1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239
//! Definition of the tetrahedron shape.
use crate::math::{Matrix, Point, Real};
use crate::shape::{Segment, Triangle};
use crate::utils;
use na::Matrix3;
use std::mem;
#[cfg(not(feature = "std"))]
use na::ComplexField; // for .abs()
#[cfg(feature = "rkyv")]
use rkyv::{bytecheck, CheckBytes};
/// A tetrahedron with 4 vertices.
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[cfg_attr(feature = "bytemuck", derive(bytemuck::Pod, bytemuck::Zeroable))]
#[cfg_attr(
feature = "rkyv",
derive(rkyv::Archive, rkyv::Deserialize, rkyv::Serialize, CheckBytes),
archive(as = "Self")
)]
#[derive(Copy, Clone, Debug)]
#[repr(C)]
pub struct Tetrahedron {
/// The tetrahedron's first point.
pub a: Point<Real>,
/// The tetrahedron's second point.
pub b: Point<Real>,
/// The tetrahedron's third point.
pub c: Point<Real>,
/// The tetrahedron's fourth point.
pub d: Point<Real>,
}
/// Logical description of the location of a point on a triangle.
#[derive(Copy, Clone, Debug)]
pub enum TetrahedronPointLocation {
/// The point lies on a vertex.
OnVertex(u32),
/// The point lies on an edge.
///
/// The 0-th edge is the segment AB.
/// The 1-st edge is the segment AC.
/// The 2-nd edge is the segment AD.
/// The 3-rd edge is the segment BC.
/// The 4-th edge is the segment BD.
/// The 5-th edge is the segment CD.
OnEdge(u32, [Real; 2]),
/// The point lies on a triangular face interior.
///
/// The first face is the triangle ABC.
/// The second face is the triangle ABD.
/// The third face is the triangle ACD.
/// The fourth face is the triangle BDC.
OnFace(u32, [Real; 3]),
/// The point lies inside of the tetrahedron.
OnSolid,
}
impl TetrahedronPointLocation {
/// The barycentric coordinates corresponding to this point location.
///
/// Returns `None` if the location is `TetrahedronPointLocation::OnSolid`.
pub fn barycentric_coordinates(&self) -> Option<[Real; 4]> {
let mut bcoords = [0.0; 4];
match self {
TetrahedronPointLocation::OnVertex(i) => bcoords[*i as usize] = 1.0,
TetrahedronPointLocation::OnEdge(i, uv) => {
let idx = Tetrahedron::edge_ids(*i);
bcoords[idx.0 as usize] = uv[0];
bcoords[idx.1 as usize] = uv[1];
}
TetrahedronPointLocation::OnFace(i, uvw) => {
let idx = Tetrahedron::face_ids(*i);
bcoords[idx.0 as usize] = uvw[0];
bcoords[idx.1 as usize] = uvw[1];
bcoords[idx.2 as usize] = uvw[2];
}
TetrahedronPointLocation::OnSolid => {
return None;
}
}
Some(bcoords)
}
/// Returns `true` if both `self` and `other` correspond to points on the same feature of a tetrahedron.
pub fn same_feature_as(&self, other: &TetrahedronPointLocation) -> bool {
match (*self, *other) {
(TetrahedronPointLocation::OnVertex(i), TetrahedronPointLocation::OnVertex(j)) => {
i == j
}
(TetrahedronPointLocation::OnEdge(i, _), TetrahedronPointLocation::OnEdge(j, _)) => {
i == j
}
(TetrahedronPointLocation::OnFace(i, _), TetrahedronPointLocation::OnFace(j, _)) => {
i == j
}
(TetrahedronPointLocation::OnSolid, TetrahedronPointLocation::OnSolid) => true,
_ => false,
}
}
}
impl Tetrahedron {
/// Creates a tetrahedron from four points.
#[inline]
pub fn new(a: Point<Real>, b: Point<Real>, c: Point<Real>, d: Point<Real>) -> Tetrahedron {
Tetrahedron { a, b, c, d }
}
/// Creates the reference to a tetrahedron from the reference to an array of four points.
pub fn from_array(arr: &[Point<Real>; 4]) -> &Tetrahedron {
unsafe { mem::transmute(arr) }
}
/// Returns the i-th face of this tetrahedron.
