First implementation of element distance functions with failing tests

packages/excalidraw/element/binding.ts

@@ -25,7 +25,6 @@ import type {
   ExcalidrawElbowArrowElement,
   FixedPoint,
   SceneElementsMap,
-  ExcalidrawRectanguloidElement,
 } from "./types";
 
 import type { Bounds } from "./bounds";
@@ -63,7 +62,7 @@ import {
   vectorToHeading,
   type Heading,
 } from "./heading";
-import type { LocalPoint, Radians } from "../../math";
+import type { LocalPoint } from "../../math";
 import {
   segment,
   point,
@@ -76,6 +75,7 @@ import {
   radians,
 } from "../../math";
 import { segmentIntersectRectangleElement } from "../../utils/geometry/shape";
+import { distanceToBindableElement } from "./distance";
 
 export type SuggestedBinding =
   | NonDeleted<ExcalidrawBindableElement>
@@ -557,10 +557,7 @@ const calculateFocusAndGap = (
       edgePoint,
       elementsMap,
     ),
-    gap: Math.max(
-      1,
-      distanceToBindableElement(hoveredElement, edgePoint, elementsMap),
-    ),
+    gap: Math.max(1, distanceToBindableElement(hoveredElement, edgePoint)),
   };
 };
 
@@ -736,11 +733,7 @@ const getDistanceForBinding = (
   bindableElement: ExcalidrawBindableElement,
   elementsMap: ElementsMap,
 ) => {
-  const distance = distanceToBindableElement(
-    bindableElement,
-    point,
-    elementsMap,
-  );
+  const distance = distanceToBindableElement(bindableElement, point);
   const bindDistance = maxBindingGap(
     bindableElement,
     bindableElement.width,
@@ -781,9 +774,7 @@ export const bindPointToSnapToElementOutline = (
     const isVertical =
       compareHeading(heading, HEADING_LEFT) ||
       compareHeading(heading, HEADING_RIGHT);
-    const dist = Math.abs(
-      distanceToBindableElement(bindableElement, p, elementsMap),
-    );
+    const dist = Math.abs(distanceToBindableElement(bindableElement, p));
     const isInner = isVertical
       ? dist < bindableElement.width * -0.1
       : dist < bindableElement.height * -0.1;
@@ -937,7 +928,7 @@ export const snapToMid = (
 ): GlobalPoint => {
   const { x, y, width, height, angle } = element;
   const center = point<GlobalPoint>(x + width / 2 - 0.1, y + height / 2 - 0.1);
-  const nonRotated = pointRotateRads(p, center, -angle as Radians);
+  const nonRotated = pointRotateRads(p, center, radians(-angle));
 
   // snap-to-center point is adaptive to element size, but we don't want to go
   // above and below certain px distance
@@ -1123,7 +1114,7 @@ export const calculateFixedPointForElbowArrowBinding = (
   const nonRotatedSnappedGlobalPoint = pointRotateRads(
     snappedPoint,
     globalMidPoint,
-    -hoveredElement.angle as Radians,
+    radians(-hoveredElement.angle),
   );
 
   return {
@@ -1351,148 +1342,6 @@ export const maxBindingGap = (
   return Math.max(16, Math.min(0.25 * smallerDimension, 32));
 };
 
