Add polygon that can check if a point is inside

..except for one super super edgy edge case, but I wanted to get this
algorithm out into a commit before I ruin it completely (probably)

3 files changed, 257 insertions, 2 deletions

diff --git a/src/math/line_segment.rs b/src/math/line_segment.rs
new file mode 100644
index 0000000..d7bcdb1
--- /dev/null
+++ b/src/math/line_segment.rs
@@ -0,0 +1,116 @@
+use super::Vec2;
+use alga::general::{ClosedMul, ClosedSub};
+use nalgebra::Scalar;
+use num_traits::Zero;
+
+pub struct LineSegment<T: Scalar + Copy> {
+    pub start: Vec2<T>,
+    pub end: Vec2<T>,
+}
+
+impl<T: Scalar + Copy> LineSegment<T> {
+    pub fn new(start: Vec2<T>, end: Vec2<T>) -> Self {
+        Self { start, end }
+    }
+
+    /* Helper function to check if this line contains a point. This function is very efficient, but
+     * must only be used for points that are collinear with the segment. This is checked only by
+     * assertion, so make sure that everything is ok in release mode.
+     */
+    pub(crate) fn contains_collinear(&self, point: Vec2<T>) -> bool
+    where
+        T: PartialOrd,
+    {
+        point.x <= super::partial_max(self.start.x, self.end.x)
+            && point.x >= super::partial_max(self.start.x, self.end.x)
+            && point.y <= super::partial_min(self.start.y, self.end.y)
+            && point.y >= super::partial_min(self.start.y, self.end.y)
+    }
+
+    /// Checks if two segments intersect. This is much more efficient than trying to find the exact
+    /// point of intersection, so it should be used if it is not strictly necessary to know it.
+    pub fn intersect(ls1: &LineSegment<T>, ls2: &LineSegment<T>) -> bool
+    where
+        T: Scalar + Copy + ClosedSub + ClosedMul + PartialOrd + Zero,
+    {
+        /* This algorithm works by checking the triplet orientation of the first lines points with the
+         * first point of the second line. After that it does the same for the second point of the
+         * second line. If the orientations are different, that must mean the second line starts
+         * "before" the first line and ends "after" it. It does the same, but with the roles of first
+         * and second line reversed. If both of these conditions are met, it follows that the lines
+         * must have crossed.
+         *
+         * Edge case: If an orientation comes out as collinear, the point of the other line that was
+         * checked may be on the other line or after/before it (if you extend the segment). If it is on
+         * the other line, this also means, the lines cross, since one line "stands" on the other.
+         * If however none of the collinear cases are like this, the lines cannot touch, because line
+         * segment a point was collinear with was not long enough.
+         */
+
+        // 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);
+
+        // Check for the first case that wase described (general case).
+        if ls1_ls2start_orientation != ls1_ls2end_orientation
+            && ls2_ls1start_orientation != ls2_ls1end_orientation
+        {
+            return true;
+        }
+
+        // Check if the start of ls2 lies on ls1
+        if ls1_ls2start_orientation == TripletOrientation::Collinear
+            && ls1.contains_collinear(ls2.start)
+        {
+            return true;
+        }
+        // Check if the end of ls2 lies on ls1
+        if ls1_ls2end_orientation == TripletOrientation::Collinear
+            && ls1.contains_collinear(ls2.end)
+        {
+            return true;
+        }
+
+        // Check if the start of ls1 lies on ls2
+        if ls2_ls1start_orientation == TripletOrientation::Collinear
+            && ls2.contains_collinear(ls1.start)
+        {
+            return true;
+        }
+        // Check if the end of ls1 lies on ls2
+        if ls2_ls1end_orientation == TripletOrientation::Collinear
+            && ls2.contains_collinear(ls1.end)
+        {
+            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::Clockwise,
+        q if q < T::zero() => TripletOrientation::Counterclockwise,
+        _ => TripletOrientation::Collinear,
+    }
+}
diff --git a/src/math/mod.rs b/src/math/mod.rs
index 07d518e..bfc2ab4 100644
--- a/src/math/mod.rs
+++ b/src/math/mod.rs
@@ -1,9 +1,15 @@
+pub mod line_segment;
+pub mod polygon;
 pub mod rect;
-pub use self::rect::*;
-
 pub mod vec2;
+
+pub use self::line_segment::*;
+pub use self::polygon::*;
+pub use self::rect::*;
 pub use self::vec2::*;
 
