feat: path closure

jest.config.js

@@ -0,0 +1,22 @@
+/** @type {import('ts-jest').JestConfigWithTsJest} */
+export default {
+  preset: 'ts-jest',
+  testEnvironment: 'node',
+  testMatch: ['**/*.test.ts'],
+  moduleFileExtensions: ['ts', 'tsx', 'js', 'jsx'],
+  transform: {
+    '^.+\\.tsx?$': [
+      'ts-jest',
+      {
+        tsconfig: {
+          target: 'ES2020',
+          module: 'ESNext',
+          moduleResolution: 'node',
+          esModuleInterop: true,
+          strict: true,
+          skipLibCheck: true
+        }
+      }
+    ]
+  }
+};

package.json

@@ -19,7 +19,8 @@
     "preview": "rsbuild preview",
     "cli:dev": "tsc -p tsconfig.cli.json --watch",
     "cli:build": "tsc -p tsconfig.cli.json",
-    "ttrpg": "node --loader ts-node/esm ./src/cli/index.ts"
+    "ttrpg": "node --loader ts-node/esm ./src/cli/index.ts",
+    "test": "jest"
   },
   "keywords": [
     "ttrpg",
@@ -50,9 +51,13 @@
     "@tailwindcss/postcss": "^4.2.1",
     "@tailwindcss/typography": "^0.5.15",
     "@tailwindcss/vite": "^4.0.0",
+    "@types/jest": "^30.0.0",
     "@types/js-yaml": "^4.0.9",
     "@types/node": "^22.19.13",
+    "jest": "^29.7.0",
+    "jest-environment-jsdom": "^29.7.0",
     "tailwindcss": "^4.0.0",
+    "ts-jest": "^29.4.6",
     "ts-node": "^10.9.2",
     "typescript": "^5.7.2"
   }

src/components/md-deck/CardPreview.tsx

@@ -19,7 +19,11 @@ export function CardPreview(props: CardPreviewProps) {
   const selectionStyle = createMemo(() =>
     getSelectionBoxStyle(store.state.selectStart, store.state.selectEnd, store.state.dimensions)
   );
-  const shapeClipPath = createMemo(() => getShapeClipPath(store.state.shape));
+  const shapeClipPath = createMemo(() => {
+    const dims = store.state.dimensions;
+    if (!dims) return 'none';
+    return getShapeClipPath(store.state.shape, dims.cardWidth, dims.cardHeight, store.state.cornerRadius);
+  });
 
   const selection = useCardSelection(store);
 

src/components/md-deck/PltPreview.tsx

@@ -154,9 +154,8 @@ export function PltPreview(props: PltPreviewProps) {
                 <path
                   d={travelPathD()}
                   fill="none"
-                  stroke="#999"
-                  stroke-width="0.2"
-                  stroke-dasharray="2 2"
+                  stroke="#f884"
+                  stroke-width="1"
                 />
               </Show>
 

src/components/md-deck/PrintPreview.tsx

@@ -152,7 +152,7 @@ export function PrintPreview(props: PrintPreviewProps) {
                       const cardWidth = store.state.dimensions?.cardWidth || 56;
                       const cardHeight = store.state.dimensions?.cardHeight || 88;
                       const clipPathId = `clip-${page.pageIndex}-${card.data.id || card.x}-${card.y}`;
-                      const shapeClipPath = getShapeSvgClipPath(clipPathId, cardWidth, cardHeight, store.state.shape);
+                      const shapeClipPath = getShapeSvgClipPath(clipPathId, cardWidth, cardHeight, store.state.shape, store.state.cornerRadius);
 
                       return (
                         <g class="card-group">

src/components/md-deck/hooks/shape-styles.ts

@@ -1,20 +1,52 @@
 import type { CardShape } from '../types';
+import { getCardShapePoints, contourToSvgPath } from '../../../plotcutter/contour';
+
+/**
+ * 将轮廓点转换为 CSS polygon() 格式
+ * @param points 轮廓点数组（相对于左上角，单位：mm）
+ * @returns CSS polygon() 字符串，使用百分比坐标
+ */
+function pointsToCssPolygon(points: [number, number][], width: number, height: number): string {
+  if (points.length === 0) return 'none';
+
+  const coords = points.map(([x, y]) => {
+    const percentX = (x / width) * 100;
+    const percentY = (y / height) * 100;
+    return `${percentX.toFixed(4)}% ${percentY.toFixed(4)}%`;
+  });
+
+  return `polygon(${coords.join(', ')})`;
+}
 
