feat: Attempt simple chaining of ovoids

Signed-off-by: Mark Tolmacs <mark@lazycat.hu>

excalidraw-app/components/DebugCanvas.tsx

@@ -75,6 +75,39 @@ const renderCubicBezier = (
   context.restore();
 };
 
+const isPolygon = (data: any): data is GlobalPoint[] => {
+  return (
+    Array.isArray(data) &&
+    data.every((point) => Array.isArray(point) && point.length === 2)
+  );
+};
+
+const renderPolygon = (
+  context: CanvasRenderingContext2D,
+  zoom: number,
+  points: GlobalPoint[],
+  color: string,
+) => {
+  if (points.length < 3) {
+    return;
+  }
+
+  context.save();
+  context.fillStyle = color;
+  context.globalAlpha = 0.3;
+  context.beginPath();
+  context.moveTo(points[0][0] * zoom, points[0][1] * zoom);
+  for (let i = 1; i < points.length; i++) {
+    context.lineTo(points[i][0] * zoom, points[i][1] * zoom);
+  }
+  context.closePath();
+  context.fill();
+  context.globalAlpha = 1.0;
+  context.strokeStyle = color;
+  context.stroke();
+  context.restore();
+};
+
 const renderOrigin = (context: CanvasRenderingContext2D, zoom: number) => {
   context.strokeStyle = "#888";
   context.save();
@@ -280,6 +313,14 @@ const render = (
           el.color,
         );
         break;
+      case isPolygon(el.data):
+        renderPolygon(
+          context,
+          appState.zoom.value,
+          el.data as GlobalPoint[],
+          el.color,
+        );
+        break;
       default:
         throw new Error(`Unknown element type ${JSON.stringify(el)}`);
     }

packages/common/src/visualdebug.ts

@@ -21,9 +21,11 @@ declare global {
   }
 }
 
+export type Polygon = GlobalPoint[];
+
 export type DebugElement = {
   color: string;
-  data: LineSegment<GlobalPoint> | Curve<GlobalPoint>;
+  data: LineSegment<GlobalPoint> | Curve<GlobalPoint> | Polygon;
   permanent: boolean;
 };
 
@@ -129,6 +131,20 @@ export const debugDrawBounds = (
   );
 };
 
+export const debugDrawPolygon = (
+  points: GlobalPoint[],
+  opts?: {
+    color?: string;
+    permanent?: boolean;
+  },
+) => {
+  addToCurrentFrame({
+    color: opts?.color ?? "blue",
+    data: points,
+    permanent: !!opts?.permanent,
+  });
+};
+
 export const debugDrawPoints = (
   {
     x,

