How Can We Efficiently Determine if Two Rectangles Overlap?

Overlapping Rectangles: A Comprehensive Analysis

Determining whether two rectangles overlap in a two-dimensional plane is a fundamental problem in computer graphics and computational geometry. In this article, we will explore an efficient algorithm to solve this problem.

Conditions for Overlap

Two rectangles, A and B, overlap if and only if four conditions are met:

• A's left edge is to the left of B's right edge: RectA.Left < RectB.Right
• A's right edge is to the right of B's left edge: RectA.Right > RectB.Left
• A's top edge is above B's bottom edge: RectA.Top > RectB.Bottom
• A's bottom edge is below B's top edge: RectA.Bottom < RectB.Top

Algorithm

Based on these conditions, we can construct an algorithm to check for overlap:

def check_overlap(RectA, RectB):
  return RectA.Left < RectB.Right and \
         RectA.Right > RectB.Left and \
         RectA.Top > RectB.Bottom and \
         RectA.Bottom < RectB.Top

Implementation

In your C code, you can implement this algorithm as follows:

#include 

class Rectangle {
public:
  int left, right, top, bottom;
};

bool check_overlap(Rectangle rect1, Rectangle rect2) {
  return rect1.left < rect2.right && \
         rect1.right > rect2.left && \
         rect1.top > rect2.bottom && \
         rect1.bottom < rect2.top ;
}

int main() {
  Rectangle rect1, rect2;
  std::cout << "Enter the coordinates of Rectangle 1 (left, right, top, bottom): ";
  std::cin >> rect1.left >> rect1.right >> rect1.top >> rect1.bottom;

  std::cout << "Enter the coordinates of Rectangle 2 (left, right, top, bottom): ";
  std::cin >> rect2.left >> rect2.right >> rect2.top >> rect2.bottom;

  if (check_overlap(rect1, rect2)) {
    std::cout << "The rectangles overlap." << std::endl;
  } else {
    std::cout << "The rectangles do not overlap." << std::endl;
  }

  return 0;
}
This implementation prompts the user for the coordinates of two rectangles and checks for overlap based on the aforementioned conditions.

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