 /**
  * 获取 CSS clip-path 值用于形状裁剪
+ * 
+ * @param shape 卡片形状
+ * @param width 卡片宽度（用于计算多边形坐标）
+ * @param height 卡片高度（用于计算多边形坐标）
+ * @param cornerRadius 圆角半径（可选，>0 时使用多边形近似）
+ * @param segmentsPerCorner 每个圆角的分段数（可选）
  */
-export function getShapeClipPath(shape: CardShape): string {
+export function getShapeClipPath(
+  shape: CardShape,
+  width: number,
+  height: number,
+  cornerRadius: number = 0,
+  segmentsPerCorner: number = 4
+): string {
+  // 无圆角的基本形状使用简化的 CSS clip-path
+  if (cornerRadius <= 0) {
     switch (shape) {
       case 'circle':
         return 'circle(50% at 50% 50%)';
-    case 'triangle':
-      return 'polygon(50% 0%, 0% 100%, 100% 100%)';
-    case 'hexagon':
-      return 'polygon(50% 0%, 100% 25%, 100% 75%, 50% 100%, 0% 75%, 0% 25%)';
       case 'rectangle':
-    default:
         return 'none';
     }
+  }
+
+  // 其他情况使用多边形近似（包括圆角形状、三角形、六边形）
+  const points = getCardShapePoints(shape, width, height, cornerRadius, segmentsPerCorner);
+  return pointsToCssPolygon(points, width, height);
 }
 
 /**
@@ -23,34 +55,41 @@ export function getShapeClipPath(shape: CardShape): string {
  * @param width 卡片宽度
  * @param height 卡片高度
  * @param shape 卡片形状
+ * @param cornerRadius 圆角半径（可选）
+ * @param segmentsPerCorner 每个圆角的分段数（可选）
  */
 export function getShapeSvgClipPath(
   id: string,
   width: number,
   height: number,
-  shape: CardShape
+  shape: CardShape,
+  cornerRadius: number = 0,
+  segmentsPerCorner: number = 4
 ): string {
-  const halfW = width / 2;
-  const halfH = height / 2;
+  const points = getCardShapePoints(shape, width, height, cornerRadius, segmentsPerCorner);
+  const pathData = contourToSvgPath(points, true);
 
-  switch (shape) {
-    case 'circle':
   return `
   <clipPath id="${id}">
-    <circle cx="${halfW}" cy="${halfH}" r="${halfW}" />
+    <path d="${pathData}" />
   </clipPath>`;
-    case 'triangle':
-      return `
-  <clipPath id="${id}">
-    <polygon points="${halfW},0 0,${height} ${width},${height}" />
-  </clipPath>`;
-    case 'hexagon':
-      return `
-  <clipPath id="${id}">
-    <polygon points="${halfW},0 ${width},${height * 0.25} ${width},${height * 0.75} ${halfW},${height} 0,${height * 0.75} 0,${height * 0.25}" />
-  </clipPath>`;
-    case 'rectangle':
-    default:
-      return '';
-  }
+}
+
+/**
+ * 获取卡片形状的 SVG path 数据
+ * @param width 卡片宽度
+ * @param height 卡片高度
+ * @param shape 卡片形状
+ * @param cornerRadius 圆角半径（可选）
+ * @param segmentsPerCorner 每个圆角的分段数（可选）
+ */
+export function getCardShapePath(
+  width: number,
+  height: number,
+  shape: CardShape,
+  cornerRadius: number = 0,
+  segmentsPerCorner: number = 4
+): string {
+  const points = getCardShapePoints(shape, width, height, cornerRadius, segmentsPerCorner);
+  return contourToSvgPath(points, true);
 }

src/plotcutter/contour.ts

@@ -1,72 +1,74 @@
 import type { CardShape, ContourPoint, ContourBounds } from './types';
+import {getRoundedPolygonPoints} from "./rounded";
 