-export const distanceToBindableElement = (
-  element: ExcalidrawBindableElement,
-  point: GlobalPoint,
-  elementsMap: ElementsMap,
-): number => {
-  switch (element.type) {
-    case "rectangle":
-    case "image":
-    case "text":
-    case "iframe":
-    case "embeddable":
-    case "frame":
-    case "magicframe":
-      return distanceToRectangle(element, point, elementsMap);
-    case "diamond":
-      return distanceToDiamond(element, point, elementsMap);
-    case "ellipse":
-      return distanceToEllipse(element, point, elementsMap);
-  }
-};
-
-const distanceToRectangle = (
-  element: ExcalidrawRectanguloidElement,
-  p: GlobalPoint,
-  elementsMap: ElementsMap,
-): number => {
-  const [, pointRel, hwidth, hheight] = pointRelativeToElement(
-    element,
-    p,
-    elementsMap,
-  );
-  return Math.max(
-    GAPoint.distanceToLine(pointRel, GALine.equation(0, 1, -hheight)),
-    GAPoint.distanceToLine(pointRel, GALine.equation(1, 0, -hwidth)),
-  );
-};
-
-const distanceToDiamond = (
-  element: ExcalidrawDiamondElement,
-  point: GlobalPoint,
-  elementsMap: ElementsMap,
-): number => {
-  const [, pointRel, hwidth, hheight] = pointRelativeToElement(
-    element,
-    point,
-    elementsMap,
-  );
-  const side = GALine.equation(hheight, hwidth, -hheight * hwidth);
-  return GAPoint.distanceToLine(pointRel, side);
-};
-
-const distanceToEllipse = (
-  element: ExcalidrawEllipseElement,
-  point: GlobalPoint,
-  elementsMap: ElementsMap,
-): number => {
-  const [pointRel, tangent] = ellipseParamsForTest(element, point, elementsMap);
-  return -GALine.sign(tangent) * GAPoint.distanceToLine(pointRel, tangent);
-};
-
-const ellipseParamsForTest = (
-  element: ExcalidrawEllipseElement,
-  point: GlobalPoint,
-  elementsMap: ElementsMap,
-): [GA.Point, GA.Line] => {
-  const [, pointRel, hwidth, hheight] = pointRelativeToElement(
-    element,
-    point,
-    elementsMap,
-  );
-  const [px, py] = GAPoint.toTuple(pointRel);
-
-  // We're working in positive quadrant, so start with `t = 45deg`, `tx=cos(t)`
-  let tx = 0.707;
-  let ty = 0.707;
-
-  const a = hwidth;
-  const b = hheight;
-
-  // This is a numerical method to find the params tx, ty at which
-  // the ellipse has the closest point to the given point
-  [0, 1, 2, 3].forEach((_) => {
-    const xx = a * tx;
-    const yy = b * ty;
-
-    const ex = ((a * a - b * b) * tx ** 3) / a;
-    const ey = ((b * b - a * a) * ty ** 3) / b;
-
-    const rx = xx - ex;
-    const ry = yy - ey;
-
-    const qx = px - ex;
-    const qy = py - ey;
-
-    const r = Math.hypot(ry, rx);
-    const q = Math.hypot(qy, qx);
-
-    tx = Math.min(1, Math.max(0, ((qx * r) / q + ex) / a));
-    ty = Math.min(1, Math.max(0, ((qy * r) / q + ey) / b));
-    const t = Math.hypot(ty, tx);
-    tx /= t;
-    ty /= t;
-  });
-
-  const closestPoint = GA.point(a * tx, b * ty);
-
-  const tangent = GALine.orthogonalThrough(pointRel, closestPoint);
-  return [pointRel, tangent];
-};
-
-// Returns:
-//   1. the point relative to the elements (x, y) position
-//   2. the point relative to the element's center with positive (x, y)
-//   3. half element width
-//   4. half element height
-//
-// Note that for linear elements the (x, y) position is not at the
-// top right corner of their boundary.
-//
-// Rectangles, diamonds and ellipses are symmetrical over axes,
-// and other elements have a rectangular boundary,
-// so we only need to perform hit tests for the positive quadrant.
-const pointRelativeToElement = (
-  element: ExcalidrawElement,
-  pointTuple: GlobalPoint,
-  elementsMap: ElementsMap,
-): [GA.Point, GA.Point, number, number] => {
-  const point = GAPoint.from(pointTuple);
-  const [x1, y1, x2, y2] = getElementAbsoluteCoords(element, elementsMap);
-  const center = coordsCenter(x1, y1, x2, y2);
-  // GA has angle orientation opposite to `rotate`
-  const rotate = GATransform.rotation(center, element.angle);
-  const pointRotated = GATransform.apply(rotate, point);
-  const pointRelToCenter = GA.sub(pointRotated, GADirection.from(center));
-  const pointRelToCenterAbs = GAPoint.abs(pointRelToCenter);
-  const elementPos = GA.offset(element.x, element.y);
-  const pointRelToPos = GA.sub(pointRotated, elementPos);
-  const halfWidth = (x2 - x1) / 2;
-  const halfHeight = (y2 - y1) / 2;
-  return [pointRelToPos, pointRelToCenterAbs, halfWidth, halfHeight];
-};
-
 const relativizationToElementCenter = (
   element: ExcalidrawElement,
   elementsMap: ElementsMap,

