Do Two Rectangles Overlap? A Deterministic Approach

Deterministic Detection of Rectangles Overlap

The objective is to ascertain whether two rectangles overlap within a 2D plane, given various parameters defining their locations and dimensions. Your implementation appears to be based on convex hull theory, but it requires further examination to validate its correctness.

Basic Overlap Algorithm

An intuitive method for overlap detection involves comparing the relative positions of each rectangle's edges:

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

This condition ensures that no part of Rectangle A lies entirely outside the bounds of Rectangle B, indicating that they overlap.

Explaining the Conditions

For clarification, the condition checks the following:

• Left edge of A: If A's left edge is positioned to the left of B's right edge, A cannot be completely to the right of B.
• Right edge of A: If A's right edge is positioned to the right of B's left edge, A cannot be completely to the left of B.
• Top edge of A: If A's top edge is situated above B's bottom edge, A cannot be completely below B.
• Bottom edge of A: If A's bottom edge is located below B's top edge, A cannot be completely above B.

In summary, if all four conditions are satisfied, the rectangles overlap, and alternatively, if any condition fails, they do not overlap.

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