新增math库
This commit is contained in:
YHH
445
packages/math/src/Collision/CollisionDetector.ts
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445
packages/math/src/Collision/CollisionDetector.ts
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import { Vector2 } from '../Vector2';
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import { Rectangle } from '../Rectangle';
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import { Circle } from '../Circle';
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/**
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* 碰撞信息接口
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*/
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export interface CollisionInfo {
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/** 是否发生碰撞 */
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collided: boolean;
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/** 碰撞法线（指向第二个对象） */
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normal?: Vector2;
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/** 穿透深度 */
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penetration?: number;
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/** 碰撞点 */
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contactPoint?: Vector2;
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}
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/**
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* 碰撞检测器
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*
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* 提供各种几何体之间的碰撞检测功能
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*/
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export class CollisionDetector {
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// 点与几何体碰撞检测
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/**
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* 点与圆形碰撞检测
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* @param point 点
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* @param circle 圆形
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* @returns 碰撞信息
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*/
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static pointCircle(point: Vector2, circle: Circle): CollisionInfo {
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const distance = Vector2.distance(point, circle.center);
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const collided = distance <= circle.radius;
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if (!collided) {
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return { collided: false };
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}
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const normal = distance > 0
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? Vector2.subtract(point, circle.center).normalize()
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: new Vector2(1, 0); // 默认法线
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return {
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collided: true,
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normal,
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penetration: circle.radius - distance,
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contactPoint: point.clone()
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};
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}
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/**
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* 点与矩形碰撞检测
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* @param point 点
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* @param rect 矩形
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* @returns 碰撞信息
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*/
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static pointRect(point: Vector2, rect: Rectangle): CollisionInfo {
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const collided = rect.containsPoint(point);
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if (!collided) {
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return { collided: false };
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}
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// 计算到各边的距离
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const distLeft = point.x - rect.left;
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const distRight = rect.right - point.x;
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const distTop = point.y - rect.top;
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const distBottom = rect.bottom - point.y;
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// 找到最小距离确定法线方向
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const minDist = Math.min(distLeft, distRight, distTop, distBottom);
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let normal: Vector2;
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let penetration = minDist;
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if (minDist === distLeft) {
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normal = new Vector2(-1, 0);
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} else if (minDist === distRight) {
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normal = new Vector2(1, 0);
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} else if (minDist === distTop) {
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normal = new Vector2(0, -1);
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} else {
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normal = new Vector2(0, 1);
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}
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return {
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collided: true,
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normal,
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penetration,
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contactPoint: point.clone()
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};
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}
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// 圆形碰撞检测
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/**
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* 圆形与圆形碰撞检测
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* @param circle1 第一个圆形
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* @param circle2 第二个圆形
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* @returns 碰撞信息
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*/
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static circleCircle(circle1: Circle, circle2: Circle): CollisionInfo {
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const distance = Vector2.distance(circle1.center, circle2.center);
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const radiusSum = circle1.radius + circle2.radius;
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const collided = distance <= radiusSum;
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if (!collided) {
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return { collided: false };
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}
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const normal = distance > 0
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? Vector2.subtract(circle2.center, circle1.center).normalize()
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: new Vector2(1, 0); // 默认法线
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const penetration = radiusSum - distance;
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const contactPoint = circle1.center.clone().add(
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normal.clone().multiply(circle1.radius - penetration * 0.5)
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);
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return {
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collided: true,
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normal,
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penetration,
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contactPoint
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};
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}
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/**
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* 圆形与矩形碰撞检测
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* @param circle 圆形
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* @param rect 矩形
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* @returns 碰撞信息
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*/
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static circleRect(circle: Circle, rect: Rectangle): CollisionInfo {
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// 找到矩形上离圆心最近的点
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const closestPoint = rect.closestPointTo(circle.center);
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// 检查是否碰撞
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const distance = Vector2.distance(circle.center, closestPoint);
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const collided = distance <= circle.radius;
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if (!collided) {
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return { collided: false };
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}
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// 计算法线和穿透深度
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const normal = distance > 0
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? Vector2.subtract(closestPoint, circle.center).normalize()