packages/element/src/freedraw.ts

@@ -0,0 +1,546 @@
+import {
+  pointFrom,
+  pointDistance,
+  type LocalPoint,
+  vectorFromPoint,
+  vectorNormalize,
+  lineSegment,
+  type GlobalPoint,
+  type Polygon,
+  polygonFromPoints,
+} from "@excalidraw/math";
+import { debugDrawLine, debugDrawPolygon } from "@excalidraw/common";
+
+import type { ExcalidrawFreeDrawElement } from "./types";
+
+// Number of segments to approximate each semicircular cap
+const CAP_SEGMENTS = 20;
+
+// Minimum radius to avoid degenerate shapes
+const MIN_RADIUS = 0.05;
+
+// Pressure to radius multiplier (scaled by strokeWidth)
+const PRESSURE_RADIUS_MULTIPLIER = 2.0;
+
+// Minimum distance between points to avoid numerical instability
+const MIN_POINT_DISTANCE = 0.001;
+
+// Epsilon for filtering near-duplicate points in polygons
+const EPSILON = 0.01;
+
+// Simple union implementation taking advantage of the following facts:
+// - The ovoids are generated in sequence along the stroke path
+// - Each ovoid overlaps only with its immediate neighbors
+// - The ovoids are convex shapes
+
+// Therefore, we can simply stitch together the outer edges of the ovoids
+// by taking the first half of the first ovoid and the second half of the last ovoid,
+// and connecting them with the outer edges of the intermediate ovoids. The overlapping
+// ovoid caps are always the same radius at the shared points, so they align perfectly.
+// It should be easy to find the closest point to the side of the previous side segment and
+// one of the closest points on the next ovoid's start cap.
+function chainOvoidsIntoSinglePolygon<P extends LocalPoint | GlobalPoint>(
+  records: {
+    polygon: Polygon<P>;
+    firstPoint: P;
+    secondPoint: P;
+  }[],
+): Polygon<P> | null {
+  if (records.length === 0) {
+    return null;
+  }
+
+  if (records.length === 1) {
+    return records[0].polygon;
+  }
+
+  const capPointCount = CAP_SEGMENTS + 1;
+
+  const isClosedPolygon = (points: P[]) => {
+    if (points.length < 2) {
+      return false;
+    }
+    const first = points[0];
+    const last = points[points.length - 1];
+    return first[0] === last[0] && first[1] === last[1];
+  };
+
+  const openPolygon = (points: P[]) =>
+    isClosedPolygon(points) ? points.slice(0, -1) : points.slice();
+
+  const distanceSq = (a: P, b: P) => {
+    const dx = a[0] - b[0];
+    const dy = a[1] - b[1];
+    return dx * dx + dy * dy;
+  };
+
+  const distanceToSegmentSq = (p: P, a: P, b: P) => {
+    const abx = b[0] - a[0];
+    const aby = b[1] - a[1];
+    const apx = p[0] - a[0];
+    const apy = p[1] - a[1];
+    const abLenSq = abx * abx + aby * aby;
+
+    if (abLenSq === 0) {
+      return distanceSq(p, a);
+    }
+
+    const t = Math.max(0, Math.min(1, (apx * abx + apy * aby) / abLenSq));
+    const closest = pointFrom<P>(a[0] + abx * t, a[1] + aby * t);
+    return distanceSq(p, closest);
+  };
+
+  const closestIndexToSegment = (points: P[], a: P, b: P) => {
+    let bestIndex = 0;
+    let bestDistance = Number.POSITIVE_INFINITY;
+
+    for (let i = 0; i < points.length; i++) {
+      const dist = distanceToSegmentSq(points[i], a, b);
+      if (dist < bestDistance) {
+        bestDistance = dist;
+        bestIndex = i;
+      }
+    }
+
+    return bestIndex;
+  };
+
+  const pushIfDistinct = (points: P[], point: P) => {
+    if (points.length === 0) {
+      points.push(point);
+      return;
+    }
+    if (distanceSq(points[points.length - 1], point) > EPSILON * EPSILON) {
+      points.push(point);
+    }
+  };
+
+  const ovoids = records.map((record) => {
+    const open = openPolygon(record.polygon);
+
+    if (open.length < capPointCount * 2) {
+      return {
+        cap1: open,
+        cap2: [] as P[],
+        p1Right: open[0],
+        p1Left: open[open.length - 1],
+        p2Left: open[0],
+        p2Right: open[open.length - 1],
+      };
+    }
+
+    const cap1 = open.slice(0, capPointCount);
+    const cap2 = open.slice(capPointCount, capPointCount * 2);
+
+    return {
+      cap1,
+      cap2,
+      p1Right: cap1[0],
+      p1Left: cap1[cap1.length - 1],
