Minkowski Sum of Convex Polygons

A ⊕ B = { a + b : a ∈ A, b ∈ B } — built by merging edge vectors in angular order

Convex ⊕ Convex: O(n + m) Naive all-pairs: O(nm log nm) Output: ≤ n + m vertices

Controls

Example:

Show all-pairs cloud (a+b)

C-space mode: inflate B by −A

Speed: slow fast

Live Stats

A vertices

0

B vertices

0

Sum edges built

0

Pointer i / j

0 / 0

Current Operation

Press Build to merge the edge vectors of A and B by polar angle, or Step one edge at a time.

Big-O

Operation	Time
Convex ⊕ convex (merge)	O(n + m)
A ⊕ {point} (translate)	O(n)
Not pre-sorted by angle	O(n log n + m log m)
Naive all-pairs + hull	O(nm log nm)
Non-convex (decompose)	O(n² m²)

Visualization

A (polygon) B (polygon) A ⊕ B (sum) C-space: B ⊕ (−A) active edge being merged

Operation Log