I clip a 3D triangle against a 3D Axis-Aligned Bounding Box (AABB) to obtain the largest planar polygon of the triangle contained in the AABB. My clipping algorithm is a (slightly modified) version of the robust (e.g. clipping planes have a small finite thickness) Sutherland-Hodgman algorithm as described in C. Ericson's Real-Time Collision Detection. I clip the triangle against each of the 6 planes constituting the AABB.

In order to avoid heap (de)allocation, I allocated a fixed size point buffer on the stack in advance for all the vertices of the obtained planar polygon. My question now is: what is the maximum number of vertices possible one can obtain after clipping a triangle against an AABB?

Based on the control flow, every examined vertex can result in two vertices during a polygon plane clipping. Thus $3*2^6$ vertices. Due to symmetry this becomes $3*2^3=24$ vertices. However, I always obtain less vertices in practice.


1 Answer 1


Funnily enough, I asked this exact question on Math.SE a couple years ago: Maximum number of vertices in intersection of triangle with box.

The answer is 9 vertices, because each of the 6 planes of the box can cut off one corner of the polygon, replacing one vertex with two. So 3 vertices + 6 added vertices due to clipping = 9 total.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.