Diameter and Convex Hull of Points Using Space Subdivision in E2 and E3

Abstract

Convex hull of points and its diameter computation is a frequent task in many engineering problems, However, in engineering solutions, the asymptotic computational complexity is less important than the computational complexity for the expected data size to be processed. This contribution describes “an engineering solution" of the convex hulls and their diameter computation using space-subdivision and data-reduction approaches. This approach proved a significant speed-up of computation with simplicity of implementation. Surprisingly, the experiments proved, that in the case of the space subdivision the reduction of points is so efficient, that the “brute force" algorithms for the convex hull and its diameter computation of the remaining points have nearly no influence to the time of computation.