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+use super::{LineSegment, Vec2};
+use alga::general::{ClosedMul, ClosedSub};
+use nalgebra::{RealField, Scalar};
+use num_traits::Zero;
+
+/// Represents a triangle
+#[derive(Debug)]
+pub struct Triangle<T: Scalar + Copy> {
+ /// The three corners of the triangle. Internally, it is made sure that the corners are always
+ /// ordered in a counterclockwise manner, to make operations like contains simpler.
+ corners: [Vec2<T>; 3],
+}
+
+impl<T: Scalar + Copy> Triangle<T> {
+ /// Create a new Triangle as defined by its three corner points
+ pub fn new(a: Vec2<T>, b: Vec2<T>, c: Vec2<T>) -> Self
+ where
+ T: ClosedSub + ClosedMul + PartialOrd + Zero,
+ {
+ // Make sure the three points are in counterclockwise order.
+ match triplet_orientation(a, b, c) {
+ TripletOrientation::Counterclockwise => Self { corners: [a, b, c] },
+ TripletOrientation::Clockwise => Self { corners: [a, c, b] },
+ TripletOrientation::Collinear => {
+ warn!(
+ "Creating triangle without any area: [{:?}, {:?}, {:?}]",
+ a, b, c
+ );
+ Self { corners: [a, b, c] }
+ }
+ }
+ }
+
+ /// Get the corners immutably
+ pub fn corners(&self) -> &[Vec2<T>; 3] {
+ &self.corners
+ }
+
+ /// Create a new Triangle from a three-point slice, instead of the three points one after
+ /// another.
+ pub fn from_slice(corners: [Vec2<T>; 3]) -> Self
+ where
+ T: ClosedSub + ClosedMul + PartialOrd + Zero,
+ {
+ Self::new(corners[0], corners[1], corners[2])
+ }
+
+ /// Check if the triangle contains a given point. If the point is right on an edge, it still
+ /// counts as inside it.
+ pub fn contains_point(&self, point: Vec2<T>) -> bool
+ where
+ T: ClosedSub + ClosedMul + PartialOrd + Zero,
+ {
+ // Since the points are ordered counterclockwise, check if the point is to the left of all
+ // edges (or on an edge) from one point to the next. When the point is to the left of all
+ // edges, it must be inside the triangle.
+ for i in 0..3 {
+ if triplet_orientation(self.corners[i], self.corners[(i + 1) % 3], point)
+ == TripletOrientation::Clockwise
+ {
+ return false;
+ }
+ }
+
+ true
+ }
+}
+
+/// Convert a three-point-slice into a triangle
+impl<T: Scalar + Copy + ClosedSub + ClosedMul + PartialOrd + Zero> From<[Vec2<T>; 3]>
+ for Triangle<T>
+{
+ fn from(corners: [Vec2<T>; 3]) -> Self {
+ Self::new(corners[0], corners[1], corners[2])
+ }
+}
+/// Convert a triangle into a three-point-slice. The corners are in counterclockwise order.
+impl<T: Scalar + Copy> Into<[Vec2<T>; 3]> for Triangle<T> {
+ fn into(self) -> [Vec2<T>; 3] {
+ self.corners
+ }
+}
+
+impl<T: Scalar + Copy + PartialEq> PartialEq for Triangle<T> {
+ fn eq(&self, other: &Self) -> bool {
+ // The indexes of the elements are not important, so try all shifting options.
+ for shift in 0..=2 {
+ if self
+ .corners
+ .iter()
+ .enumerate()
+ .find(|(i, &c)| c != other.corners[(i + shift) % 3])
+ .is_none()
+ {
+ return true;
+ }
+ }
+
+ false
+ }
+}
+
+#[derive(PartialEq, Eq)]
+pub(crate) enum TripletOrientation {
+ Clockwise,
+ Counterclockwise,
+ Collinear,
+}
+
+/// Helper function to determine which direction one would turn to traverse from the first point
+/// over the second to the third point. The third option is collinear, in which case the three points
+/// are on the same line.
+pub(crate) fn triplet_orientation<T>(a: Vec2<T>, b: Vec2<T>, c: Vec2<T>) -> TripletOrientation
+where
+ T: Scalar + Copy + ClosedSub + ClosedMul + PartialOrd + Zero,
+{
+ /* Check the slopes of the vector from a to b and b to c. If the slope of ab is greater than
+ * that of bc, the rotation is clockwise. If ab is smaller than bc it's counterclockwise. If
+ * they are the same it follows that the three points are collinear.