 // 重新导出类型以兼容旧导入路径
 export type { CardShape, ContourPoint, ContourBounds };
 
+
 /**
- * 生成带圆角的矩形轮廓点
- * @param width 矩形宽度
- * @param height 矩形高度
- * @param cornerRadius 圆角半径（mm）
- * @param segmentsPerCorner 每个圆角的分段数
+ * 生成内接正三角形的轮廓点（无圆角版本）
+ * @param width 外框宽度
+ * @param height 外框高度
+ * @returns 正三角形轮廓点（相对于外框左下角，顺时针）
  */
-export function getRoundedRectPoints(
+export function getInscribedTrianglePoints(
   width: number,
-  height: number,
-  cornerRadius: number,
-  segmentsPerCorner: number = 4
+  height: number
 ): [number, number][] {
-  const points: [number, number][] = [];
-  const r = Math.min(cornerRadius, width / 2, height / 2);
+  // 以短边为基准计算内接正三角形的边长
+  const minDim = Math.min(width, height / Math.sqrt(3) * 2);
+  // 正三角形的高 = 边长 * sqrt(3) / 2
+  const triangleHeight = minDim * Math.sqrt(3) / 2;
+  const sideLength = minDim;
+
+  // 计算居中偏移
+  const offsetX = (width - sideLength) / 2;
+  const offsetY = (height - triangleHeight) / 2;
+
+  // 正三角形三个顶点（底边在下，顶点在上，顺时针：左上→右上→下）
+  const points: [number, number][] = [
+    [offsetX, offsetY + triangleHeight],                     // 左下顶点
+    [offsetX + sideLength, offsetY + triangleHeight],        // 右下顶点
+    [offsetX + sideLength / 2, offsetY]                      // 顶部顶点
+  ];
 
-  if (r <= 0) {
-    // 无圆角，返回普通矩形
-    points.push([0, 0]);
-    points.push([width, 0]);
-    points.push([width, height]);
-    points.push([0, height]);
   return points;
-  }
+}
 
-  // 左上角圆角（从顶部开始，顺时针）
-  for (let i = 0; i <= segmentsPerCorner; i++) {
-    const angle = (Math.PI / 2) * (i / segmentsPerCorner) - Math.PI;
-    points.push([
-      r + r * Math.cos(angle),
-      r + r * Math.sin(angle)
-    ]);
-  }
+/**
+ * 生成内接正六边形的轮廓点（无圆角版本）
+ * @param width 外框宽度
+ * @param height 外框高度
+ * @returns 正六边形轮廓点（相对于外框左下角，顺时针）
+ */
+export function getInscribedHexagonPoints(
+  width: number,
+  height: number
+): [number, number][] {
+  const minDim = Math.min(width, height / Math.sqrt(3) * 2);
+  const radius = minDim / 2;
 
-  // 右上角圆角
-  for (let i = 0; i <= segmentsPerCorner; i++) {
-    const angle = (Math.PI / 2) * (i / segmentsPerCorner) - Math.PI/2;
-    points.push([
-      width - r + r * Math.cos(angle),
-      r + r * Math.sin(angle)
-    ]);
-  }
+  // 中心点
+  const centerX = width / 2;
+  const centerY = height / 2;
 