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: new Vector2(0, -1); // 默认法线（圆心在矩形内部时）
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const penetration = circle.radius - distance;
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return {
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collided: true,
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normal,
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penetration,
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contactPoint: closestPoint
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};
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}
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// 矩形碰撞检测
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/**
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* 矩形与矩形碰撞检测（AABB）
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* @param rect1 第一个矩形
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* @param rect2 第二个矩形
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* @returns 碰撞信息
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*/
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static rectRect(rect1: Rectangle, rect2: Rectangle): CollisionInfo {
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const collided = rect1.intersects(rect2);
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if (!collided) {
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return { collided: false };
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}
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// 计算重叠区域
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const overlapLeft = Math.max(rect1.left, rect2.left);
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const overlapRight = Math.min(rect1.right, rect2.right);
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const overlapTop = Math.max(rect1.top, rect2.top);
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const overlapBottom = Math.min(rect1.bottom, rect2.bottom);
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const overlapWidth = overlapRight - overlapLeft;
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const overlapHeight = overlapBottom - overlapTop;
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// 确定分离方向（最小重叠轴）
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let normal: Vector2;
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let penetration: number;
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if (overlapWidth < overlapHeight) {
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// 水平分离
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penetration = overlapWidth;
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if (rect1.centerX < rect2.centerX) {
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normal = new Vector2(-1, 0);
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} else {
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normal = new Vector2(1, 0);
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}
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} else {
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// 垂直分离
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penetration = overlapHeight;
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if (rect1.centerY < rect2.centerY) {
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normal = new Vector2(0, -1);
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} else {
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normal = new Vector2(0, 1);
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}
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}
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const contactPoint = new Vector2(
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(overlapLeft + overlapRight) * 0.5,
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(overlapTop + overlapBottom) * 0.5
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);
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return {
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collided: true,
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normal,
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penetration,
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contactPoint
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};
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}
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// 射线投射
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/**
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* 射线与圆形相交检测
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* @param rayOrigin 射线起点
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* @param rayDirection 射线方向（单位向量）
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* @param circle 圆形
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* @param maxDistance 最大检测距离，默认无限
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* @returns 碰撞信息，包含距离信息
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*/
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static rayCircle(
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rayOrigin: Vector2,
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rayDirection: Vector2,
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circle: Circle,
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maxDistance: number = Infinity
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): CollisionInfo & { distance?: number } {
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const oc = Vector2.subtract(rayOrigin, circle.center);
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const a = rayDirection.lengthSquared;
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const b = 2 * Vector2.dot(oc, rayDirection);
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const c = oc.lengthSquared - circle.radius * circle.radius;
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const discriminant = b * b - 4 * a * c;
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if (discriminant < 0) {
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return { collided: false };
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}
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const sqrt = Math.sqrt(discriminant);
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const t1 = (-b - sqrt) / (2 * a);
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const t2 = (-b + sqrt) / (2 * a);
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// 选择最近的正距离
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let t = t1 >= 0 ? t1 : t2;
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if (t < 0 || t > maxDistance) {
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return { collided: false };
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}
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const contactPoint = rayOrigin.clone().add(rayDirection.clone().multiply(t));
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const normal = Vector2.subtract(contactPoint, circle.center).normalize();
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return {
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collided: true,
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normal,
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contactPoint,
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distance: t,
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penetration: 0 // 射线检测不计算穿透
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};
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}
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/**
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* 射线与矩形相交检测
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* @param rayOrigin 射线起点
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* @param rayDirection 射线方向（单位向量）
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* @param rect 矩形
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* @param maxDistance 最大检测距离，默认无限
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* @returns 碰撞信息，包含距离信息
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*/
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static rayRect(
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rayOrigin: Vector2,
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rayDirection: Vector2,
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rect: Rectangle,
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maxDistance: number = Infinity
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): CollisionInfo & { distance?: number } {
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// 避免除零
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const invDirX = rayDirection.x !== 0 ? 1 / rayDirection.x : 1e10;
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const invDirY = rayDirection.y !== 0 ? 1 / rayDirection.y : 1e10;
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// 计算与各边的交点参数
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const t1 = (rect.left - rayOrigin.x) * invDirX;
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const t2 = (rect.right - rayOrigin.x) * invDirX;
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const t3 = (rect.top - rayOrigin.y) * invDirY;
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const t4 = (rect.bottom - rayOrigin.y) * invDirY;
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const tmin = Math.max(Math.min(t1, t2), Math.min(t3, t4));
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const tmax = Math.min(Math.max(t1, t2), Math.max(t3, t4));
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// 没有交点或交点在射线反方向
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if (tmax < 0 || tmin > tmax || tmin > maxDistance) {
