From a22faae428f7ff51a0b2eaea902e5b5ed1a7c8a5 Mon Sep 17 00:00:00 2001
From: Arne Dußin
Date: Wed, 11 Nov 2020 21:36:44 +0100
Subject: 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)
---
 src/math/line_segment.rs | 116 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 116 insertions(+)
 create mode 100644 src/math/line_segment.rs

(limited to 'src/math/line_segment.rs')

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,
+    }
+}
-- 
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