2021-32-bit-holiday-jam/src/physics.rs

use glam::{Vec2, Vec3};
use partial_min_max::{min, max};

pub struct PhysicsBody {
	pos: Vec3,
	vel: Vec3,
}

pub struct PhysicsResult {
	body: PhysicsBody,
	triangles_hit: Vec <usize>,
	kill: bool,
}

pub struct Triangle {
	verts: [Vec3; 3],
}

pub trait MeshBuffer {
	fn num_triangles (&self) -> usize;
	fn get_triangle (&self, i: usize) -> Triangle;
}

fn vec_min (a: &Vec3, b: &Vec3) -> Vec3 {
	Vec3::from ((
		min (a.x (), b.x ()),
		min (a.y (), b.y ()),
		min (a.z (), b.z ())
	))
}

fn vec_max (a: &Vec3, b: &Vec3) -> Vec3 {
	Vec3::from ((
		max (a.x (), b.x ()),
		max (a.y (), b.y ()),
		max (a.z (), b.z ())
	))
}

impl Triangle {
	pub fn min (&self) -> Vec3 {
		self.verts [1..].iter ().fold (
			self.verts [0],
			|pre, v| vec_min (&pre, v)
		)
	}
	
	pub fn max (&self) -> Vec3 {
		self.verts [1..].iter ().fold (
			self.verts [0],
			|pre, v| vec_max (&pre, v)
		)
	}
}

#[derive (Clone)]
pub struct Collision {
	t: f32,
	p_impact: Vec3,
	normal: Vec3,
	i: usize,
}

impl Collision {
	pub fn take_if_closer (&self, o: &Self) -> Self {
		if o.t < self.t && o.t >= 0.0 {
			o.clone ()
		}
		else {
			self.clone ()
		}
	}
}

pub fn get_candidate <MB> (world: &MB, p0: Vec3, p1: Vec3)
-> Collision
where MB: MeshBuffer
{
	let radius = 0.0625f32;
	let radius3 = Vec3::from ((
		radius,
		radius,
		radius
	));
	let v = p1 - p0;
	
	let mut candidate = Collision {
		t: 2.0,
		p_impact: Default::default (),
		normal: Default::default (),
		i: 0,
	};
	
	for i in 0..world.num_triangles () {
		let tri = world.get_triangle (i);
		
		let tri_min = tri.min () - radius3;
		let tri_max = tri.max () + radius3;
		
		let ray_min = min (p0, p1);
		let ray_max = max (p0, p1);
		
		if 
			ray_max.x () < tri_min.x () || ray_min.x () > tri_max.x () ||
			ray_max.y () < tri_min.y () || ray_min.y () > tri_max.y () ||
			ray_max.z () < tri_min.z () || ray_min.z () > tri_max.z ()
		{
			// AABB reject
			continue;
		}
		
		// Collision for each triangle is roughly split into:
		// Face collisions
		// Edge collisions
		// Vertex collisions
		
		let normal = Vec3::cross (tri.verts [2] - tri.verts [1], tri.verts [1] - tri.verts [0]).normalize ();
		
		let speed_towards_face = -Vec3::dot (v, normal);
		
		// Face collisions
		
		if speed_towards_face >= 0.0 {
			let distance_to_face0 = Vec3::dot (normal, p0 - tri.verts [0]) - radius;
			let distance_to_face1 = Vec3::dot (normal, p1 - tri.verts [0]) - radius;
			
			let passed_plane = distance_to_face0 > 0.0 && distance_to_face1 < 0.0;
			
			if passed_plane {
				let t = distance_to_face0 / (distance_to_face0 - distance_to_face1);
				
				// Because of previous early returns we know that 0.0 < t < 1.0
				
				let p_impact = p0 * (1.0 - t) + p1 * (t);
				
				let impact_inside_tri = (|| {
					for j in 0..3 {
						let a = tri.verts [j];
						let b = tri.verts [(j + 1) % 3];
						let tangent = Vec3::cross (b - a, normal);
						
						if Vec3::dot (tangent, p_impact - a) < 0.0 {
							return false;
						}
					}
					true
				})();
				
				if impact_inside_tri {
					// Stop it
					
					let c = Collision {
						t,
						p_impact,
						normal,
						i,
					};
					
					candidate = candidate.take_if_closer (&c);
					
					// goto triangle_collided
				}
			}
		}
		
		// Edge collisions
		
		let ray_dir = (p1 - p0).normalize ();
		
		for j in 0..3 {
			let a = tri.verts [j];
			let b = tri.verts [(j + 1) % 3];
			
			let cylinder_axis = (b - a).normalize ();
			let third_axis = Vec3::cross (cylinder_axis, ray_dir).normalize ();
			let perp_ray_axis = Vec3::cross (third_axis, cylinder_axis);
			
			let into_triangle = Vec3::cross (cylinder_axis, normal);
			
			let a_minus_p0 = a - p0;
			
			let a_ray = Vec2::from ((
				Vec3::dot (a_minus_p0, perp_ray_axis),
				Vec3::dot (a_minus_p0, third_axis)
			));
			
			// a_ray is now in a space where X is the ray's t,
			// Z is the cylinder axis (and irrelevant for now),
			// and Y is the cross of those.
			
