total area of intersecting rectangles

Question

I need an algorithm to solve this problem: Given 2 rectangles intersecting or overlapping together in any corner, how do I determine the total area for the two rectangles without the overlapped (intersection) area? Meaning the area of intersection has to be calculated once, either with the first rectangle, or with second one.

Answer 1

That's easy. First compute coordinates of intersection, which is also a rectangle.

left = max(r1.left, r2.left) right = min(r1.right, r2.right) bottom = max(r1.bottom, r2.bottom) top = min(r1.top, r2.top) 

Then, if intersection is not empty (left < right && bottom < top), subtract it from the common area of two rectangles: r1.area + r2.area - intersection.area.

PS:

1. Assumption 1: rectangles are aligned by the coordinate axes, that's usually the case.
2. Assumption 2: y axis here increases upwards, for example, in a graphics application, the y axis increases downwards, you may need to use:

bottom = min(r1.bottom, r2.bottom) top = max(r1.top, r2.top)

Answer 2

Here is complete solution for this algorithm using Java:

public static int solution(int K, int L, int M, int N, int P, int Q, int R,         int S) {     int left = Math.max(K, P);     int right = Math.min(M, R);     int bottom = Math.max(L, Q);     int top = Math.min(N, S);      if (left < right && bottom < top) {         int interSection = (right - left) * (top - bottom);         int unionArea = ((M - K) * (N - L)) + ((R - P) * (S - Q))                 - interSection;         return unionArea;     }     return 0; }