Computational geometry: an introduction
Computational geometry: an introduction
Convex hulls of piecewise-smooth Jordan curves
Journal of Algorithms
Loop detection in surface patch intersections
Computer Aided Geometric Design
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
The convex Hull of Rational Plane Curves
Graphical Models
A Parametric Solution to Common Tangents
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
The convex hull of freeform surfaces
Computing - Geometric modelling dagstuhl 2002
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Coons BVH for freeform geometric models
Proceedings of the 2011 SIGGRAPH Asia Conference
| Hi-index | 0.00 |
We present an interactive-speed algorithm for computing the precise convex hull of freeform geometric models. The algorithm is based on two pre-built data structures: (i) a Gauss map organized in a hierarchy of normal pyramids and (ii) a Coons bounding volume hierarchy (CBVH) which effectively approximates freeform surfaces with a hierarchy of bilinear surfaces. For the axis direction of each normal pyramid, we sample a point on the convex hull boundary using the CBVH. The sampled points together with the hierarchy of normal pyramids serve as a hierarchical approximation of the convex hull, with which we can eliminate the majority of redundant surface patches. We compute the precise trimmed surface patches on the convex hull boundary using a numerical tracing technique and then stitch them together in a correct topology while filling the gaps with tritangent planes and bitangent developable scrolls. We demonstrate the effectiveness of our algorithm using experimental results.