+      p2Left: cap2[0],
+      p2Right: cap2[cap2.length - 1],
+    };
+  });
+
+  const leftChain: P[] = [];
+  const rightChain: P[] = [];
+
+  ovoids[0].cap1.forEach((point) => pushIfDistinct(leftChain, point));
+  pushIfDistinct(rightChain, ovoids[0].p1Right);
+
+  for (let i = 0; i < ovoids.length; i++) {
+    const current = ovoids[i];
+
+    pushIfDistinct(leftChain, current.p2Left);
+    pushIfDistinct(rightChain, current.p2Right);
+
+    if (i + 1 >= ovoids.length) {
+      continue;
+    }
+
+    const next = ovoids[i + 1];
+
+    const leftIndex = closestIndexToSegment(
+      next.cap1,
+      current.p1Left,
+      current.p2Left,
+    );
+
+    for (let j = leftIndex; j < next.cap1.length; j++) {
+      pushIfDistinct(leftChain, next.cap1[j]);
+    }
+
+    const rightIndex = closestIndexToSegment(
+      next.cap1,
+      current.p1Right,
+      current.p2Right,
+    );
+
+    for (let j = rightIndex; j >= 0; j--) {
+      pushIfDistinct(rightChain, next.cap1[j]);
+    }
+  }
+
+  const lastOvoid = ovoids[ovoids.length - 1];
+  lastOvoid.cap2.forEach((point) => pushIfDistinct(leftChain, point));
+
+  const rightChainReversed = rightChain.slice(0, -1).reverse();
+  const outline = filterNearDuplicates<P>([
+    ...leftChain,
+    ...rightChainReversed,
+  ]);
+
+  return polygonFromPoints<P>(outline);
+}
+
+/**
+ * Compute the radius for a point based on pressure and strokeWidth.
+ * Pressure is typically in [0, 1] range, default to 0.5 if simulating.
+ */
+function getRadiusForPressure(pressure: number, strokeWidth: number): number {
+  return Math.max(
+    MIN_RADIUS,
+    pressure * strokeWidth * PRESSURE_RADIUS_MULTIPLIER,
+  );
+}
+
+/**
+ * Generate points along a semicircular arc (dome/cap).
+ * The arc goes from startAngle to endAngle (counterclockwise).
+ *
+ * @param center - Center point of the arc
+ * @param radius - Radius of the arc
+ * @param startAngle - Start angle in radians
+ * @param endAngle - End angle in radians (counterclockwise from start)
+ * @param segments - Number of segments to divide the arc into
+ * @returns Array of points along the arc
+ */
+function generateArcPoints<P extends LocalPoint | GlobalPoint>(
+  center: LocalPoint,
+  radius: number,
+  startAngle: number,
+  endAngle: number,
+  segments: number,
+): P[] {
+  const points: P[] = [];
+  const angleStep = (endAngle - startAngle) / segments;
+
+  for (let i = 0; i <= segments; i++) {
+    const angle = startAngle + i * angleStep;
+    points.push(
+      pointFrom<P>(
+        center[0] + radius * Math.cos(angle),
+        center[1] + radius * Math.sin(angle),
+      ),
+    );
+  }
+
+  return points;
+}
+
+/**
+ * Create an ovoid shape between two consecutive points.
+ * The ovoid consists of:
+ * - A semicircular cap at the first point (facing away from point 2)
+ * - A semicircular cap at the second point (facing away from point 1)
+ * - Connecting lines (tangent lines between the two circles)
+ *
+ * @param p1 - First point
+ * @param r1 - Radius at first point (from pressure)
+ * @param p2 - Second point
+ * @param r2 - Radius at second point (from pressure)
+ * @param forcePerpendicularCap1 - Force cap1 to be perpendicular (for stroke start)
+ * @param forcePerpendicularCap2 - Force cap2 to be perpendicular (for stroke end)
+ * @returns Array of points forming the ovoid polygon
+ */
+function createOvoid<P extends LocalPoint | GlobalPoint>(
+  p1: LocalPoint,
+  r1: number,
+  p2: LocalPoint,
+  r2: number,
+  forcePerpendicularCap1: boolean = false,
+  forcePerpendicularCap2: boolean = false,
+): Polygon<P> {
+  const dist = pointDistance(p1, p2);
+
+  // If points are too close, create a circle at the midpoint
+  if (dist < MIN_POINT_DISTANCE) {
+    const avgRadius = (r1 + r2) / 2;
+    return polygonFromPoints<P>(
+      generateArcPoints(p1, avgRadius, 0, Math.PI * 2, CAP_SEGMENTS * 2),
+    );
+  }
+
+  // Direction vector from p1 to p2
+  const dirVec = vectorFromPoint(p2, p1);
+  const normalizedDir = vectorNormalize(dirVec);
+
+  // Calculate the angle of the direction vector
+  const baseAngle = Math.atan2(normalizedDir[1], normalizedDir[0]);
