java - 带填充的矩形圆交点

Question

我有以下方法非常适合测试矩形是否与圆相交。我如何修改它以提供一个额外的参数，即填充，这意味着矩形和圆形需要彼此相距一定数量的像素？

public static boolean rectangleCircleIntersection(RectangleRegion rect, CircularRegion circle, int padding) {
        int circleDistance_x = PsyMath.abs((circle.getX()+circle.getRadius()) - (rect.getX()+rect.getWidth()/2));
        int circleDistance_y = PsyMath.abs((circle.getY()+circle.getRadius()) - (rect.getY()+rect.getHeight()/2));

        if (circleDistance_x > (rect.getWidth()/2 + circle.getRadius())) { return false; }
        if (circleDistance_y > (rect.getHeight()/2 + circle.getRadius())) { return false; }

        if (circleDistance_x <= (rect.getWidth()/2)) { return true; } 
        if (circleDistance_y <= (rect.getHeight()/2)) { return true; }

        int cornerDistance_sq = (int)Math.pow((circleDistance_x - rect.getWidth()/2),2) +
                             (int)Math.pow((circleDistance_y - rect.getHeight()/2),2);

        return (cornerDistance_sq <= (int)Math.pow(circle.getRadius(),2));
    }

这是我的尝试，但我不太相信它是正确的:

public static boolean rectangleCircleIntersection(RectangleRegion rect, CircularRegion circle, int padding) {
        int circleDistance_x = PsyMath.abs((circle.getX()+circle.getRadius()) - (rect.getX()+rect.getWidth()/2));
        int circleDistance_y = PsyMath.abs((circle.getY()+circle.getRadius()) - (rect.getY()+rect.getHeight()/2));

        if (circleDistance_x > (rect.getWidth()/2 + circle.getRadius() + padding)) { return false; }
        if (circleDistance_y > (rect.getHeight()/2 + circle.getRadius() + padding)) { return false; }

        if ((circleDistance_x+padding) <= (rect.getWidth()/2)) { return true; } 
        if ((circleDistance_y+padding) <= (rect.getHeight()/2)) { return true; }

        int cornerDistance_sq = (int)Math.pow((circleDistance_x - rect.getWidth()/2),2) +
                             (int)Math.pow((circleDistance_y - rect.getHeight()/2),2);

        return (cornerDistance_sq <= (int)Math.pow(circle.getRadius(),2));
    }

Answer 1

您可以安全地填充圆圈，然后检查它们是否相交。 填充矩形不太好，因为填充矩形的角与原始矩形角的间距是填充的 sqrt(2) 倍。

因此，假设上面的代码运行良好，并且半径是一个整数，您将得到:

public static boolean rectangleCircleIntersection(RectangleRegion rect, CircularRegion circle, int padding) {
    int paddedRadius = circle.getRadius() + padding;
    int circleDistance_x = PsyMath.abs((circle.getX()+paddedRadius) - (rect.getX()+rect.getWidth()/2));
    int circleDistance_y = PsyMath.abs((circle.getY()+paddedRadius) - (rect.getY()+rect.getHeight()/2));

    if (circleDistance_x > (rect.getWidth()/2 + paddedRadius)) { return false; }
    if (circleDistance_y > (rect.getHeight()/2 + paddedRadius)) { return false; }

    if (circleDistance_x <= (rect.getWidth()/2)) { return true; } 
    if (circleDistance_y <= (rect.getHeight()/2)) { return true; }

    int cornerDistance_sq = (int)Math.pow((circleDistance_x - rect.getWidth()/2),2) +
                         (int)Math.pow((circleDistance_y - rect.getHeight()/2),2);

    return (cornerDistance_sq <= (int)Math.pow(paddedRadius,2));
}