+ */
+ match (b.y - a.y) * (c.x - b.x) - (b.x - a.x) * (c.y - b.y) {
+ q if q > T::zero() => TripletOrientation::Counterclockwise,
+ q if q < T::zero() => TripletOrientation::Clockwise,
+ _ => TripletOrientation::Collinear,
+ }
+}
+
+/// Calculate the angle between three points. Guaranteed to have 0 <= angle < 2Pi. The angle is
+/// calculated as the angle between a line from a to b and then from b to c, increasing
+/// counterclockwise.
+///
+/// # Panics
+/// If the length from a to b or the length from b to c is zero.
+pub(crate) fn triplet_angle<T>(a: Vec2<T>, b: Vec2<T>, c: Vec2<T>) -> T
+where
+ T: Scalar + Copy + ClosedSub + RealField + Zero,
+{
+ assert!(a != b);
+ assert!(b != c);
+
+ // Handle the extreme 0 and 180 degree cases
+ let orientation = triplet_orientation(a, b, c);
+ if orientation == TripletOrientation::Collinear {
+ if LineSegment::new(a, b).contains_collinear(c)
+ || LineSegment::new(b, c).contains_collinear(a)
+ {
+ return T::zero();
+ } else {
+ return T::pi();
+ }
+ }
+
+ // Calculate the vectors out of the points
+ let ba = a - b;
+ let bc = c - b;
+
+ // Calculate the angle between 0 and Pi.
+ let angle = ((ba * bc) / (ba.length() * bc.length())).acos();
+
+ // Make angle into a full circle angle by looking at the orientation of the triplet.
+ match orientation {
+ TripletOrientation::Counterclockwise => T::pi() + (T::pi() - angle),
+ _ => angle,
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::*;
+ use std::f64::consts::PI;
+
+ #[test]
+ fn new() {
+ let a = Vec2::new(0., 0.);
+ let b = Vec2::new(0., 1.);
+ let c = Vec2::new(1., 1.);
+
+ // Create with counterclockwise order.
+ let triangle = Triangle::new(a, b, c);
+ assert_eq!(triangle.corners(), &[a, b, c]);
+
+ // Create with clockwise order.
+ let triangle = Triangle::new(a, c, b);
+ assert_eq!(triangle.corners(), &[a, b, c]);
+
+ // Create with different starting corner
+ let triangle = Triangle::from([b, c, a]);
+ assert_eq!(triangle.corners(), &[b, c, a]);
+
+ // Create with collinear corners
+ let triangle = Triangle::new(c, c, b);
+ assert_eq!(triangle.corners(), &[c, c, b]);
+ }
+
+ #[test]
+ fn contains_point() {
+ let a = Vec2::new(0., 0.);
+ let b = Vec2::new(-1., -1.);
+ let c = Vec2::new(-2., 0.);
+
+ let triangle = Triangle::new(a, b, c);
+
+ assert!(triangle.contains_point(b));
+ assert!(triangle.contains_point(Vec2::new(-0.5, -0.5)));
+ assert!(triangle.contains_point(Vec2::new(-1., -0.5)));
+ assert!(!triangle.contains_point(Vec2::new(-2., -2.)));
+ }
+
+ #[test]
+ fn equality() {
+ let a = Vec2::new(0., 0.);
+ let b = Vec2::new(-1., -1.);
+ let c = Vec2::new(-2., 0.);
+ let d = Vec2::new(-3., 0.);
+
+ let cmp = Triangle::new(a, b, c);
+
+ assert_eq!(Triangle::new(a, b, c), cmp);
+ assert_eq!(Triangle::new(c, b, a), cmp);
+ assert_eq!(Triangle::new(b, a, c), cmp);
+ assert!(Triangle::new(a, b, d) != cmp);
+ }
+
+ #[test]
+ fn triplet_angle() {
+ assert_eq!(
+ super::triplet_angle(Vec2::new(0., 0.), Vec2::new(0., -1.), Vec2::new(-1., -1.)),
+ 1.5 * PI
+ );
+ assert_eq!(
+ super::triplet_angle(Vec2::new(2., 2.), Vec2::new(0., 0.), Vec2::new(-1., -1.)),
+ PI
+ );
+ assert_eq!(
+ super::triplet_angle(Vec2::new(3., 1.), Vec2::new(0., 0.), Vec2::new(6., 2.)),
+ 0.
+ );
+ assert_eq!(
+ super::triplet_angle(Vec2::new(3., 1.), Vec2::new(0., 0.), Vec2::new(-6., -2.)),
+ PI
+ );
+ assert_eq!(
+ super::triplet_angle(Vec2::new(0., 1.), Vec2::new(0., 2.), Vec2::new(-3., 2.)),
+ 0.5 * PI
+ );
+ assert_eq!(
+ super::triplet_angle(Vec2::new(3., 1.), Vec2::new(2., 2.), Vec2::new(0., 2.)),
+ 0.75 * PI
+ );
+ }
+}
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