+
+  // For connecting the circles with tangent lines when radii differ,
+  // we need to compute the tangent points
+  // When r1 != r2, the tangent lines are not perpendicular to the center line
+
+  // Tangent angle offset (when radii differ)
+  const radiusDiff = r1 - r2;
+  const tangentAngleOffset =
+    dist > Math.abs(radiusDiff) ? Math.asin(radiusDiff / dist) : 0;
+
+  // Compute tangent points on each circle
+  // The perpendicular offset needs to be adjusted for the tangent angle
+  const tangentPerpAngle = baseAngle + Math.PI / 2 + tangentAngleOffset;
+  const purePerpAngle = baseAngle + Math.PI / 2;
+
+  // Cap at p1 (semicircle facing AWAY from p2, i.e., toward baseAngle + PI)
+  // Use perpendicular cap for stroke start, otherwise use tangent-adjusted
+  const p1PerpAngle = forcePerpendicularCap1 ? purePerpAngle : tangentPerpAngle;
+  const p1RightAngle = p1PerpAngle;
+  const p1LeftAngle = p1PerpAngle + Math.PI;
+  const cap1Points = generateArcPoints<P>(
+    p1,
+    r1,
+    p1RightAngle,
+    p1LeftAngle,
+    CAP_SEGMENTS,
+  );
+
+  // Cap at p2 (semicircle facing AWAY from p1, i.e., toward baseAngle)
+  // Use perpendicular cap for stroke end, otherwise use tangent-adjusted
+  const p2PerpAngle = forcePerpendicularCap2 ? purePerpAngle : tangentPerpAngle;
+  const p2LeftAngle = p2PerpAngle + Math.PI;
+  const p2RightAngle = p2LeftAngle + Math.PI;
+  const cap2Points = generateArcPoints<P>(
+    p2,
+    r2,
+    p2LeftAngle,
+    p2RightAngle,
+    CAP_SEGMENTS,
+  );
+
+  // Assemble the ovoid polygon:
+  // cap1 goes around the back of p1, cap2 goes around the front of p2
+  // The arc endpoints naturally connect with the tangent lines
+  const ovoidPoints: P[] = [
+    ...cap1Points, // p1's back cap
+    ...cap2Points, // p2's front cap
+  ];
+
+  // Filter out near-duplicate consecutive points to avoid numerical issues
+  return polygonFromPoints<P>(filterNearDuplicates<P>(ovoidPoints));
+}
+
+/**
+ * Filter out consecutive points that are too close together.
+ * This prevents numerical instability in polygon boolean operations.
+ */
+function filterNearDuplicates<P extends LocalPoint | GlobalPoint>(
+  points: P[],
+): P[] {
+  if (points.length < 2) {
+    return points;
+  }
+
+  const filtered: P[] = [points[0]];
+
+  for (let i = 1; i < points.length; i++) {
+    const prev = filtered[filtered.length - 1];
+    const curr = points[i];
+    const dx = curr[0] - prev[0];
+    const dy = curr[1] - prev[1];
+    const distSq = dx * dx + dy * dy;
+
+    // Only add if far enough from previous point
+    if (distSq > EPSILON * EPSILON) {
+      filtered.push(curr);
+    }
+  }
+
+  // Also check if last point is too close to first point
+  if (filtered.length > 2) {
+    const first = filtered[0];
+    const last = filtered[filtered.length - 1];
+    const dx = last[0] - first[0];
+    const dy = last[1] - first[1];
+    const distSq = dx * dx + dy * dy;
+
+    if (distSq < EPSILON * EPSILON) {
+      filtered.pop();
+    }
+  }
+
+  return filtered.length >= 3 ? filtered : points;
+}
+
+/**
+ * Generate the outline of a freedraw element using the ovoid-union approach.
+ *
+ * This creates ovoid shapes between each consecutive pair of points,
+ * where each ovoid is defined by:
+ * - Semicircular caps at each point (radius based on pressure)
+ * - Connecting tangent lines between the caps
+ *
+ * All ovoids are then unioned together to form the final outline.
+ *
+ * @param element - The freedraw element to generate outline for
+ * @returns Array of [x, y] points representing the outline polygon
+ */
+export function generateFreeDrawOvoidOutline(
+  element: ExcalidrawFreeDrawElement,
+): [number, number][] {
+  const { x, y, points, pressures, simulatePressure, strokeWidth } = element;
+
+  // Debug draw the raw segments from the freedraw element points
+  const colors = ["red", "green", "blue", "orange", "purple"];
+
+  points.forEach((pt, i) => {
+    if (i === points.length - 1) {
+      return;
+    }
+    debugDrawLine(
+      lineSegment(
+        pointFrom<GlobalPoint>(x + pt[0], y + pt[1]),
