How to get overlapping rectangle coordinates

Question

Assume I have the following overlapping rectangles (\"a\" and \"b\"):

aaaaaaaa
aaaaccccbbbbb
aaaaccccbbbbb
aaaaccccbbbbb
    bbbbbbbbb
    bbbbbbbbb

Answer 1

The X coordinates of the overlap area of two rectangles can be found according to the following logic.

To find the Y coordinates, substitute Y for X in the last of the four assumptions, as well as in all of the three cases.

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Assumptions:

• A and B are rectangles (with their sides aligned along the X and Y axes),

• each of the rectangles is defined by two points   (x_min / y_min) – (x_max / y_max)

• where x_min < x_max   and   y_min < y_max  .

• A.x_min < B.x_min

---

Case 1 — No overlap:

+--------+
|A       |    
|        |    +----+
|        |    |B   |
|        |    +----+
|        |
+--------+

A.x_min < A.x_max < B.x_min < B.x_max   ⇒   No overlap.

---

Case 2 — Some overlap:

+--------+
|A       |
|     +--+-+
|     |B | |
|     +--+-+
|        |
+--------+

A.x_min < B.x_min < A.x_max < B.x_max   ⇒   Overlap X coordinates: B.x_min – A.x_max

---

Case 3 — Complete overlap:

+--------+
|A       |
| +----+ |
| |B   | |
| +----+ |
|        |
+--------+

A.x_min < B.x_min < B.x_max < A.x_max   ⇒   Overlap X coordinates: B.x_min – B.x_max

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P.S.: You can actually further simplify this algorithm. The overlap X coordinates are always:

max(A.x_min, B.x_min) – min(A.x_max, B.x_max)

except when the second value is less than the first; that means that there is no overlap.