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//! Definition of the tetrahedron shape.
use crate::math::{Matrix, Point};
use crate::shape::{Segment, Triangle};
use na::RealField;
use std::mem;
/// A tetrahedron with 4 vertices.
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[repr(C)]
#[derive(Copy, Clone, Debug)]
pub struct Tetrahedron<N: RealField + Copy> {
/// The tetrahedron first point.
pub a: Point<N>,
/// The tetrahedron first point.
pub b: Point<N>,
/// The tetrahedron first point.
pub c: Point<N>,
/// The tetrahedron first point.
pub d: Point<N>,
}
/// Logical description of the location of a point on a triangle.
#[derive(Copy, Clone, Debug)]
pub enum TetrahedronPointLocation<N: RealField + Copy> {
/// The point lies on a vertex.
OnVertex(usize),
/// The point lies on an edge.
///
/// The 0-st 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(usize, [N; 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(usize, [N; 3]),
/// The point lies inside of the tetrahedron.
OnSolid,
}
impl<N: RealField + Copy> TetrahedronPointLocation<N> {
/// The barycentric coordinates corresponding to this point location.
///
/// Returns `None` if the location is `TetrahedronPointLocation::OnSolid`.
pub fn barycentric_coordinates(&self) -> Option<[N; 4]> {
let mut bcoords = [N::zero(); 4];
match self {
TetrahedronPointLocation::OnVertex(i) => bcoords[*i] = N::one(),
TetrahedronPointLocation::OnEdge(i, uv) => {
let idx = Tetrahedron::<N>::edge_ids(*i);
bcoords[idx.0] = uv[0];
bcoords[idx.1] = uv[1];
}
TetrahedronPointLocation::OnFace(i, uvw) => {
let idx = Tetrahedron::<N>::face_ids(*i);
bcoords[idx.0] = uvw[0];
bcoords[idx.1] = uvw[1];
bcoords[idx.2] = 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<N>) -> 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<N: RealField + Copy> Tetrahedron<N> {
/// Creates a tetrahedron from three points.
#[inline]
pub fn new(a: Point<N>, b: Point<N>, c: Point<N>, d: Point<N>) -> Tetrahedron<N> {
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<N>; 4]) -> &Tetrahedron<N> {
unsafe { mem::transmute(arr) }
}
/// The fist point of this tetrahedron.
#[inline]
#[deprecated(note = "use the `self.a` public field directly.")]
pub fn a(&self) -> &Point<N> {
&self.a
}
/// The second point of this tetrahedron.
#[inline]
#[deprecated(note = "use the `self.b` public field directly.")]
pub fn b(&self) -> &Point<N> {
&self.b
}
/// The third point of this tetrahedron.
#[inline]
#[deprecated(note = "use the `self.c` public field directly.")]
pub fn c(&self) -> &Point<N> {
&self.c
}
/// The fourth point of this tetrahedron.
#[inline]
#[deprecated(note = "use the `self.d` public field directly.")]
pub fn d(&self) -> &Point<N> {
&self.d
}
/// 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<N> {
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: usize) -> (usize, usize, usize) {
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-st 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: usize) -> Segment<N> {
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-st 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: usize) -> (usize, usize) {
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<N>) -> Option<[N; 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);
[
N::one() - bcoords.x - bcoords.y - bcoords.z,
bcoords.x,
bcoords.y,
bcoords.z,
]
})
}
}