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return { collided: false };
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}
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const t = tmin >= 0 ? tmin : tmax;
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const contactPoint = rayOrigin.clone().add(rayDirection.clone().multiply(t));
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// 确定法线方向
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let normal: Vector2;
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const epsilon = 1e-6;
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if (Math.abs(contactPoint.x - rect.left) < epsilon) {
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normal = new Vector2(-1, 0);
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} else if (Math.abs(contactPoint.x - rect.right) < epsilon) {
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normal = new Vector2(1, 0);
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} else if (Math.abs(contactPoint.y - rect.top) < epsilon) {
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normal = new Vector2(0, -1);
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} else {
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normal = new Vector2(0, 1);
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}
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return {
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collided: true,
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normal,
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contactPoint,
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distance: t,
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penetration: 0 // 射线检测不计算穿透
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};
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}
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// 线段相交检测
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/**
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* 线段与线段相交检测
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* @param p1 第一条线段起点
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* @param p2 第一条线段终点
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* @param p3 第二条线段起点
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* @param p4 第二条线段终点
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* @returns 碰撞信息
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*/
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static lineSegmentLineSegment(p1: Vector2, p2: Vector2, p3: Vector2, p4: Vector2): CollisionInfo {
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const d1 = Vector2.subtract(p2, p1);
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const d2 = Vector2.subtract(p4, p3);
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const d3 = Vector2.subtract(p3, p1);
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const cross = Vector2.cross(d1, d2);
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if (Math.abs(cross) < Number.EPSILON) {
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// 平行或共线
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return { collided: false };
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}
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const t1 = Vector2.cross(d3, d2) / cross;
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const t2 = Vector2.cross(d3, d1) / cross;
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if (t1 >= 0 && t1 <= 1 && t2 >= 0 && t2 <= 1) {
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const contactPoint = p1.clone().add(d1.clone().multiply(t1));
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// 计算法线（垂直于第一条线段）
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const normal = d1.perpendicular().normalize();
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return {
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collided: true,
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normal,
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contactPoint,
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penetration: 0 // 线段相交不计算穿透
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};
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}
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return { collided: false };
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}
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/**
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* 线段与圆形相交检测
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* @param lineStart 线段起点
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* @param lineEnd 线段终点
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* @param circle 圆形
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* @returns 碰撞信息
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*/
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static lineSegmentCircle(lineStart: Vector2, lineEnd: Vector2, circle: Circle): CollisionInfo {
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const d = Vector2.subtract(lineEnd, lineStart);
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const f = Vector2.subtract(lineStart, circle.center);
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const a = Vector2.dot(d, d);
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const b = 2 * Vector2.dot(f, d);
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const c = Vector2.dot(f, f) - circle.radius * circle.radius;
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const discriminant = b * b - 4 * a * c;
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if (discriminant < 0) {
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return { collided: false };
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}
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const sqrt = Math.sqrt(discriminant);
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const t1 = (-b - sqrt) / (2 * a);
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const t2 = (-b + sqrt) / (2 * a);
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// 检查交点是否在线段上
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const validT = [];
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if (t1 >= 0 && t1 <= 1) validT.push(t1);
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if (t2 >= 0 && t2 <= 1) validT.push(t2);
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if (validT.length === 0) {
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return { collided: false };
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}
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// 使用最近的交点
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const t = validT[0];
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const contactPoint = lineStart.clone().add(d.clone().multiply(t));
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const normal = Vector2.subtract(contactPoint, circle.center).normalize();
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return {
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collided: true,
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normal,
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contactPoint,
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penetration: 0 // 线段相交不计算穿透
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};
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}
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// 快速排斥测试
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/**
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* AABB包围盒快速排斥测试
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* @param bounds1 第一个包围盒
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* @param bounds2 第二个包围盒
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* @returns 是否可能相交
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*/
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static aabbTest(bounds1: Rectangle, bounds2: Rectangle): boolean {
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return bounds1.intersects(bounds2);
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}
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/**
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* 圆形包围盒快速排斥测试
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* @param center1 第一个圆心
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* @param radius1 第一个半径
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* @param center2 第二个圆心
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* @param radius2 第二个半径
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* @returns 是否可能相交
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*/
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static circleTest(center1: Vector2, radius1: number, center2: Vector2, radius2: number): boolean {
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const distance = Vector2.distance(center1, center2);
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return distance <= radius1 + radius2;
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}
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}
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7
packages/math/src/Collision/index.ts
Normal file
7
packages/math/src/Collision/index.ts
Normal file
@@ -0,0 +1,7 @@
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/**
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* 碰撞检测模块
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*
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* 提供各种几何体间的碰撞检测功能
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*/
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export { CollisionDetector, type CollisionInfo } from './CollisionDetector';
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