First implementation of element distance functions with failing tests

packages/math/arc.ts

@@ -1,6 +1,8 @@
+import { invariant } from "../excalidraw/utils";
 import { cartesian2Polar, radians } from "./angle";
 import { ellipse, ellipseSegmentInterceptPoints } from "./ellipse";
-import { point } from "./point";
+import { point, pointDistance } from "./point";
+import { segment } from "./segment";
 import type { GenericPoint, Segment, Radians, Arc } from "./types";
 import { PRECISION } from "./utils";
 
@@ -42,6 +44,25 @@ export function arcIncludesPoint<P extends GenericPoint>(
     : startAngle <= angle || endAngle >= angle;
 }
 
+/**
+ *
+ * @param a
+ * @param p
+ */
+export function arcDistanceFromPoint<Point extends GenericPoint>(
+  a: Arc<Point>,
+  p: Point,
+) {
+  const intersectPoint = arcSegmentInterceptPoint(a, segment(p, a.center));
+
+  invariant(
+    intersectPoint.length !== 1,
+    "Arc distance intersector cannot have multiple intersections",
+  );
+
+  return pointDistance(intersectPoint[0], p);
+}
+
 /**
  * Returns the intersection point(s) of a line segment represented by a start
  * point and end point and a symmetric arc.

packages/math/polygon.ts

@@ -1,6 +1,6 @@
 import { pointsEqual } from "./point";
-import { segment, segmentIncludesPoint } from "./segment";
-import type { GenericPoint, Polygon } from "./types";
+import { segment, segmentIncludesPoint, segmentsIntersectAt } from "./segment";
+import type { GenericPoint, Polygon, Segment } from "./types";
 import { PRECISION } from "./utils";
 
 export function polygon<Point extends GenericPoint>(...points: Point[]) {
@@ -62,3 +62,25 @@ function polygonClose<Point extends GenericPoint>(polygon: Point[]) {
 function polygonIsClosed<Point extends GenericPoint>(polygon: Point[]) {
   return pointsEqual(polygon[0], polygon[polygon.length - 1]);
 }
+
+/**
+ * Returns the points of intersection of a line segment, identified by exactly
+ * one start pointand one end point, and the polygon identified by a set of
+ * ponits representing a set of connected lines.
+ */
+export function polygonSegmentIntersectionPoints<Point extends GenericPoint>(
+  polygon: Readonly<Polygon<Point>>,
+  segment: Readonly<Segment<Point>>,
+): Point[] {
+  return polygon
+    .reduce((segments, current, idx, poly) => {
+      return idx === 0
+        ? []
+        : ([
+            ...segments,
+            [poly[idx - 1] as Point, current],
+          ] as Segment<Point>[]);
+    }, [] as Segment<Point>[])
+    .map((s) => segmentsIntersectAt(s, segment))
+    .filter((point) => point !== null) as Point[];
+}

packages/math/segment.ts

@@ -122,11 +122,11 @@ export const segmentIncludesPoint = <Point extends GenericPoint>(
 };
 
 export const segmentDistanceToPoint = <Point extends GenericPoint>(
-  point: Point,
-  line: Segment<Point>,
+  p: Point,
+  s: Segment<Point>,
 ) => {
-  const [x, y] = point;
-  const [[x1, y1], [x2, y2]] = line;
+  const [x, y] = p;
+  const [[x1, y1], [x2, y2]] = s;
 
   const A = x - x1;
   const B = y - y1;