ncollide3d/utils/
triangle.rs

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1use crate::math::Point;
2use crate::utils;
3use na;
4use simba::scalar::RealField;
5
6/// Computes the area of a triangle.
7#[inline]
8pub fn triangle_area<N: RealField + Copy>(pa: &Point<N>, pb: &Point<N>, pc: &Point<N>) -> N {
9    // Kahan's formula.
10    let mut a = na::distance(pa, pb);
11    let mut b = na::distance(pb, pc);
12    let mut c = na::distance(pc, pa);
13
14    let (c, b, a) = utils::sort3(&mut a, &mut b, &mut c);
15    let a = *a;
16    let b = *b;
17    let c = *c;
18
19    let sqr = (a + (b + c)) * (c - (a - b)) * (c + (a - b)) * (a + (b - c));
20
21    sqr.sqrt() * na::convert(0.25)
22}
23
24/// Computes the center of a triangle.
25#[inline]
26pub fn triangle_center<N: RealField + Copy>(
27    pa: &Point<N>,
28    pb: &Point<N>,
29    pc: &Point<N>,
30) -> Point<N> {
31    utils::center(&[*pa, *pb, *pc])
32}
33
34/// Computes the perimeter of a triangle.
35#[inline]
36pub fn triangle_perimeter<N: RealField + Copy>(pa: &Point<N>, pb: &Point<N>, pc: &Point<N>) -> N {
37    na::distance(pa, pb) + na::distance(pb, pc) + na::distance(pc, pa)
38}
39
40/// Computes the circumcircle of a triangle.
41pub fn circumcircle<N: RealField + Copy>(
42    pa: &Point<N>,
43    pb: &Point<N>,
44    pc: &Point<N>,
45) -> (Point<N>, N) {
46    let a = *pa - *pc;
47    let b = *pb - *pc;
48
49    let na = a.norm_squared();
50    let nb = b.norm_squared();
51
52    let dab = a.dot(&b);
53
54    let _2: N = na::convert(2.0);
55    let denom = _2 * (na * nb - dab * dab);
56
57    if denom.is_zero() {
58        // The triangle is degenerate (the three points are colinear).
59        // So we find the longest segment and take its center.
60        let c = *pa - *pb;
61        let nc = c.norm_squared();
62
63        if nc >= na && nc >= nb {
64            // Longest segment: [pa, pb]
65            (na::center(pa, pb), nc.sqrt() / na::convert(2.0f64))
66        } else if na >= nb && na >= nc {
67            // Longest segment: [pa, pc]
68            (na::center(pa, pc), na.sqrt() / na::convert(2.0f64))
69        } else {
70            // Longest segment: [pb, pc]
71            (na::center(pb, pc), nb.sqrt() / na::convert(2.0f64))
72        }
73    } else {
74        let k = b * na - a * nb;
75
76        let center = *pc + (a * k.dot(&b) - b * k.dot(&a)) / denom;
77        let radius = na::distance(pa, &center);
78
79        (center, radius)
80    }
81}
82
83/// Tests if three 3D points are approximately aligned.
84#[cfg(feature = "dim3")]
85pub fn is_affinely_dependent_triangle<N: RealField + Copy>(
86    p1: &Point<N>,
87    p2: &Point<N>,
88    p3: &Point<N>,
89) -> bool {
90    let p1p2 = *p2 - *p1;
91    let p1p3 = *p3 - *p1;
92
93    // FIXME: use this as nalgebra standard epsilon?
94    let _eps = N::default_epsilon(); // FIXME: use Float::epsilon instead?
95    let _eps_tol = _eps * na::convert(100.0f64);
96
97    relative_eq!(
98        p1p2.cross(&p1p3).norm_squared(),
99        na::zero(),
100        epsilon = _eps_tol * _eps_tol
101    )
102}
103
104/// Tests if a point is inside of a triangle.
105pub fn is_point_in_triangle<N: RealField + Copy>(
106    p: &Point<N>,
107    p1: &Point<N>,
108    p2: &Point<N>,
109    p3: &Point<N>,
110) -> bool {
111    let p1p2 = *p2 - *p1;
112    let p2p3 = *p3 - *p2;
113    let p3p1 = *p1 - *p3;
114
115    let p1p = *p - *p1;
116    let p2p = *p - *p2;
117    let p3p = *p - *p3;
118
119    let d11 = p1p.dot(&p1p2);
120    let d12 = p2p.dot(&p2p3);
121    let d13 = p3p.dot(&p3p1);
122
123    d11 >= na::zero()
124        && d11 <= p1p2.norm_squared()
125        && d12 >= na::zero()
126        && d12 <= p2p3.norm_squared()
127        && d13 >= na::zero()
128        && d13 <= p3p1.norm_squared()
129}
130
131#[cfg(feature = "dim3")]
132#[cfg(test)]
133mod test {
134    use na::Point3;
135
136    #[test]
137    fn test_triangle_area() {
138        let pa = Point3::new(0.0f64, 5.0, 0.0);
139        let pb = Point3::new(0.0f64, 0.0, 0.0);
140        let pc = Point3::new(0.0f64, 0.0, 4.0);
141
142        assert!(relative_eq!(super::triangle_area(&pa, &pb, &pc), 10.0));
143    }
144}
ncollide3d/utils/triangle.rs

ncollide3d/utils/
triangle.rs
