How Do You Determine if Two Rectangles Overlap?

Determining Overlap Between Rectangles:

Your initial approach to determining overlap between rectangles appears to be based on a different algorithm than the one linked in the question. The provided algorithm uses a more straightforward comparison of rectangle coordinates, as shown below:

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

 // Assuming Left, Right, Top and Bottom are the coordinates of the rectangles along the X and Y axis

In Cartesian coordinates, this condition can be expressed as:

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

Proof by Contradiction:

This condition is based on the principle of proof by contradiction. If any one of the following conditions is true, then the rectangles cannot overlap:

• RectA's left edge is to the right of RectB's right edge (RectA is completely to the right of RectB)
• RectA's right edge is to the left of RectB's left edge (RectA is completely to the left of RectB)
• RectA's top edge is below RectB's bottom edge (RectA is completely below RectB)
• RectA's bottom edge is above RectB's top edge (RectA is completely above RectB)

Therefore, the condition for overlap is the opposite of these conditions:

• RectA's left edge is to the left of RectB's right edge
• RectA's right edge is to the right of RectB's left edge
• RectA's top edge is above RectB's bottom edge
• RectA's bottom edge is below RectB's top edge

Additional Notes:

• This algorithm assumes that the rectangles are parallel to the X and Y axes.
• To allow for overlaps of one pixel, change the < and > operators to <= and >= on the relevant boundaries.
• The algorithm can be easily adjusted for different coordinate systems (e.g., if Y increases from top to bottom).

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