esengine/source/src/Physics/Collision.ts

enum PointSectors {
    center = 0,
    top = 1,
    bottom = 2,
    topLeft = 9,
    topRight = 5,
    left = 8,
    right = 4,
    bottomLeft = 10,
    bottomRight = 6
}

class Collisions {
    public static isLineToLine(a1: Vector2, a2: Vector2, b1: Vector2, b2: Vector2): boolean {
        let b = Vector2.subtract(a2, a1);
        let d = Vector2.subtract(b2, b1);
        let bDotDPerp = b.x * d.y - b.y * d.x;

        // 如果b*d = 0，表示这两条直线平行，因此有无穷个交点
        if (bDotDPerp == 0)
            return false;

        let c = Vector2.subtract(b1, a1);
        let t = (c.x * d.y - c.y * d.x) / bDotDPerp;
        if (t < 0 || t > 1)
            return false;

        let u = (c.x * b.y - c.y * b.x) / bDotDPerp;
        if (u < 0 || u > 1)
            return false;

        return true;
    }

    public static lineToLineIntersection(a1: Vector2, a2: Vector2, b1: Vector2, b2: Vector2): Vector2 {
        let intersection = Vector2.Zero;

        let b = Vector2.subtract(a2, a1);
        let d = Vector2.subtract(b2, b1);
        let bDotDPerp = b.x * d.y - b.y * d.x;

        // 如果b*d = 0，表示这两条直线平行，因此有无穷个交点
        if (bDotDPerp == 0)
            return intersection;

        let c = Vector2.subtract(b1, a1);
        let t = (c.x * d.y - c.y * d.x) / bDotDPerp;
        if (t < 0 || t > 1)
            return intersection;

        let u = (c.x * b.y - c.y * b.x) / bDotDPerp;
        if (u < 0 || u > 1)
            return intersection;

        intersection = Vector2.add(a1, new Vector2(t * b.x, t * b.y));

        return intersection;
    }

    public static closestPointOnLine(lineA: Vector2, lineB: Vector2, closestTo: Vector2) {
        let v = Vector2.subtract(lineB, lineA);
        let w = Vector2.subtract(closestTo, lineA);
        let t = Vector2.dot(w, v) / Vector2.dot(v, v);
        t = MathHelper.clamp(t, 0, 1);

        return Vector2.add(lineA, new Vector2(v.x * t, v.y * t));
    }

    public static isCircleToCircle(circleCenter1: Vector2, circleRadius1: number, circleCenter2: Vector2, circleRadius2: number): boolean {
        return Vector2.distanceSquared(circleCenter1, circleCenter2) < (circleRadius1 + circleRadius2) * (circleRadius1 + circleRadius2);
    }

    public static isCircleToLine(circleCenter: Vector2, radius: number, lineFrom: Vector2, lineTo: Vector2): boolean {
        return Vector2.distanceSquared(circleCenter, this.closestPointOnLine(lineFrom, lineTo, circleCenter)) < radius * radius;
    }

    public static isCircleToPoint(circleCenter: Vector2, radius: number, point: Vector2): boolean {
        return Vector2.distanceSquared(circleCenter, point) < radius * radius;
    }

    public static isRectToCircle(rect: Rectangle, cPosition: Vector2, cRadius: number): boolean {
        if (this.isRectToPoint(rect.x, rect.y, rect.width, rect.height, cPosition))
            return true;

        let edgeFrom: Vector2;
        let edgeTo: Vector2;
        let sector = this.getSector(rect.x, rect.y, rect.width, rect.height, cPosition);

        if ((sector & PointSectors.top) != 0) {
            edgeFrom = new Vector2(rect.x, rect.y);
            edgeTo = new Vector2(rect.x + rect.width, rect.y);
            if (this.isCircleToLine(cPosition, cRadius, edgeFrom, edgeTo))
                return true;
        }

        if ((sector & PointSectors.bottom) != 0) {
            edgeFrom = new Vector2(rect.x, rect.y + rect.height);
            edgeTo = new Vector2(rect.x + rect.width, rect.y + rect.height);
            if (this.isCircleToLine(cPosition, cRadius, edgeFrom, edgeTo))
                return true;
        }

        if ((sector & PointSectors.left) != 0) {
            edgeFrom = new Vector2(rect.x, rect.y);
            edgeTo = new Vector2(rect.x, rect.y + rect.height);
            if (this.isCircleToLine(cPosition, cRadius, edgeFrom, edgeTo))
                return true;
        }

        if ((sector & PointSectors.right) != 0) {
            edgeFrom = new Vector2(rect.x + rect.width, rect.y);
            edgeTo = new Vector2(rect.x + rect.width, rect.y + rect.height);
            if (this.isCircleToLine(cPosition, cRadius, edgeFrom, edgeTo))
                return true;
        }

        return false;
    }

    public static isRectToLine(rect: Rectangle, lineFrom: Vector2, lineTo: Vector2){
        let fromSector = this.getSector(rect.x, rect.y, rect.width, rect.height, lineFrom);
        let toSector = this.getSector(rect.x, rect.y, rect.width, rect.height, lineTo);

        if (fromSector == PointSectors.center || toSector == PointSectors.center){
            return true;
        } else if((fromSector & toSector) != 0){
            return false;
        } else{
            let both = fromSector | toSector;
            // 线对边进行检查
            let edgeFrom: Vector2;
            let edgeTo: Vector2;

            if ((both & PointSectors.top) != 0){
                edgeFrom = new Vector2(rect.x, rect.y);
                edgeTo = new Vector2(rect.x + rect.width, rect.y);
                if (this.isLineToLine(edgeFrom, edgeTo, lineFrom, lineTo))
                    return true;
            }

            if ((both & PointSectors.bottom) != 0){
                edgeFrom = new Vector2(rect.x, rect.y + rect.height);
                edgeTo = new Vector2(rect.x + rect.width, rect.y + rect.height);
                if (this.isLineToLine(edgeFrom, edgeTo, lineFrom, lineTo))
                    return true;
            }

            if ((both & PointSectors.left) != 0){
                edgeFrom = new Vector2(rect.x, rect.y);
                edgeTo = new Vector2(rect.x, rect.y + rect.height);
                if (this.isLineToLine(edgeFrom, edgeTo, lineFrom, lineTo))
                    return true;
            }

            if ((both & PointSectors.right) != 0){
                edgeFrom = new Vector2(rect.x + rect.width, rect.y);
                edgeTo = new Vector2(rect.x + rect.width, rect.y + rect.height);
                if (this.isLineToLine(edgeFrom, edgeTo, lineFrom, lineTo))
                    return true;
            }
        }

        return false;
    }

    public static isRectToPoint(rX: number, rY: number, rW: number, rH: number, point: Vector2) {
        return point.x >= rX && point.y >= rY && point.x < rX + rW && point.y < rY + rH;
    }

    /**
     * 位标志和帮助使用Cohen–Sutherland算法
     * 
     * 位标志:
     * 1001 1000 1010
     * 0001 0000 0010
     * 0101 0100 0110
     * @param rX 
     * @param rY 
     * @param rW 
     * @param rH 
     * @param point 
     */
    public static getSector(rX: number, rY: number, rW: number, rH: number, point: Vector2): PointSectors {
        let sector = PointSectors.center;

        if (point.x < rX)
            sector |= PointSectors.left;
        else if (point.x >= rX + rW)
            sector |= PointSectors.right;

        if (point.y < rY)
            sector |= PointSectors.top;
        else if (point.y >= rY + rH)
            sector |= PointSectors.bottom;

        return sector;
    }
}