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use crate::math::{Real, Vector};
use crate::query::gjk::{self, CsoPoint};
use crate::query::{PointQuery, PointQueryWithLocation};
use crate::shape::{
Segment, SegmentPointLocation, Tetrahedron, TetrahedronPointLocation, Triangle,
TrianglePointLocation,
};
/// A simplex of dimension up to 3 that uses Voronoï regions for computing point projections.
#[derive(Clone, Debug)]
pub struct VoronoiSimplex {
prev_vertices: [usize; 4],
prev_proj: [Real; 3],
prev_dim: usize,
vertices: [CsoPoint; 4],
proj: [Real; 3],
dim: usize,
}
impl Default for VoronoiSimplex {
fn default() -> Self {
Self::new()
}
}
impl VoronoiSimplex {
/// Creates a new empty simplex.
pub fn new() -> VoronoiSimplex {
VoronoiSimplex {
prev_vertices: [0, 1, 2, 3],
prev_proj: [0.0; 3],
prev_dim: 0,
vertices: [CsoPoint::ZERO; 4],
proj: [0.0; 3],
dim: 0,
}
}
/// Swap two vertices of this simplex.
pub fn swap(&mut self, i1: usize, i2: usize) {
self.vertices.swap(i1, i2);
self.prev_vertices.swap(i1, i2);
}
/// Resets this simplex to a single point.
pub fn reset(&mut self, pt: CsoPoint) {
self.dim = 0;
self.prev_dim = 0;
self.vertices[0] = pt;
}
/// Add a point to this simplex.
pub fn add_point(&mut self, pt: CsoPoint) -> bool {
self.prev_dim = self.dim;
self.prev_proj = self.proj;
self.prev_vertices = [0, 1, 2, 3];
match self.dim {
0 => {
if (self.vertices[0] - pt).length_squared() < gjk::eps_tol() {
return false;
}
}
1 => {
let ab = self.vertices[1] - self.vertices[0];
let ac = pt - self.vertices[0];
if ab.cross(ac).length_squared() < gjk::eps_tol() {
return false;
}
}
2 => {
let ab = self.vertices[1] - self.vertices[0];
let ac = self.vertices[2] - self.vertices[0];
let ap = pt - self.vertices[0];
let n = ab.cross(ac).normalize();
if n.dot(ap).abs() < gjk::eps_tol() {
return false;
}
}
_ => unreachable!(),
}
self.dim += 1;
self.vertices[self.dim] = pt;
true
}
/// Retrieves the barycentric coordinate associated to the `i`-th by the last call to `project_origin_and_reduce`.
pub fn proj_coord(&self, i: usize) -> Real {
assert!(i <= self.dim, "Index out of bounds.");
self.proj[i]
}
/// The i-th point of this simplex.
pub fn point(&self, i: usize) -> &CsoPoint {
assert!(i <= self.dim, "Index out of bounds.");
&self.vertices[i]
}
/// Retrieves the barycentric coordinate associated to the `i`-th before the last call to `project_origin_and_reduce`.
pub fn prev_proj_coord(&self, i: usize) -> Real {
assert!(i <= self.prev_dim, "Index out of bounds.");
self.prev_proj[i]
}
/// The i-th point of the simplex before the last call to `project_origin_and_reduce`.
pub fn prev_point(&self, i: usize) -> &CsoPoint {
assert!(i <= self.prev_dim, "Index out of bounds.");
&self.vertices[self.prev_vertices[i]]
}
/// Projects the origin on the boundary of this simplex and reduces `self` the smallest subsimplex containing the origin.
///
/// Returns the result of the projection or `Vector::ZERO` if the origin lies inside of the simplex.
/// The state of the simplex before projection is saved, and can be retrieved using the methods prefixed
/// by `prev_`.
