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

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

packages/math/polygon.ts

@@ -0,0 +1,72 @@
+import { pointsEqual } from "./point";
+import { lineSegment, pointOnLineSegment } from "./segment";
+import type { GlobalPoint, LocalPoint, Polygon } from "./types";
+import { PRECISION } from "./utils";
+
+export function polygon<Point extends GlobalPoint | LocalPoint>(
+  ...points: Point[]
+) {
+  return polygonClose(points) as Polygon<Point>;
+}
+
+export function polygonFromPoints<Point extends GlobalPoint | LocalPoint>(
+  points: Point[],
+) {
+  return polygonClose(points) as Polygon<Point>;
+}
+
+export const polygonIncludesPoint = <Point extends LocalPoint | GlobalPoint>(
+  point: Point,
+  polygon: Polygon<Point>,
+) => {
+  const x = point[0];
+  const y = point[1];
+  let inside = false;
+
+  for (let i = 0, j = polygon.length - 1; i < polygon.length; j = i++) {
+    const xi = polygon[i][0];
+    const yi = polygon[i][1];
+    const xj = polygon[j][0];
+    const yj = polygon[j][1];
+
+    if (
+      ((yi > y && yj <= y) || (yi <= y && yj > y)) &&
+      x < ((xj - xi) * (y - yi)) / (yj - yi) + xi
+    ) {
+      inside = !inside;
+    }
+  }
+
+  return inside;
+};
+
+export const pointOnPolygon = <Point extends LocalPoint | GlobalPoint>(
+  p: Point,
+  poly: Polygon<Point>,
+  threshold = PRECISION,
+) => {
+  let on = false;
+
+  for (let i = 0, l = poly.length - 1; i < l; i++) {
+    if (pointOnLineSegment(p, lineSegment(poly[i], poly[i + 1]), threshold)) {
+      on = true;
+      break;
+    }
+  }
+
+  return on;
+};
+
+function polygonClose<Point extends LocalPoint | GlobalPoint>(
+  polygon: Point[],
+) {
+  return polygonIsClosed(polygon)
+    ? polygon
+    : ([...polygon, polygon[0]] as Polygon<Point>);
+}
+
+function polygonIsClosed<Point extends LocalPoint | GlobalPoint>(
+  polygon: Point[],
+) {
+  return pointsEqual(polygon[0], polygon[polygon.length - 1]);
+}