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max: number };\n\n/**\n * @private\n * 1. 获取投影轴\n */\nfunction getAxes(points: Point[] /** 多边形的关键点 */): Vec2[] {\n // 目前先处理 平行矩形 的场景, 其他多边形不处理\n if (points.length > 4) {\n return [];\n }\n // 获取向量\n const vector = (start: Point, end: Point): Vec2 => {\n return [end.x - start.x, end.y - start.y];\n };\n\n // 由于 矩形的平行原理，所以只有 2 条投影轴: A -> B, B -> C\n const AB = vector(points[0], points[1]);\n const BC = vector(points[1], points[2]);\n\n return [AB, BC];\n}\n\n/**\n * @private\n * 绕指定点顺时针旋转后的点坐标\n * 默认绕原点旋转\n */\nfunction rotateAtPoint(point: Point, deg = 0, origin = { x: 0, y: 0 }): Point {\n const { x, y } = point;\n return {\n x: (x - origin.x) * Math.cos(-deg) + (y - origin.y) * Math.sin(-deg) + origin.x,\n y: (origin.x - x) * Math.sin(-deg) + (y - origin.y) * Math.cos(-deg) + origin.y,\n };\n}\n\n/**\n * @private\n * 转化为顶点坐标数组\n *\n * @param {Object} box\n */\nfunction getRectPoints(box: Box): Point[] {\n const points = [\n { x: box.x, y: box.y },\n { x: box.x + box.width, y: box.y },\n { x: box.x + box.width, y: box.y + box.height },\n { x: box.x, y: box.y + box.height },\n ];\n\n const rotation = box.rotation;\n if (rotation) {\n return [\n rotateAtPoint(points[0], rotation, points[0]),\n rotateAtPoint(points[1], rotation, points[0]),\n rotateAtPoint(points[2], rotation, points[0]),\n rotateAtPoint(points[3], rotation, points[0]),\n ];\n }\n\n return points;\n}\n\n/**\n * @private\n * 2. 获取多边形在投影轴上的投影\n *\n * 向量的点积的其中一个几何含义是：一个向量在平行于另一个向量方向上的投影的数值乘积。\n * 由于投影轴是单位向量（长度为1），投影的长度为 x1 * x2 + y1 * y2\n */\nfunction getProjection(points: Point[] /** 多边形的关键点 */, axis: Vec2): Projection {\n // 目前先处理矩形的场景\n if (points.length > 4) {\n return { min: 0, max: 0 };\n }\n\n const scalars = [];\n points.forEach((point) => {\n scalars.push(dot([point.x, point.y], axis));\n });\n\n return { min: Math.min(...scalars), max: Math.max(...scalars) };\n}\n\nfunction isProjectionOverlap(projection1: Projection, projection2: Projection): boolean {\n return projection1.max > projection2.min && projection1.min < projection2.max;\n}\n\nfunction isValidNumber(d: number) {\n return isNumber(d) && !Number.isNaN(d) && d !== Infinity && d !== -Infinity;\n}\n\nfunction isValidBox(box: Box) {\n return Object.values(box).every(isValidNumber);\n}\n\n/**\n * 快速判断两个无旋转矩形是否遮挡\n */\nexport function isIntersectRect(box1: Box, box2: Box, margin: number = 0): boolean {\n return !(\n box2.x > box1.x + box1.width + margin ||\n box2.x + box2.width < box1.x - margin ||\n box2.y > box1.y + box1.height + margin ||\n box2.y + box2.height < box1.y - margin\n );\n}\n\n/**\n * detect whether two shape is intersected, useful when shape is been rotated\n * 判断两个矩形是否重叠（相交和包含, 是否旋转）\n *\n * - 原理: 分离轴定律\n */\nexport function isIntersect(box1: Box, box2: Box) {\n // 如果两个 box 中有一个是不合法的 box，也就是不会被渲染出来的，那么它们就不相交。\n if (!isValidBox(box1) || !isValidBox(box2)) return false;\n\n // 如果两个矩形没有旋转，使用快速判断\n if (!box1.rotation && !box2.rotation) {\n return isIntersectRect(box1, box2);\n }\n\n // 分别获取 4 个关键点\n const rect1Points = getRectPoints(box1);\n const rect2Points = getRectPoints(box2);\n\n // 获取所有投影轴\n const axes = [...getAxes(rect1Points), ...getAxes(rect2Points)];\n\n for (let i = 0; i < axes.length; i++) {\n const axis = axes[i];\n const projection1 = getProjection(rect1Points, axis);\n const projection2 = getProjection(rect2Points, axis);\n\n // 判断投影轴上的投影是否存在重叠，若检测到存在间隙则立刻退出判断，消除不必要的运算。\n if (!isProjectionOverlap(projection1, projection2)) return false;\n }\n\n return true;\n}\n"]} |