			// I forgot the maths word for this
			let discriminant = radius * radius - a_ray.y () * a_ray.y ();
			
			if discriminant < 0.0 {
				// No possible collision
				continue;
			}
			
			let t = (a_ray.x () - discriminant.sqrt ()) / (p1 - p0).length ();
			
			if t < 0.0 || t > 1.0 {
				// The cylinder is along the line,
				// but outside the line segment
				//triangles_hit.push_back (i);
				continue;
			}
			
			let p_impact = p0 * (1.0 - t) + p1 * (t);
			
			let impact_along_cylinder = Vec3::dot (cylinder_axis, p_impact);
			let a_along_cylinder = Vec3::dot (cylinder_axis, a);
			
			if impact_along_cylinder < a_along_cylinder || impact_along_cylinder > Vec3::dot (cylinder_axis, b)
			{
				// The infinite cylinder is on the line segment,
				// but the finite cylinder is not.
				//cout << "Finite cylinder reject" << endl;
				continue;
			}
			
			let edge_normal = (p_impact - (a + (impact_along_cylinder - a_along_cylinder) * cylinder_axis)).normalize ();
			
			let speed_towards_edge = -Vec3::dot (v, edge_normal);
			let speed_into_triangle = Vec3::dot (v, into_triangle);
			
			if speed_towards_edge > 0.0 && speed_into_triangle >= 0.0 {
				let c = Collision {
					t,
					p_impact,
					normal: edge_normal,
					i,
				};
				
				candidate = candidate.take_if_closer (&c);
			}
		}
		
		// Vertex collisions
		
		for j in 0..3 {
			let a = tri.verts [j];
			let a_minus_p0 = a - p0;
			
			let a_ray_x = Vec3::dot (a_minus_p0, ray_dir);
			let nearest_on_ray = p0 + a_ray_x * ray_dir;
			let a_ray_y = (a - nearest_on_ray).length ();
			
			let discriminant = radius * radius - a_ray_y * a_ray_y;
			
			if discriminant < 0.0 {
				// The sphere is not on the line
				continue;
			}
			
			let t = (a_ray_x - discriminant.sqrt ()) / (p1 - p0).length ();
			
			if t < 0.0 || t > 1.0 {
				// The sphere is along the line,
				// but outside the line segment
				continue;
			}
			
			let p_impact = p0 * (1.0 - t) + p1 * (t);
			let vert_normal = (p_impact - a).normalize ();
			
			// I skip the speed check here cause I'm pretty sure
			// the previous work makes it redundant
			
			let c = Collision {
				t,
				p_impact,
				normal: vert_normal,
				i,
			};
			
			candidate = candidate.take_if_closer (&c);
		}
	}
	
	candidate
}

pub fn physics_step <MB> (input: &PhysicsBody, world: &MB)
-> PhysicsResult
where MB: MeshBuffer
{
	let dt = 1.0 / 60.0;
	let z = Vec3::from ((0.0, 0.0, 1.0));
	let gravity = z * -16.0 * dt;
	let margin = 0.00125;
	
	let mut t_remaining = 1.0;
	
	let mut old_pos = input.pos;
	let mut new_vel = input.vel + gravity;
	let mut new_pos = old_pos + new_vel * dt * t_remaining;
	
	let mut triangles_hit = Vec::new ();
	
	for i in 0..5 {
		let candidate = get_candidate (world, old_pos, new_pos);
		
		if candidate.t <= 1.0 {
			t_remaining *= 1.0 - candidate.t;
			let speed_towards_normal = -Vec3::dot (new_vel, candidate.normal);
			
			let push_out_pos = candidate.p_impact + candidate.normal * margin;
			
			// Rewind the object to when it hit the margin
			let speed = new_vel.length ();
			let dir = new_vel / speed;
			old_pos = candidate.p_impact + dir * margin / Vec3::dot (candidate.normal, dir);
			
			// Push the object out of the triangle along the normal
			new_vel += candidate.normal * speed_towards_normal;
			// But also compensate for the slide distance it lost
			new_pos = push_out_pos + new_vel * dt * t_remaining;
		}
		else {
			t_remaining = 0.0;
			old_pos = new_pos;
			break;
		}
	}
	
	PhysicsResult {
		body: PhysicsBody {
			pos: old_pos,
			vel: new_vel,
		},
		triangles_hit,
		kill: false,
	}
}