Splitting a complex of convex polytopes in any dimension
Chandrajit Bajaj, Valerio Pascucci · 1996
Introduction We present a locality-based algorithm to solve the problem of splitting a complex of convex polytopes with a hyperplane or a convex subset of it. The solution to this problem has several applications. One goal is to perform boolean set operations. The solution can also be used to decompose a polyhedron into convex polytopes [3] and to generate good meshes [4]. In higher dimensional spaces it can be used to efficiently compute isocontours of linear approximations of scalar fields (a basic technique of Scientific Visualization) [17, 19]. The approach taken here can also be included in a set of robust algorithms [11, 13, 15, 20, 27, 28] based on finite precision arithmetic. It is also defined in a dimension independent framework [5, 16, 24, 25]. The main contributions of this approach are: (i) it can be applied to polyhedral complexes of any dimension d; (ii) the algorithm is robust (it always produces valid output) and consistent (the topological structure of the resu