Add triangle struct and triangulation template

4 files changed, 183 insertions, 101 deletions

diff --git a/src/math/line_segment.rs b/src/math/line_segment.rs
index e6ca70f..244b0af 100644
--- a/src/math/line_segment.rs
+++ b/src/math/line_segment.rs
@@ -1,4 +1,4 @@
-use super::{Rect, Vec2};
+use super::{Rect, TripletOrientation, Vec2};
 use alga::general::{ClosedDiv, ClosedMul, ClosedSub};
 use nalgebra::{RealField, Scalar};
 use num_traits::Zero;
@@ -50,10 +50,10 @@ impl<T: Scalar + Copy> LineSegment<T> {
          */
 
         // Cache the necessary orientations.
-        let ls1_ls2start_orientation = triplet_orientation(ls1.start, ls1.end, ls2.start);
-        let ls1_ls2end_orientation = triplet_orientation(ls1.start, ls1.end, ls2.end);
-        let ls2_ls1start_orientation = triplet_orientation(ls2.start, ls2.end, ls1.start);
-        let ls2_ls1end_orientation = triplet_orientation(ls2.start, ls2.end, ls1.end);
+        let ls1_ls2start_orientation = super::triplet_orientation(ls1.start, ls1.end, ls2.start);
+        let ls1_ls2end_orientation = super::triplet_orientation(ls1.start, ls1.end, ls2.end);
+        let ls2_ls1start_orientation = super::triplet_orientation(ls2.start, ls2.end, ls1.start);
+        let ls2_ls1end_orientation = super::triplet_orientation(ls2.start, ls2.end, ls1.end);
 
         // Check for the first case that wase described (general case).
         if ls1_ls2start_orientation != ls1_ls2end_orientation
@@ -139,7 +139,7 @@ impl<T: Scalar + Copy> LineSegment<T> {
         assert_eq!(
             split_points
                 .iter()
-                .find(|&p| triplet_orientation(self.start, self.end, *p)
+                .find(|&p| super::triplet_orientation(self.start, self.end, *p)
                     != TripletOrientation::Collinear),
             None
         );
@@ -173,76 +173,9 @@ impl<T: Scalar + Copy> LineSegment<T> {
     }
 }
 
-#[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.
-    let angle = match orientation {
-        TripletOrientation::Counterclockwise => T::pi() + (T::pi() - angle),
-        _ => angle,
-    };
-
-    angle
-}
-
 #[cfg(test)]
 mod test {
     use super::*;
-    use std::f64::consts::PI;
 
     #[test]
     fn contains_collinear() {
@@ -256,32 +189,4 @@ mod test {
         assert!(!segment.contains_collinear(Vec2::new(3., 3.)));
         assert!(!segment.contains_collinear(Vec2::new(-1., 0.)));
     }
-
-    #[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
-        );
-    }
 }
diff --git a/src/math/mod.rs b/src/math/mod.rs
index 0b591d7..07bc36b 100644
--- a/src/math/mod.rs
+++ b/src/math/mod.rs
@@ -2,12 +2,16 @@ pub mod line_segment;
 pub mod polygon;
 pub mod polygon_graph;
 pub mod rect;
+pub mod triangle;
+pub mod triangulate;
 pub mod vec2;
 
 pub use self::line_segment::*;
 pub use self::polygon::*;
 pub use self::polygon_graph::*;
 pub use self::rect::*;
+pub use self::triangle::*;
+pub use self::triangulate::*;
 pub use self::vec2::*;
 
 use std::cmp::Ordering;
diff --git a/src/math/triangle.rs b/src/math/triangle.rs
new file mode 100644
index 0000000..53c7560
--- /dev/null
+++ b/src/math/triangle.rs
@@ -0,0 +1,161 @@
+use super::{LineSegment, Vec2};
+use alga::general::{ClosedMul, ClosedSub};
+use nalgebra::{RealField, Scalar};
+use num_traits::Zero;
+
+/// Represents a triangle
+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] }
+            }
+        }
+    }
+
+    /// 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
+    }
+}
+
+#[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.
+    let angle = match orientation {
+        TripletOrientation::Counterclockwise => T::pi() + (T::pi() - angle),
+        _ => angle,
+    };
+
+    angle
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use std::f64::consts::PI;
+
+    #[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
+        );
+    }
+}
diff --git a/src/math/triangulate.rs b/src/math/triangulate.rs
new file mode 100644
index 0000000..8ef92f1
--- /dev/null
+++ b/src/math/triangulate.rs
@@ -0,0 +1,12 @@
+//! Module for turning a polygon into a number of non-overlapping triangles.
+
+use super::{Polygon, Triangle};
+use nalgebra::Scalar;
+
+/// Uses earclipping algorithm (see https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf)
+/// to find an explanation of what exactly is happening.
+/// Currently only handles simple polygons, but once the polygon struct supports holes must be
+/// extended to also support those.
+pub fn triangulate<T: Scalar + Copy>(_polygon: &Polygon<T>) -> Vec<Triangle<T>> {
+    unimplemented!()
+}