-  // 右下角圆角
-  for (let i = 0; i <= segmentsPerCorner; i++) {
-    const angle = (Math.PI / 2) * (i / segmentsPerCorner);
+  // 正六边形六个顶点（平顶，从左上角开始顺时针）
+  // 角度：210°, 270°, 330°, 30°, 90°, 150° (数学坐标系，Y向上)
+  // 在屏幕坐标系 (Y向下)，我们直接按顺时针计算
+  const points: [number, number][] = [];
+  for (let i = 0; i < 6; i++) {
+    // 从 -120度开始，每 60 度一个点，实现平顶且顺时针
+    const angle = (-2 * Math.PI / 3) + (i * Math.PI / 3);
     points.push([
-      width - r + r * Math.cos(angle),
-      height - r + r * Math.sin(angle)
-    ]);
-  }
-
-  // 左下角圆角
-  for (let i = 0; i <= segmentsPerCorner; i++) {
-    const angle = (Math.PI / 2) * (i / segmentsPerCorner) + Math.PI/2;
-    points.push([
-      r + r * Math.cos(angle),
-      height - r + r * Math.sin(angle)
+      centerX + radius * Math.cos(angle),
+      centerY + radius * Math.sin(angle)
     ]);
   }
 
   return points;
 }
 
+
 /**
  * 根据形状生成卡片轮廓点（单位：mm，相对于卡片左下角）
  */
@@ -74,10 +76,28 @@ export function getCardShapePoints(
   shape: CardShape,
   width: number,
   height: number,
-  cornerRadius: number = 0
+  cornerRadius: number = 0,
+  segmentsPerCorner: number = 4
 ): [number, number][] {
-  if (shape === 'rectangle' && cornerRadius > 0) {
-    return getRoundedRectPoints(width, height, cornerRadius);
+  // 处理带圆角的情况 - 统一使用 getRoundedPolygonPoints
+  if (cornerRadius > 0) {
+    if (shape === 'rectangle') {
+      const vertices: [number, number][] = [
+        [0, 0],
+        [width, 0],
+        [width, height],
+        [0, height]
+      ];
+      return getRoundedPolygonPoints(vertices, cornerRadius, segmentsPerCorner);
+    }
+    if (shape === 'triangle') {
+      const vertices = getInscribedTrianglePoints(width, height);
+      return getRoundedPolygonPoints(vertices, cornerRadius, segmentsPerCorner);
+    }
+    if (shape === 'hexagon') {
+      const vertices = getInscribedHexagonPoints(width, height);
+      return getRoundedPolygonPoints(vertices, cornerRadius, segmentsPerCorner);
+    }
   }
 
   const points: [number, number][] = [];
@@ -97,21 +117,10 @@ export function getCardShapePoints(
       break;
     }
     case 'triangle': {
-      points.push([width / 2, 0]);
-      points.push([0, height]);
-      points.push([width, height]);
-      break;
+      return getInscribedTrianglePoints(width, height);
     }
     case 'hexagon': {
-      const halfW = width / 2;
-      const quarterH = height / 4;
-      points.push([halfW, 0]);
-      points.push([width, quarterH]);
-      points.push([width, height - quarterH]);
-      points.push([halfW, height]);
-      points.push([0, height - quarterH]);
-      points.push([0, quarterH]);
-      break;
+      return getInscribedHexagonPoints(width, height);
     }
     case 'rectangle':
     default: {
@@ -194,7 +203,7 @@ export function getPointOnPath(points: [number, number][], progress: number): [n
  * @param points 轮廓点数组
  * @param closed 是否闭合路径
  */
-export function contourToSvgPath(points: [number, number][], closed = true): string {
+export function contourToSvgPath(points: [number, number][], closed = false): string {
   if (points.length === 0) return '';
 
   const [startX, startY] = points[0];

src/plotcutter/plotter.ts

@@ -22,15 +22,8 @@ export function pts2plotter(
 
   let str = init(width * px2mm, height * px2mm);
 
-  // 按 X 轴然后 Y 轴排序路径
-  const sorted = pts.slice();
-  sorted.sort(function (a, b) {
-    const [ax, ay] = topleft(a);
-    const [bx, by] = topleft(b);
-
-    if (ax !== bx) return ax - bx;
-    return ay - by;
-  });
+  // 使用最近邻算法排序路径
+  const sorted = sortPathsByNearestNeighbor(pts, start);
 