packages/excalidraw/element/distance.ts

@@ -0,0 +1,210 @@
+import type { GlobalPoint, Segment } from "../../math";
+import {
+  arc,
+  arcDistanceFromPoint,
+  ellipse,
+  ellipseDistanceFromPoint,
+  ellipseSegmentInterceptPoints,
+  point,
+  pointRotateRads,
+  radians,
+  rectangle,
+  segment,
+  segmentDistanceToPoint,
+} from "../../math";
+import { getCornerRadius } from "../shapes";
+import type {
+  ExcalidrawBindableElement,
+  ExcalidrawDiamondElement,
+  ExcalidrawEllipseElement,
+  ExcalidrawRectanguloidElement,
+} from "./types";
+
+export const distanceToBindableElement = (
+  element: ExcalidrawBindableElement,
+  point: GlobalPoint,
+): number => {
+  switch (element.type) {
+    case "rectangle":
+    case "image":
+    case "text":
+    case "iframe":
+    case "embeddable":
+    case "frame":
+    case "magicframe":
+      return distanceToRectangleElement(element, point);
+    case "diamond":
+      return distanceToDiamondElement(element, point);
+    case "ellipse":
+      return distanceToEllipseElement(element, point);
+  }
+};
+
+export const distanceToRectangleElement = (
+  element: ExcalidrawRectanguloidElement,
+  p: GlobalPoint,
+) => {
+  const center = point(
+    element.x + element.width / 2,
+    element.y + element.height / 2,
+  );
+  const r = rectangle(
+    pointRotateRads(
+      point(element.x, element.y),
+      center,
+      radians(element.angle),
+    ),
+    pointRotateRads(
+      point(element.x + element.width, element.y + element.height),
+      center,
+      radians(element.angle),
+    ),
+  );
+  const roundness = getCornerRadius(
+    Math.min(element.width, element.height),
+    element,
+  );
+  const rotatedPoint = pointRotateRads(p, center, element.angle);
+  const sideDistances = [
+    segment(
+      point(r[0][0] + roundness, r[0][1]),
+      point(r[1][0] - roundness, r[0][1]),
+    ),
+    segment(
+      point(r[1][0], r[0][1] + roundness),
+      point(r[1][0], r[1][1] - roundness),
+    ),
+    segment(
+      point(r[1][0] - roundness, r[1][1]),
+      point(r[0][0] + roundness, r[1][1]),
+    ),
+    segment(
+      point(r[0][0], r[1][1] - roundness),
+      point(r[0][0], r[0][1] + roundness),
+    ),
+  ].map((s) => segmentDistanceToPoint(rotatedPoint, s));
+  const cornerDistances =
+    roundness > 0
+      ? [
+          arc(
+            point(r[0][0] + roundness, r[0][1] + roundness),
+            roundness,
+            radians(Math.PI),
+            radians((3 / 4) * Math.PI),
+          ),
+          arc(
+            point(r[1][0] - roundness, r[0][1] + roundness),
+            roundness,
+            radians((3 / 4) * Math.PI),
+            radians(0),
+          ),
+          arc(
+            point(r[1][0] - roundness, r[1][1] - roundness),
+            roundness,
+            radians(0),
+            radians((1 / 2) * Math.PI),
+          ),
+          arc(
+            point(r[0][0] + roundness, r[1][1] - roundness),
+            roundness,
+            radians((1 / 2) * Math.PI),
+            radians(Math.PI),
+          ),
+        ].map((a) => arcDistanceFromPoint(a, rotatedPoint))
+      : [];
+
+  return Math.min(...[...sideDistances, ...cornerDistances]);
+};
+
+const roundedCutoffSegment = (
+  s: Segment<GlobalPoint>,
+  r: number,
+): Segment<GlobalPoint> => {
+  const t = (4 * r) / Math.sqrt(2);
+
+  return segment(
+    ellipseSegmentInterceptPoints(ellipse(s[0], radians(0), t, t), s)[0],
+    ellipseSegmentInterceptPoints(ellipse(s[1], radians(0), t, t), s)[0],
+  );
+};
+
+const diamondArc = (left: GlobalPoint, right: GlobalPoint, r: number) => {
+  const c = point((left[0] + right[0]) / 2, left[1]);
+
+  return arc(
+    c,
+    r,
+    radians(Math.asin((left[1] - c[1]) / r)),
+    radians(Math.asin((right[1] - c[1]) / r)),
+  );
+};
+
+export const distanceToDiamondElement = (
+  element: ExcalidrawDiamondElement,
+  p: GlobalPoint,
+): number => {
+  const center = point<GlobalPoint>(
+    element.x + element.width / 2,
+    element.y + element.height / 2,
+  );
+  const roundness = getCornerRadius(
+    Math.min(element.width, element.height),
+    element,
+  );
+  const rotatedPoint = pointRotateRads(p, center, element.angle);
+  const top = pointRotateRads<GlobalPoint>(
+    point(element.x + element.width / 2, element.y),
+    center,
+    element.angle,
+  );
+  const right = pointRotateRads<GlobalPoint>(
+    point(element.x + element.width, element.y + element.height / 2),
+    center,
+    element.angle,
+  );
+  const bottom = pointRotateRads<GlobalPoint>(
+    point(element.x + element.width / 2, element.y + element.height),
+    center,
+    element.angle,
+  );
+  const left = pointRotateRads<GlobalPoint>(
+    point(element.x, element.y + element.height / 2),
+    center,
+    element.angle,
+  );
+  const topRight = roundedCutoffSegment(segment(top, right), roundness);
+  const bottomRight = roundedCutoffSegment(segment(right, bottom), roundness);
+  const bottomLeft = roundedCutoffSegment(segment(bottom, left), roundness);
+  const topLeft = roundedCutoffSegment(segment(left, top), roundness);
+
+  return Math.min(
+    ...[
+      ...[topRight, bottomRight, bottomLeft, topLeft].map((s) =>
+        segmentDistanceToPoint(rotatedPoint, s),
+      ),
+      ...(roundness > 0
+        ? [
+            diamondArc(topLeft[1], topRight[0], roundness),
+            diamondArc(topRight[1], bottomRight[0], roundness),
+            diamondArc(bottomRight[1], bottomLeft[0], roundness),
+            diamondArc(bottomLeft[1], topLeft[0], roundness),
+          ].map((a) => arcDistanceFromPoint(a, rotatedPoint))
+        : []),
+    ],
+  );
+};
+
+export const distanceToEllipseElement = (
+  element: ExcalidrawEllipseElement,
+  p: GlobalPoint,
+): number => {
+  return ellipseDistanceFromPoint(
+    p,
+    ellipse(
+      point(element.x + element.width / 2, element.y + element.height / 2),
+      element.angle,
+      element.width / 2,
+      element.height / 2,
+    ),
+  );
+};

