three point generation functions

src/lib/shapes/points.ts

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+export interface Point {
+    x: number;
+    y: number;
+}
+
+const DEFAULT_NUM_POINTS = 64;
+
+export function generateCirclePoints(
+    cx: number,
+    cy: number,
+    radius: number,
+    numPoints: number = DEFAULT_NUM_POINTS,
+): Point[] {
+    const points: Point[] = [];
+    for (let i = 0; i < numPoints; i++) {
+        const angle = (i / numPoints) * Math.PI * 2 - Math.PI / 2;
+        points.push({
+            x: cx + Math.cos(angle) * radius,
+            y: cy + Math.sin(angle) * radius,
+        });
+    }
+    return points;
+}
+
+// points distributed along the three edges with higher density near corners for rounding
+export function generateTrianglePoints(
+    cx: number,
+    cy: number,
+    radius: number,
+    numPoints: number = DEFAULT_NUM_POINTS,
+): Point[] {
+    const vertices = [
+        { x: cx, y: cy - radius }, // top
+        { x: cx + radius * Math.cos(Math.PI / 6), y: cy + radius * Math.sin(Math.PI / 6) }, // bottom right
+        { x: cx - radius * Math.cos(Math.PI / 6), y: cy + radius * Math.sin(Math.PI / 6) }, // bottom left
+    ];
+
+    return distributePointsAlongPolygon(vertices, numPoints);
+}
+
+// points distributed along the four edges with higher density near corners for rounding
+export function generateSquarePoints(
+    cx: number,
+    cy: number,
+    radius: number,
+    numPoints: number = DEFAULT_NUM_POINTS,
+): Point[] {
+    // rotate 45 degrees so a flat edge is at bottom
+    const angle = -Math.PI / 4;
+    const vertices = [
+        { x: cx + radius * Math.cos(angle), y: cy + radius * Math.sin(angle) }, // right
+        { x: cx + radius * Math.cos(angle + Math.PI / 2), y: cy + radius * Math.sin(angle + Math.PI / 2) }, // bottom
+        { x: cx + radius * Math.cos(angle + Math.PI), y: cy + radius * Math.sin(angle + Math.PI) }, // left
+        {
+            x: cx + radius * Math.cos(angle + (3 * Math.PI) / 2),
+            y: cy + radius * Math.sin(angle + (3 * Math.PI) / 2),
+        }, // top
+    ];
+
+    return distributePointsAlongPolygon(vertices, numPoints);
+}
+
+// points distributed along X edges
+function distributePointsAlongPolygon(vertices: Point[], numPoints: number): Point[] {
+    const points: Point[] = [];
+    const numEdges = vertices.length;
+    const pointsPerEdge = Math.floor(numPoints / numEdges);
+    const remainder = numPoints % numEdges;
+
+    for (let i = 0; i < numEdges; i++) {
+        const start = vertices[i];
+        const end = vertices[(i + 1) % numEdges];
+        // distribute remainder points to first edges
+        const edgePoints = pointsPerEdge + (i < remainder ? 1 : 0);
+
+        for (let j = 0; j < edgePoints; j++) {
+            const t = j / edgePoints;
+            points.push({
+                x: start.x + (end.x - start.x) * t,
+                y: start.y + (end.y - start.y) * t,
+            });
+        }
+    }
+
+    return points;
+}