Do Two Rectangles Overlap?

Determining Overlap of Rectangles

In scenarios where parallel rectangles exist, a crucial task is determining if they overlap. The provided code snippet attempts to implement an algorithm for this purpose, but it requires further clarification.

To effectively evaluate overlap, we can utilize the following mathematical conditions:

if (RectA.Left < RectB.Right && RectA.Right > RectB.Left
    && RectA.Top > RectB.Bottom && RectA.Bottom < RectB.Top)

In Cartesian coordinates, this translates to:

if (RectA.X1 < RectB.X2 && RectA.X2 > RectB.X1
    && RectA.Y1 > RectB.Y2 && RectA.Y2 < RectB.Y1)

Let's analyze this in detail:

• Condition 1: If Rectangle A's left edge is to the left of Rectangle B's right edge, then A is not entirely to the right of B.
• Condition 2: If Rectangle A's right edge is to the right of Rectangle B's left edge, then A is not entirely to the left of B.
• Condition 3: If Rectangle A's top edge is above Rectangle B's bottom edge, then A is not entirely below B.
• Condition 4: If Rectangle A's bottom edge is below Rectangle B's top edge, then A is not entirely above B.

By combining these conditions using AND operators, we ensure that all four conditions are satisfied concurrently. This establishes the necessary and sufficient criteria for two rectangles to overlap.

Note: The method can be extended to arbitrary dimensions, making it applicable to various use cases involving non-rectangular objects. Furthermore, by adjusting the comparison operators, we can modify the conditions to determine partial or complete overlap scenarios as needed.

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