判断区域相交的方法

 

package KconniePong;

// 两个矩形都是平行于X,Y轴，判断是否相交。两种方法，都需要检查特殊情况。
public class RectangleIntersect {
	// 方法一：矩阵在X,Y轴上的投影都在另一矩形投影的一侧，则矩阵必定无交集；否则，有交集。
	boolean isRectIntersect(Rectangle a, Rectangle b) {
		// 需要排除特殊情况：一个矩形在另一个矩形内
		if ((a.top < b.top && a.bottom > b.bottom && a.right < b.right && a.left > b.left) || (b.top < a.top && b.bottom > a.bottom && b.right < a.right && b.left > a.left)) {
			return false;
		}
		if ((a.top < b.bottom && a.right < b.left) || (a.bottom > b.top && a.left > b.right)) {
			return false;
		}
		return true;
	}

	// 方法二：若两矩形的中心满足一定的条件，则必定相交
	boolean isRectIntersect2(Rectangle a, Rectangle b) {
		float aCenterX = (a.left + a.right) / 2;
		float aCenterY = (a.bottom + a.top) / 2;
		float bCenterX = (b.left + b.right) / 2;
		float bCenterY = (b.bottom + b.top) / 2;
		float radiusX = (a.right - a.left) / 2 + (b.right - b.left) / 2;
		float radiusY = (a.top - a.bottom) / 2 + (b.top - b.bottom) / 2;
		// 需要排除特殊情况：一个矩形在另一个矩形内
		if ((a.top < b.top && a.bottom > b.bottom && a.right < b.right && a.left > b.left) || (b.top < a.top && b.bottom > a.bottom && b.right < a.right && b.left > a.left)) {
			return false;
		}
		if ((Math.abs(aCenterX - bCenterX) < radiusX) || (Math.abs(aCenterY - bCenterY) < radiusY)) {
			return true;
		}
		return false;
	}

	// 若两矩形相交，相交区域必定有：top = min(top),bottom = max(bottom),right =
	// min(right),left = max(left)
	float intersectArea(Rectangle a, Rectangle b) {
		if (isRectIntersect(a, b)) {
			return (Math.min(a.top, b.top) - Math.max(a.bottom, b.bottom)) * (Math.min(a.right, b.right) - Math.max(a.left, b.left));
		}
		return 0;
	}

	public static void main(String[] args) {
		Rectangle ra = new Rectangle(0, 3, 0, 6);
		Rectangle rb = new Rectangle(2, 4, 2, 4);
		RectangleIntersect r = new RectangleIntersect();
		if (r.isRectIntersect(ra, rb)) {
			System.out.println("两矩阵相交");
		} else {
			System.out.println("两矩形不相交");
		}
		if (r.isRectIntersect2(ra, rb)) {
			System.out.println("两矩阵相交");
		} else {
			System.out.println("两矩形不相交");
		}

		System.out.println("相交区域面积： " + r.intersectArea(ra, rb));
	}
}

class Rectangle {
	// 分别表示最上下左右上的坐标
	float left;
	float right;
	float bottom;
	float top;

	Rectangle(float left, float right, float bottom, float top) {
		if (left >= right || top <= bottom) {
			System.out.println("矩形坐标初始化错误！");
			return;
		}
		this.left = left;
		this.right = right;
		this.top = top;
		this.bottom = bottom;
	}
}