packages/excalidraw/shapes.tsx

@@ -140,10 +140,10 @@ export const findShapeByKey = (key: string) => {
  * get the pure geometric shape of an excalidraw element
  * which is then used for hit detection
  */
-export const getElementShape = <Point extends GlobalPoint | LocalPoint>(
+export const getElementShape = (
   element: ExcalidrawElement,
   elementsMap: ElementsMap,
-): GeometricShape<Point> => {
+): GeometricShape<GlobalPoint> => {
   switch (element.type) {
     case "rectangle":
     case "diamond":
@@ -163,16 +163,16 @@ export const getElementShape = <Point extends GlobalPoint | LocalPoint>(
       const [, , , , cx, cy] = getElementAbsoluteCoords(element, elementsMap);
 
       return shouldTestInside(element)
-        ? getClosedCurveShape<Point>(
+        ? getClosedCurveShape<GlobalPoint>(
             element,
             roughShape,
-            point<Point>(element.x, element.y),
+            point<GlobalPoint>(element.x, element.y),
             element.angle,
             point(cx, cy),
           )
-        : getCurveShape<Point>(
+        : getCurveShape<GlobalPoint>(
             roughShape,
-            point<Point>(element.x, element.y),
+            point<GlobalPoint>(element.x, element.y),
             element.angle,
             point(cx, cy),
           );
@@ -192,10 +192,10 @@ export const getElementShape = <Point extends GlobalPoint | LocalPoint>(
   }
 };
 
-export const getBoundTextShape = <Point extends GlobalPoint | LocalPoint>(
+export const getBoundTextShape = (
   element: ExcalidrawElement,
   elementsMap: ElementsMap,
-): GeometricShape<Point> | null => {
+): GeometricShape<GlobalPoint> | null => {
   const boundTextElement = getBoundTextElement(element, elementsMap);
 
   if (boundTextElement) {

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;