ttrpg-tools/src/plotcutter/rounded.ts

/**
 * 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
    ];
}