+        pointFrom<GlobalPoint>(x + points[i + 1][0], y + points[i + 1][1]),
+      ),
+      {
+        color: colors[i % colors.length],
+        permanent: true,
+      },
+    );
+  });
+
+  if (points.length === 0) {
+    return [];
+  }
+
+  // Single point: just return a circle
+  if (points.length === 1) {
+    const pressure = simulatePressure ? 0.5 : pressures[0] ?? 0.5;
+    const radius = getRadiusForPressure(pressure, strokeWidth);
+    const circlePoints = generateArcPoints(
+      points[0] as LocalPoint,
+      radius,
+      0,
+      Math.PI * 2,
+      CAP_SEGMENTS * 2,
+    );
+    return circlePoints.map((p) => [p[0], p[1]]);
+  }
+
+  // Generate ovoids for each consecutive pair of points
+  const ovoids: Polygon<LocalPoint>[] = [];
+
+  for (let i = 0; i < points.length - 1; i++) {
+    const p1 = points[i] as LocalPoint;
+    const p2 = points[i + 1] as LocalPoint;
+
+    // Get pressures (use 0.5 as default when simulating)
+    const pressure1 = simulatePressure ? 0.5 : pressures[i] ?? 0.5;
+    const pressure2 = simulatePressure ? 0.5 : pressures[i + 1] ?? 0.5;
+
+    const r1 = getRadiusForPressure(pressure1, strokeWidth);
+    const r2 = getRadiusForPressure(pressure2, strokeWidth);
+
+    // Force perpendicular caps at stroke endpoints
+    const isFirstSegment = i === 0;
+    const isLastSegment = i === points.length - 2;
+
+    const ovoidPoints = createOvoid<LocalPoint>(
+      p1,
+      r1,
+      p2,
+      r2,
+      isFirstSegment, // Force perpendicular cap at stroke start
+      isLastSegment, // Force perpendicular cap at stroke end
+    );
+
+    // Draw the ovoid with different colors for debugging
+    debugDrawPolygon(
+      ovoidPoints.map((p) => pointFrom<GlobalPoint>(x + p[0], y + p[1])),
+      {
+        color: colors[i % colors.length],
+        permanent: true,
+      },
+    );
+
+    if (ovoidPoints.length >= 3) {
+      ovoids.push(ovoidPoints);
+    }
+  }
+
+  if (ovoids.length === 0) {
+    return [];
+  }
+
+  // Union all ovoids together
+  const result = chainOvoidsIntoSinglePolygon<LocalPoint>(
+    ovoids.map((poly, i) => ({
+      polygon: poly,
+      firstPoint: points[i],
+      secondPoint: points[i + 1],
+    })),
+  );
+
+  if (result === null) {
+    return [];
+  }
+
+  if (result === null) {
+    return [];
+  }
+
+  // Return the first (outer) polygon
+  return result;
+}
+
+/**
+ * Convert the ovoid outline to an SVG path string. Uses quadratic curves
+ * for smoothing.
+ */
+export function generateFreeDrawOvoidSvgPath(
+  element: ExcalidrawFreeDrawElement,
+): string {
+  const points = generateFreeDrawOvoidOutline(element);
+
+  if (points.length === 0) {
+    console.warn("No outline points generated for freedraw element");
+    return "";
+  }
+
+  if (points.length < 3) {
+    console.warn("Not enough outline points to form a closed path");
+    return "";
+  }
+
+  // Use a similar approach to the original getSvgPathFromStroke
+  // but with the ovoid-generated points
+  const med = (a: number[], b: number[]) => [
+    (a[0] + b[0]) / 2,
+    (a[1] + b[1]) / 2,
+  ];
+
+  const pathData = points
+    // Build a closed, smoothed SVG path from the outline polygon
+    .reduce(
+      (acc: (string | number[])[], point, i, arr) => {
+        if (i === points.length - 1) {
+          // For the last point, add a line-to ("L") back to the first point and close
+          // ("Z").
+          acc.push(point, med(point, arr[0]), "L", arr[0], "Z");
+        } else {
+          // Use a single quadratic command ("Q") and then emit point + midpoint pairs
+          // so each segment curves through the current point toward the midpoint of
+          // the next segment.
+          acc.push(point, med(point, arr[i + 1]));
+        }
+        return acc;
+      },
+      // Start with a move-to ("M") to the first point.
+      ["M", points[0], "Q"],
+    )
+    .join(" ")
+    // Trim excessive float precision to keep the path string compact/stable.
+    .replace(/(\s?[A-Z]?,?-?[0-9]*\.[0-9]{0,2})(([0-9]|e|-)*)/g, "$1");
+
+  return pathData;
+}