   // 从起点到第一个路径
   if (sorted.length > 0) {
@@ -44,6 +37,11 @@ export function pts2plotter(
       str += ` D${plu(pt[0] * px2mm)},${plu((height - pt[1]) * px2mm)}`;
     }
 
+    // 如果第一个路径未闭合，添加闭合命令
+    if (!isPathClosed(firstPath)) {
+      str += ` D${plu(firstPath[0][0] * px2mm)},${plu((height - firstPath[0][1]) * px2mm)}`;
+    }
+
     // 路径之间移动
     for (let i = 1; i < sorted.length; i++) {
       const prevPath = sorted[i - 1];
@@ -58,6 +56,11 @@ export function pts2plotter(
         const pt = currPath[j];
         str += ` D${plu(pt[0] * px2mm)},${plu((height - pt[1]) * px2mm)}`;
       }
+
+      // 如果当前路径未闭合，添加闭合命令
+      if (!isPathClosed(currPath)) {
+        str += ` D${plu(currPath[0][0] * px2mm)},${plu((height - currPath[0][1]) * px2mm)}`;
+      }
     }
   }
 
@@ -88,6 +91,72 @@ function topleft(pts: [number, number][]) {
   return [minx, miny] as [number, number];
 }
 
+/**
+ * 检测路径是否已闭合（起点和终点距离小于阈值）
+ * @param path 路径点数组
+ * @param threshold 距离阈值（像素），默认 0.01
+ */
+function isPathClosed(path: [number, number][], threshold = 0.01): boolean {
+  if (path.length < 2) return true;
+  const [sx, sy] = path[0];
+  const [ex, ey] = path[path.length - 1];
+  const dist = Math.sqrt((sx - ex) ** 2 + (sy - ey) ** 2);
+  return dist < threshold;
+}
+
+/**
+ * 计算点到路径的最近距离
+ * @param pt 点坐标
+ * @param path 路径点数组
+ */
+function distanceToPath(pt: [number, number], path: [number, number][]): number {
+  let minDist = Infinity;
+  for (const p of path) {
+    const dist = Math.sqrt((pt[0] - p[0]) ** 2 + (pt[1] - p[1]) ** 2);
+    if (dist < minDist) minDist = dist;
+  }
+  return minDist;
+}
+
+/**
+ * 使用最近邻算法排序路径
+ * @param paths 路径数组
+ * @param startPos 起始位置
+ */
+function sortPathsByNearestNeighbor(
+  paths: [number, number][][],
+  startPos: [number, number]
+): [number, number][][] {
+  if (paths.length === 0) return [];
+
+  const result: [number, number][][] = [];
+  const remaining = paths.slice();
+  let currentPos = startPos;
+
+  while (remaining.length > 0) {
+    // 找到距离当前位置最近的路径
+    let nearestIndex = 0;
+    let nearestDist = Infinity;
+
+    for (let i = 0; i < remaining.length; i++) {
+      const dist = distanceToPath(currentPos, remaining[i]);
+      if (dist < nearestDist) {
+        nearestDist = dist;
+        nearestIndex = i;
+      }
+    }
+
+    // 将最近的路径添加到结果中
+    const nearestPath = remaining.splice(nearestIndex, 1)[0];
+    result.push(nearestPath);
+
+    // 更新当前位置为该路径的终点
+    currentPos = nearestPath[nearestPath.length - 1];
+  }
+
+  return result;
+}
+
 function init(w: number, h: number) {
   return ` IN TB26,${plu(w)},${plu(h)} CT1`;
 }

