Maximum overlap and minimum convex hull of two convex polyhedra under translations

Citations of this article
Mendeley users who have this article in their library.


Given two convex polyhedra P and Q in three-dimensional space, we consider two related problems of shape matching: (1) finding a translation t1∈ R3 of Q that maximizes the volume of their overlap P∩(Q+ t1), and (2) finding a translation t2∈ R3 that minimizes the volume of the convex hull of P∪(Q+ t2). For the maximum overlap problem, we observe that the dth root of the objective function is concave and present an algorithm that computes the optimal translation in expected time O( n3log4n). This method generalizes to higher dimensions d>3 with expected running time O(nd+ 1-3d( logn)d+1). For the minimum convex hull problem, we show that the objective function is convex. The same method used for the maximum overlap problem can be applied to this problem and the optimal translation can be computed in the same time bound. © 2007 Elsevier B.V.




Ahn, H. K., Brass, P., & Shin, C. S. (2008). Maximum overlap and minimum convex hull of two convex polyhedra under translations. Computational Geometry: Theory and Applications, 40(2), 171–177.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free