packages/element/src/shape.ts

@@ -63,6 +63,7 @@ import {
   getElementAbsoluteCoords,
 } from "./bounds";
 import { shouldTestInside } from "./collision";
+import { generateFreeDrawOvoidSvgPath } from "./freedraw";
 
 import type {
   ExcalidrawElement,
@@ -78,6 +79,10 @@ import type {
 import type { Drawable, Options } from "roughjs/bin/core";
 import type { Point as RoughPoint } from "roughjs/bin/geometry";
 
+// Toggle between old (perfect-freehand) and new (ovoid-union) freedraw rendering
+// Set to true to use the new ovoid-based implementation
+export const USE_NEW_FREEDRAW_RENDERER = true;
+
 export class ShapeCache {
   private static rg = new RoughGenerator();
   private static cache = new WeakMap<
@@ -852,8 +857,12 @@ const _generateElementShape = (
         );
       }
 
-      // (2) stroke
-      shapes.push(getFreeDrawSvgPath(element));
+      // (2) stroke - use new ovoid renderer or legacy perfect-freehand
+      if (USE_NEW_FREEDRAW_RENDERER) {
+        shapes.push(generateFreeDrawOvoidSvgPath(element) as SVGPathString);
+      } else {
+        shapes.push(getFreeDrawSvgPath(element));
+      }
 
       return shapes;
     }

yarn.lock

@@ -7882,6 +7882,14 @@ points-on-path@^0.2.1:
     path-data-parser "0.1.0"
     points-on-curve "0.2.0"
 
+polygon-clipping@^0.15.7:
+  version "0.15.7"
+  resolved "https://registry.yarnpkg.com/polygon-clipping/-/polygon-clipping-0.15.7.tgz#3823ca1e372566f350795ce9dd9a7b19e97bdaad"
+  integrity sha512-nhfdr83ECBg6xtqOAJab1tbksbBAOMUltN60bU+llHVOL0e5Onm1WpAXXWXVB39L8AJFssoIhEVuy/S90MmotA==
+  dependencies:
+    robust-predicates "^3.0.2"
+    splaytree "^3.1.0"
+
 portfinder@^1.0.28:
   version "1.0.33"
   resolved "https://registry.yarnpkg.com/portfinder/-/portfinder-1.0.33.tgz#03dbc51455aa8f83ad9fb86af8345e063bb51101"
@@ -8761,6 +8769,11 @@ sourcemap-codec@^1.4.8:
   resolved "https://registry.yarnpkg.com/sourcemap-codec/-/sourcemap-codec-1.4.8.tgz#ea804bd94857402e6992d05a38ef1ae35a9ab4c4"
   integrity sha512-9NykojV5Uih4lgo5So5dtw+f0JgJX30KCNI8gwhz2J9A15wD0Ml6tjHKwf6fTSa6fAdVBdZeNOs9eJ71qCk8vA==
 
+splaytree@^3.1.0:
+  version "3.2.3"
+  resolved "https://registry.yarnpkg.com/splaytree/-/splaytree-3.2.3.tgz#5e4836bc54cc939344bba8dc826f82fbde453106"
+  integrity sha512-7OXrNWzy6CK+r7Ch9OLPBDTKfB6XlWHjX4P0RU5B3IgFuWPeYN0XtRtlexGRjgbQxpfaUve6jTAwBGWuGntz/w==
+
 split.js@^1.6.0:
   version "1.6.5"
   resolved "https://registry.yarnpkg.com/split.js/-/split.js-1.6.5.tgz#f7f61da1044c9984cb42947df4de4fadb5a3f300"