pub fn project_origin_and_reduce(&mut self) -> Vector {
if self.dim == 0 {
self.proj[0] = 1.0;
self.vertices[0].point
} else if self.dim == 1 {
let (proj, location) = Segment::new(self.vertices[0].point, self.vertices[1].point)
.project_local_point_and_get_location(Vector::ZERO, true);
match location {
SegmentPointLocation::OnVertex(0) => {
self.proj[0] = 1.0;
self.dim = 0;
}
SegmentPointLocation::OnVertex(1) => {
self.swap(0, 1);
self.proj[0] = 1.0;
self.dim = 0;
}
SegmentPointLocation::OnEdge(coords) => {
self.proj[0] = coords[0];
self.proj[1] = coords[1];
}
_ => unreachable!(),
}
proj.point
} else if self.dim == 2 {
let (proj, location) = Triangle::new(
self.vertices[0].point,
self.vertices[1].point,
self.vertices[2].point,
)
.project_local_point_and_get_location(Vector::ZERO, true);
match location {
TrianglePointLocation::OnVertex(i) => {
self.swap(0, i as usize);
self.proj[0] = 1.0;
self.dim = 0;
}
TrianglePointLocation::OnEdge(0, coords) => {
self.proj[0] = coords[0];
self.proj[1] = coords[1];
self.dim = 1;
}
TrianglePointLocation::OnEdge(1, coords) => {
self.swap(0, 2);
self.proj[0] = coords[1];
self.proj[1] = coords[0];
self.dim = 1;
}
TrianglePointLocation::OnEdge(2, coords) => {
self.swap(1, 2);
self.proj[0] = coords[0];
self.proj[1] = coords[1];
self.dim = 1;
}
TrianglePointLocation::OnFace(_, coords) => {
self.proj = coords;
}
_ => {}
}
proj.point
} else {
assert!(self.dim == 3);
let (proj, location) = Tetrahedron::new(
self.vertices[0].point,
self.vertices[1].point,
self.vertices[2].point,
self.vertices[3].point,
)
.project_local_point_and_get_location(Vector::ZERO, true);
match location {
TetrahedronPointLocation::OnVertex(i) => {
self.swap(0, i as usize);
self.proj[0] = 1.0;
self.dim = 0;
}
TetrahedronPointLocation::OnEdge(i, coords) => {
match i {
0 => {
// ab
}
1 => {
// ac
self.swap(1, 2)
}
2 => {
// ad
self.swap(1, 3)
}
3 => {
// bc
self.swap(0, 2)
}
4 => {
// bd
self.swap(0, 3)
}
5 => {
// cd
self.swap(0, 2);
self.swap(1, 3);
}
_ => unreachable!(),
}
match i {
0 | 1 | 2 | 5 => {
self.proj[0] = coords[0];
self.proj[1] = coords[1];
}
3 | 4 => {
self.proj[0] = coords[1];
self.proj[1] = coords[0];
}
_ => unreachable!(),
}
self.dim = 1;
}
TetrahedronPointLocation::OnFace(i, coords) => {
match i {
0 => {
// abc
self.proj = coords;
}
1 => {
// abd
self.vertices[2] = self.vertices[3];
self.proj = coords;
}
2 => {
// acd
self.vertices[1] = self.vertices[3];
self.proj[0] = coords[0];
self.proj[1] = coords[2];
self.proj[2] = coords[1];
}
3 => {
// bcd
self.vertices[0] = self.vertices[3];
self.proj[0] = coords[2];
self.proj[1] = coords[0];
self.proj[2] = coords[1];
}
_ => unreachable!(),
}
self.dim = 2;
}
_ => {}
}
proj.point
}
}
/// Compute the projection of the origin on the boundary of this simplex.
pub fn project_origin(&mut self) -> Vector {
if self.dim == 0 {
self.vertices[0].point
} else if self.dim == 1 {
let seg = Segment::new(self.vertices[0].point, self.vertices[1].point);
seg.project_local_point(Vector::ZERO, true).point
} else if self.dim == 2 {
let tri = Triangle::new(
self.vertices[0].point,
self.vertices[1].point,
self.vertices[2].point,
);
tri.project_local_point(Vector::ZERO, true).point
} else {
let tetr = Tetrahedron::new(
self.vertices[0].point,
self.vertices[1].point,
self.vertices[2].point,
self.vertices[3].point,
);
tetr.project_local_point(Vector::ZERO, true).point
}
}
/// Tests if the given point is already a vertex of this simplex.
pub fn contains_point(&self, pt: Vector) -> bool {
for i in 0..self.dim + 1 {
if self.vertices[i].point == pt {
return true;
}
}
false
}
/// The dimension of the smallest subspace that can contain this simplex.
pub fn dimension(&self) -> usize {
self.dim
}
/// The dimension of the simplex before the last call to `project_origin_and_reduce`.
pub fn prev_dimension(&self) -> usize {
self.prev_dim
}
/// The maximum squared length of the vertices of this simplex.
pub fn max_sq_len(&self) -> Real {
let mut max_sq_len = 0.0;
for i in 0..self.dim + 1 {
let norm = self.vertices[i].point.length_squared();
if norm > max_sq_len {
max_sq_len = norm
}
}
max_sq_len
}
/// Apply a function to all the vertices of this simplex.
pub fn modify_pnts(&mut self, f: &dyn Fn(&mut CsoPoint)) {
for i in 0..self.dim + 1 {
f(&mut self.vertices[i])
}
}
}