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#[derive(Debug)]
pub struct Point {
pub x: f64,
pub y: f64,
pub z: f64,
}
impl Point {
pub fn distance_to(&self, pt: &Point) -> f64 {
((self.x - pt.x).powi(2) + (self.y - pt.y).powi(2) + (self.z - pt.z).powi(2)).sqrt()
}
}
#[derive(Debug)]
pub struct Triangle {
pub a: Point,
pub b: Point,
pub c: Point,
}
impl Triangle {
pub fn aabb(&self) -> [Point; 2] {
let mut c_x = [self.a.x, self.b.x, self.c.x];
let mut c_y = [self.a.y, self.b.y, self.c.y];
let mut c_z = [self.a.z, self.b.z, self.c.z];
c_x.sort_by(|i, j| i.partial_cmp(j).unwrap());
c_y.sort_by(|i, j| i.partial_cmp(j).unwrap());
c_z.sort_by(|i, j| i.partial_cmp(j).unwrap());
[
Point {
x: c_x[0],
y: c_y[0],
z: c_z[0],
},
Point {
x: c_x[2],
y: c_y[2],
z: c_z[2],
},
]
}
pub fn angles(&self) -> Option<[f64; 3]> {
if self.is_collinear() {
return None;
}
let [la, lb, lc] = self.sides();
let alpha = ((lb.powi(2) + lc.powi(2) - la.powi(2)) / (2.0 * lb * lc)).acos();
let beta = ((la.powi(2) + lc.powi(2) - lb.powi(2)) / (2.0 * la * lc)).acos();
let gamma = std::f64::consts::PI - alpha - beta;
Some([alpha, beta, gamma])
}
pub fn area(&self) -> f64 {
let s = self.semiperimeter();
let [la, lb, lc] = self.sides();
(s * (s - la) * (s - lb) * (s - lc)).sqrt()
}
pub fn barycentric_to_cartesian(&self, pt: &Point) -> Point {
let x = pt.x * self.a.x + pt.y * self.b.x + pt.z * self.c.x;
let y = pt.x * self.a.y + pt.y * self.b.y + pt.z * self.c.y;
let z = pt.x * self.a.z + pt.y * self.b.z + pt.z * self.c.z;
Point { x: x, y: y, z: z }
}
pub fn cartesian_to_barycentric(&self, pt: &Point) -> Point {
let v0 = Point {
x: self.b.x - self.a.x,
y: self.b.y - self.a.y,
z: self.b.z - self.a.z,
};
let v1 = Point {
x: self.c.x - self.a.x,
y: self.c.y - self.a.y,
z: self.c.z - self.a.z,
};
let v2 = Point {
x: pt.x - self.a.x,
y: pt.y - self.a.y,
z: pt.z - self.a.z,
};
let den = 1.0 / (v0.x * v1.y - v1.x * v0.y);
let v = (v2.x * v1.y - v1.x * v2.y) * den;
let w = (v0.x * v2.y - v2.x * v0.y) * den;
let u = 1.0 - v - w;
Point { x: u, y: v, z: w }
}
pub fn centroid(&self) -> Point {
let cx = (self.a.x + self.b.x + self.c.x) / 3.0;
let cy = (self.a.y + self.b.y + self.c.y) / 3.0;
let cz = (self.a.z + self.b.z + self.c.z) / 3.0;
Point {
x: cx,
y: cy,
z: cz,
}
}
pub fn circumradius(&self) -> Option<f64> {
if self.is_collinear() {
return None;
}
Some(self.sides().iter().product::<f64>() / (4.0 * self.area()))
}
pub fn has_point(&self, pt: Point) -> bool {
fn sign(a: &Point, b: &Point, c: &Point) -> f32 {
((a.x - c.x) * (b.y - c.y) - (b.x - c.x) * (a.y - c.y)) as f32
}
let d1 = sign(&pt, &self.a, &self.b);
let d2 = sign(&pt, &self.b, &self.c);
let d3 = sign(&pt, &self.c, &self.a);
let has_neg = (d1 < 0.0) || (d2 < 0.0) || (d3 < 0.0);
let has_pos = (d1 > 0.0) || (d2 > 0.0) || (d3 > 0.0);
!(has_neg && has_pos)
}
pub fn heights(&self) -> Option<[f64; 3]> {
if self.is_collinear() {
return None;
}
let double_area = 2.0 * self.area();
let [la, lb, lc] = self.sides();
Some([double_area / la, double_area / lb, double_area / lc])
}
pub fn inradius(&self) -> Option<f64> {
if self.is_collinear() {
return None;
}
Some(self.area() / self.semiperimeter())
}
pub fn is_collinear(&self) -> bool {
self.area() == 0.0
}
pub fn perimeter(&self) -> f64 {
self.sides().iter().sum()
}
pub fn semiperimeter(&self) -> f64 {
self.perimeter() / 2.0
}
pub fn sides(&self) -> [f64; 3] {
[
self.b.distance_to(&self.c),
self.c.distance_to(&self.a),
self.a.distance_to(&self.b),
]
}
}