Robust, Generic and Efficient Construction of Envelopes of Surfaces in Three-Dimensional Spaces

Lower envelopes are fundamental structures in computational geometry, which have many applications, such as computing general Voronoi diagrams and performing hidden surface removal in computer graphics. We present a generic, robust and efficient implementation of the divide-and-conquer algorithm for computing the envelopes of surfaces in IR3 . To the best of our knowledge, this is the first exact implementation that computes envelopes in three-dimensional space. Our implementation is based on Cgal (the Computational Geometry Algorithms Library) and is designated as a Cgal package. The separation of topology and geometry in our solution allows for the reuse of the algorithm with different families of surfaces, provided that a small set of geometric objects and operations on them is supplied. We used our algorithm to compute the lower and upper envelope for several types of surfaces. Exact arithmetic is typically slower than floating-point arithmetic, especially when higher order surface...

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Michal Meyerovitch
• Keywords: Algorithm, Algorithms, Envelopes, ESA 2006, Lower Envelopes