src/plotcutter/rounded.test.ts

@@ -0,0 +1,80 @@
+import { getRoundedPolygonPoints, getTangentCircleCenter, getProjectedPoint } from './rounded';
+
+/* eslint-disable @typescript-eslint/no-explicit-any */
+declare const describe: any;
+declare const test: any;
+declare const expect: any;
+
+describe('getProjectedPoint', () => {
+    test('should project point onto line segment', () => {
+        // 点 (2, 2) 投影到线段 (0, 0) -> (4, 0)
+        const result = getProjectedPoint([2, 2], [0, 0], [4, 0]);
+        expect(result).toEqual([2, 0]);
+    });
+
+    test('should project point onto vertical line segment', () => {
+        const result = getProjectedPoint([3, 2], [0, 0], [0, 4]);
+        expect(result).toEqual([0, 2]);
+    });
+
+    test('should handle point already on line', () => {
+        const result = getProjectedPoint([2, 0], [0, 0], [4, 0]);
+        expect(result).toEqual([2, 0]);
+    });
+});
+
+describe('getTangentCircleCenter', () => {
+    test('should find center for 90 degree corner', () => {
+        // 直角：a(0,1), b(0,0), c(1,0)
+        const center = getTangentCircleCenter([0, 1], [0, 0], [1, 0], 1);
+        // 圆心应该在 (1, 1)
+        expect(center[0]).toBeCloseTo(1, 5);
+        expect(center[1]).toBeCloseTo(1, 5);
+    });
+
+    test('should find center for equilateral triangle corner', () => {
+        // 等边三角形的一个角
+        const center = getTangentCircleCenter([0, 1], [0, 0], [Math.sqrt(3) / 2, -0.5], 0.5);
+        // 验证圆心到两条边的距离都是半径
+        expect(center).toBeDefined();
+    });
+});
+
+describe('getRoundedPolygonPoints', () => {
+    test('should return empty array for empty input', () => {
+        const result = getRoundedPolygonPoints([], 1);
+        expect(result).toEqual([]);
+    });
+
+    test('should return same points for less than 3 vertices', () => {
+        const result = getRoundedPolygonPoints([[0, 0], [1, 0]], 1);
+        expect(result).toEqual([[0, 0], [1, 0]]);
+    });
+
+    test('should round a square', () => {
+        // 单位正方形
+        const square: [number, number][] = [[0, 0], [2, 0], [2, 2], [0, 2]];
+        const result = getRoundedPolygonPoints(square, 0.5, 4);
+        
+        // 结果应该有 4 个角 * (4+1) 段 = 20 个点
+        expect(result.length).toBe(20);
+        
+        // 验证所有点都是有效的坐标
+        result.forEach(point => {
+            expect(typeof point[0]).toBe('number');
+            expect(typeof point[1]).toBe('number');
+        });
+    });
+
+    test('should round an equilateral triangle', () => {
+        // 等边三角形
+        const triangle: [number, number][] = [
+            [0, 1],
+            [Math.sqrt(3) / 2, -0.5],
+            [-Math.sqrt(3) / 2, -0.5]
+        ];
+        const result = getRoundedPolygonPoints(triangle, 0.2, 4);
+        
+        expect(result.length).toBe(15); // 3 个角 * (4+1) 段
+    });
+});

