chore: Unify math types, utils and functions (#8389)

Co-authored-by: dwelle <5153846+dwelle@users.noreply.github.com>

packages/math/triangle.ts

@@ -0,0 +1,28 @@
+import type { GlobalPoint, LocalPoint, Triangle } from "./types";
+
+// Types
+
+/**
+ * Tests if a point lies inside a triangle. This function
+ * will return FALSE if the point lies exactly on the sides
+ * of the triangle.
+ *
+ * @param triangle The triangle to test the point for
+ * @param p The point to test whether is in the triangle
+ * @returns TRUE if the point is inside of the triangle
+ */
+export function triangleIncludesPoint<P extends GlobalPoint | LocalPoint>(
+  [a, b, c]: Triangle<P>,
+  p: P,
+): boolean {
+  const triangleSign = (p1: P, p2: P, p3: P) =>
+    (p1[0] - p3[0]) * (p2[1] - p3[1]) - (p2[0] - p3[0]) * (p1[1] - p3[1]);
+  const d1 = triangleSign(p, a, b);
+  const d2 = triangleSign(p, b, c);
+  const d3 = triangleSign(p, c, a);
+
+  const has_neg = d1 < 0 || d2 < 0 || d3 < 0;
+  const has_pos = d1 > 0 || d2 > 0 || d3 > 0;
+
+  return !(has_neg && has_pos);
+}