 3.0), dir: vec2(4.0, 0.0) }), Ray { pos: vec2(2.0, 3.0), dir: vec2(4.0, 0.0) });
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let r = Rect { size: vec2(2.0, 3.0) };
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assert_eq!(r.trace_into(Ray { pos: vec2(3.0, 3.0), dir: vec2(1.0, 1.0) }), None);
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assert_eq!(r.trace_into(Ray { pos: vec2(-3.0, 2.0), dir: vec2(1.0, 0.0) }), Some(1.0));
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assert_eq!(r.trace_into(Ray { pos: vec2(-3.0, 2.0), dir: vec2(-1.0, 0.0) }), None);
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assert_eq!(r.trace_into(Ray { pos: vec2(-3.0, 1.0), dir: vec2(2.0, 2.0) }), Some(0.5));
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assert_eq!(r.trace_into(Ray { pos: vec2(-3.0, 2.1), dir: vec2(2.0, 2.0) }), None);
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assert_eq!(r.trace_into(Ray { pos: vec2(2.0, 3.0), dir: vec2(1.0, 1.0) }), None);
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assert_eq!(r.trace_into(Ray { pos: vec2(-2.0, 3.0), dir: vec2(-1.0, 1.0) }), None);
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assert_eq!(r.trace_into(Ray { pos: vec2(2.0, 3.0), dir: vec2(-1.0, -1.0) }), Some(0.0));
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assert_eq!(r.trace_into(Ray { pos: vec2(2.0, -3.0), dir: vec2(-1.0, 1.0) }), Some(0.0));
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assert_eq!(r.trace_out_of(Ray { pos: vec2(0.0, 0.0), dir: vec2(1.0, 1.0) }), Some(2.0));
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assert_eq!(r.trace_out_of(Ray { pos: vec2(0.0, 0.0), dir: vec2(0.0, 1.0) }), Some(3.0));
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assert_eq!(r.trace_out_of(Ray { pos: vec2(0.0, 1.0), dir: vec2(0.0, -1.0) }), Some(4.0));
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assert_eq!(r.trace_out_of(Ray { pos: vec2(1.0, 1.0), dir: vec2(0.0, -1.0) }), Some(4.0));
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assert_eq!(r.trace_out_of(Ray { pos: vec2(2.0, 3.0), dir: vec2(1.0, 1.0) }), Some(0.0));
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}
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