+use std::cmp::Ordering;
+
 /// Round a floating point number to the nearest step given by the step argument. For instance, if
 /// the step is 0.5, then all numbers from 0.0 to 0.24999... will be 0., while all numbers from
 /// 0.25 to 0.74999... will be 0.5 and so on.
@@ -21,3 +27,24 @@ pub fn round(num: f32, step: f32) -> f32 {
         upper_bound
     }
 }
+
+/// Works like `std::cmp::max`, however also allows partial comparisons. It is specifically
+/// designed so functions that should be able to use f32 and f64 work, eventhough these do not
+/// implement Ord. The downside of this function however is, that its behaviour is undefined when
+/// `f32::NaN` for instance were to be passed.
+fn partial_max<T>(a: T, b: T) -> T
+where
+    T: PartialOrd,
+{
+    match a.partial_cmp(&b) {
+        Some(Ordering::Greater) => a,
+        _ => b,
+    }
+}
+/// Like `partial_max`, but for minimum values. Comes with the same downside, too.
+fn partial_min<T>(a: T, b: T) -> T
+where
+    T: PartialOrd,
+{
+    partial_max(b, a)
+}
diff --git a/src/math/polygon.rs b/src/math/polygon.rs
new file mode 100644
index 0000000..e70cd2c
--- /dev/null
+++ b/src/math/polygon.rs
@@ -0,0 +1,112 @@
+use super::{LineSegment, TripletOrientation, Vec2};
+use alga::general::{ClosedMul, ClosedSub};
+use nalgebra::Scalar;
+use num_traits::Zero;
+
+pub struct Polygon<T: Scalar + Copy> {
+    pub corners: Vec<Vec2<T>>,
+}
+
+impl<T: Scalar + Copy> Polygon<T> {
+    pub fn new(corners: Vec<Vec2<T>>) -> Self {
+        Self { corners }
+    }
+
+    /// Check whether a point is inside a polygon or not. If a point lies on an edge, it also
+    /// counts as inside the polygon.
+    pub fn contains(&self, point: Vec2<T>) -> bool
+    where
+        T: Scalar + Copy + ClosedSub + ClosedMul + PartialOrd + Zero,
+    {
+        // Must be at least a triangle to contain anything
+        if self.corners.len() < 3 {
+            return false;
+        }
+
+        /* What's happening here:
+         *
+         * This algorithm creates a horizontal line for the point that should be checked. It goes
+         * to infinity (since infinite lines are not possible, it just goes to the maximum x value
+         * of all corner points). Then, the times the line crosses a polygon edge is counted. If
+         * the times it hit a polygon edge is uneven, it must have been inside, otherwise outside.
+         *
+         * There is an edge case however (pun not intended); When the line from the point is collinear
+         * to a polygon edge. it might hit this edge once and no other (it's at the top y or bottom y
+         * of the polygon), but may still not be inside the polygon. In this case, it's checked
+         * whether the point is in between the corner points of this polygon edge or not. If it is
+         * in between, it is still inside the polygon, otherwise outside.
+         */
+
+        // Get the maximum x for the horizontal lines for "Infinity".
+        let mut max_x = self.corners[0].x;
+        for corner in self.corners.iter().skip(1) {
+            max_x = super::partial_max(corner.x, max_x);
+        }
+        println!("Max x is {:?}", max_x);
+        // The horizontally "infinite" point of the test point.
+        let line_to_infinity = LineSegment::new(point, Vec2::new(max_x, point.y));
+
+        // Check for intersection for all the polygon edges.
+        let mut num_intersects = 0;
+        for i in 0..self.corners.len() {
+            // Wrap around for the edge that returns to the start.
+            let j = (i + 1) % self.corners.len();
+            let current_edge = LineSegment::new(self.corners[i], self.corners[j]);
+
+            if LineSegment::intersect(&current_edge, &line_to_infinity) {
+                /* Check for the edge case, where the point might lie right on an edge of the
+                 * polygon.
+                 */
+                if super::triplet_orientation(current_edge.start, current_edge.end, point)
+                    == TripletOrientation::Collinear
+                {
+                    // The point is right on an edge
+                    if current_edge.contains_collinear(point) {
+                        return true;
+                    }
+                } else {
+                    num_intersects += 1;
+                }
+            }
+        }
+
+        num_intersects % 2 == 1
+    }
+
+    /// Join this polygon with another, ensuring the area of the two stays the same, minus the
+    /// overlap.
+    ///
+    /// # Panics
+    /// If the two polygons do not intersect, it is impossible to unite them into a single polygon,
+    /// in which case this function is bound to fail.
+    // TODO: Create a function that only tries to join the polygons.
+    pub fn unite(&mut self, mut _other: Polygon<T>) {
+        unimplemented!()
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn polygon_contains() {
+        let polygon = Polygon::new(vec![
+            Vec2::new(0., 0.),
+            Vec2::new(-1., 1.),
+            Vec2::new(0., 2.),
+            Vec2::new(1., 3.),
+            Vec2::new(3., 1.5),
+            Vec2::new(2., 0.),
+            Vec2::new(1., 1.),
+        ]);
+
+        assert!(!polygon.contains(Vec2::new(1., -2.)));
+        assert!(!polygon.contains(Vec2::new(-1., 0.5)));
+        assert!(polygon.contains(Vec2::new(0., 0.5)));
+        assert!(polygon.contains(Vec2::new(0.5, 1.)));
+        assert!(polygon.contains(Vec2::new(0.5, 1.5)));
+        assert!(!polygon.contains(Vec2::new(-2., 1.9)));
+        assert!(!polygon.contains(Vec2::new(0., 3.)));
+    }
+}