///
/// The 0-th face is the triangle ABC.
/// The 1-st face is the triangle ABD.
/// The 2-nd face is the triangle ACD.
/// The 3-rd face is the triangle BCD.
pub fn face(&self, i: usize) -> Triangle {
match i {
0 => Triangle::new(self.a, self.b, self.c),
1 => Triangle::new(self.a, self.b, self.d),
2 => Triangle::new(self.a, self.c, self.d),
3 => Triangle::new(self.b, self.c, self.d),
_ => panic!("Tetrahedron face index out of bounds (must be < 4."),
}
}
/// Returns the i-th face of this tetrahedron.
///
/// The 0-th face is the triangle ABC.
/// The 1-st face is the triangle ABD.
/// The 2-nd face is the triangle ACD.
/// The 3-rd face is the triangle BCD.
pub fn face_ids(i: u32) -> (u32, u32, u32) {
match i {
0 => (0, 1, 2),
1 => (0, 1, 3),
2 => (0, 2, 3),
3 => (1, 2, 3),
_ => panic!("Tetrahedron face index out of bounds (must be < 4."),
}
}
/// Returns the i-th edge of this tetrahedron.
///
/// The 0-th edge is the segment AB.
/// The 1-st edge is the segment AC.
/// The 2-nd edge is the segment AD.
/// The 3-rd edge is the segment BC.
/// The 4-th edge is the segment BD.
/// The 5-th edge is the segment CD.
pub fn edge(&self, i: u32) -> Segment {
match i {
0 => Segment::new(self.a, self.b),
1 => Segment::new(self.a, self.c),
2 => Segment::new(self.a, self.d),
3 => Segment::new(self.b, self.c),
4 => Segment::new(self.b, self.d),
5 => Segment::new(self.c, self.d),
_ => panic!("Tetrahedron edge index out of bounds (must be < 6)."),
}
}
/// Returns the indices of the vertices of the i-th edge of this tetrahedron.
///
/// The 0-th edge is the segment AB.
/// The 1-st edge is the segment AC.
/// The 2-nd edge is the segment AD.
/// The 3-rd edge is the segment BC.
/// The 4-th edge is the segment BD.
/// The 5-th edge is the segment CD.
pub fn edge_ids(i: u32) -> (u32, u32) {
match i {
0 => (0, 1),
1 => (0, 2),
2 => (0, 3),
3 => (1, 2),
4 => (1, 3),
5 => (2, 3),
_ => panic!("Tetrahedron edge index out of bounds (must be < 6)."),
}
}
/// Computes the barycentric coordinates of the given point in the coordinate system of this tetrahedron.
///
/// Returns `None` if this tetrahedron is degenerate.
pub fn barycentric_coordinates(&self, p: &Point<Real>) -> Option<[Real; 4]> {
let ab = self.b - self.a;
let ac = self.c - self.a;
let ad = self.d - self.a;
let m = Matrix::new(ab.x, ac.x, ad.x, ab.y, ac.y, ad.y, ab.z, ac.z, ad.z);
m.try_inverse().map(|im| {
let bcoords = im * (p - self.a);
[
1.0 - bcoords.x - bcoords.y - bcoords.z,
bcoords.x,
bcoords.y,
bcoords.z,
]
})
}
/// Computes the volume of this tetrahedron.
#[inline]
pub fn volume(&self) -> Real {
self.signed_volume().abs()
}
/// Computes the signed volume of this tetrahedron.
///
/// If it is positive, `p4` is on the half-space pointed by the normal
/// of the oriented triangle `(p1, p2, p3)`.
#[inline]
pub fn signed_volume(&self) -> Real {
let p1p2 = self.b - self.a;
let p1p3 = self.c - self.a;
let p1p4 = self.d - self.a;
let mat = Matrix3::new(
p1p2[0], p1p3[0], p1p4[0], p1p2[1], p1p3[1], p1p4[1], p1p2[2], p1p3[2], p1p4[2],
);
mat.determinant() / na::convert::<f64, Real>(6.0f64)
}
/// Computes the center of this tetrahedron.
#[inline]
pub fn center(&self) -> Point<Real> {
utils::center(&[self.a, self.b, self.c, self.d])
}
}