src/plotcutter/rounded.ts

@@ -0,0 +1,129 @@
+/**
+ * 为正多边形添加圆角
+ * 将每个角转换为 segmentsPerCorner 条线段，线段的端点在圆角的圆弧上
+ *
+ * 对每个角：
+ * 1. 寻找圆心
+ * 2. 将圆心投影到两条边上
+ * 3. 以圆弧连接投影点
+ * @param vertices 多边形顶点数组（顺时针或逆时针）
+ * @param cornerRadius 圆角半径
+ * @param segmentsPerCorner 每个圆角的分段数
+ * @returns 带圆角的多边形轮廓点
+ */
+export function getRoundedPolygonPoints(
+    vertices: [number, number][],
+    cornerRadius: number,
+    segmentsPerCorner: number = 4
+): [number, number][] {
+    if (vertices.length < 3) {
+        return [...vertices];
+    }
+
+    const result: [number, number][] = [];
+
+    for (let i = 0; i < vertices.length; i++) {
+        const prev = vertices[(i - 1 + vertices.length) % vertices.length];
+        const curr = vertices[i];
+        const next = vertices[(i + 1) % vertices.length];
+
+        // 获取圆角圆心
+        const center = getTangentCircleCenter(prev, curr, next, cornerRadius);
+
+        // 获取圆心到两条边的投影点（圆角的起点和终点）
+        const start = getProjectedPoint(center, prev, curr);
+        const end = getProjectedPoint(center, curr, next);
+
+        // 计算起始角度和结束角度
+        const startAngle = Math.atan2(start[1] - center[1], start[0] - center[0]);
+        const endAngle = Math.atan2(end[1] - center[1], end[0] - center[0]);
+
+        // 判断方向（顺时针或逆时针）
+        const cross = (curr[0] - prev[0]) * (next[1] - prev[1]) - (curr[1] - prev[1]) * (next[0] - prev[0]);
+        const isClockwise = cross < 0;
+
+        // 计算角度差，确保沿着正确的方向
+        let angleDiff = endAngle - startAngle;
+        if (isClockwise) {
+            if (angleDiff > 0) angleDiff -= Math.PI * 2;
+        } else {
+            if (angleDiff < 0) angleDiff += Math.PI * 2;
+        }
+
+        // 生成圆弧上的点
+        for (let j = 0; j <= segmentsPerCorner; j++) {
+            const t = j / segmentsPerCorner;
+            const angle = startAngle + angleDiff * t;
+            const x = center[0] + cornerRadius * Math.cos(angle);
+            const y = center[1] + cornerRadius * Math.sin(angle);
+            result.push([x, y]);
+        }
+    }
+
+    return result;
+}
+
+/**
+ * 对于给定的角 abc，获取与 ab 和 bc 相切的半径为 radius 的圆的圆心位置。
+ * @param va
+ * @param vb
+ * @param vc
+ * @param radius
+ */
+export function getTangentCircleCenter(
+    va: [number, number],
+    vb: [number, number],
+    vc: [number, number],
+    radius: number
+): [number, number] {
+    // 计算两条边的单位向量
+    const ba: [number, number] = [va[0] - vb[0], va[1] - vb[1]];
+    const bc: [number, number] = [vc[0] - vb[0], vc[1] - vb[1]];
+
+    const baLen = Math.sqrt(ba[0] ** 2 + ba[1] ** 2);
+    const bcLen = Math.sqrt(bc[0] ** 2 + bc[1] ** 2);
+
+    const baUnit: [number, number] = [ba[0] / baLen, ba[1] / baLen];
+    const bcUnit: [number, number] = [bc[0] / bcLen, bc[1] / bcLen];
+
+    // 角平分线方向
+    const bisector: [number, number] = [baUnit[0] + bcUnit[0], baUnit[1] + bcUnit[1]];
+    const bisectorLen = Math.sqrt(bisector[0] ** 2 + bisector[1] ** 2);
+    const bisectorUnit: [number, number] = [bisector[0] / bisectorLen, bisector[1] / bisectorLen];
+
+    // 计算半角的正弦值
+    const halfAngle = Math.acos((baUnit[0] * bcUnit[0] + baUnit[1] * bcUnit[1]));
+    const sinHalfAngle = Math.sin(halfAngle / 2);
+
+    // 圆心到顶点的距离
+    const centerDist = radius / sinHalfAngle;
+
+    // 圆心位置（从顶点沿角平分线向外）
+    return [
+        vb[0] + bisectorUnit[0] * centerDist,
+        vb[1] + bisectorUnit[1] * centerDist
+    ];
+}
+
+/**
+ * 将 v 投影到 ab 线段上
+ * @param v
+ * @param a
+ * @param b
+ */
+export function getProjectedPoint(
+    v: [number, number],
+    a: [number, number],
+    b: [number, number],
+): [number, number] {
+    const ab: [number, number] = [b[0] - a[0], b[1] - a[1]];
+    const av: [number, number] = [v[0] - a[0], v[1] - a[1]];
+
+    const abLenSq = ab[0] ** 2 + ab[1] ** 2;
+    const t = (av[0] * ab[0] + av[1] * ab[1]) / abLenSq;
+
+    return [
+        a[0] + ab[0] * t,
+        a[1] + ab[1] * t
+    ];
+}