Computational geometry: an introduction
Computational geometry: an introduction
Convex hulls of piecewise-smooth Jordan curves
Journal of Algorithms
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
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
Medial axis computation for planar free-form shapes
Computer-Aided Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Efficient offset trimming for planar rational curves using biarc trees
Computer Aided Geometric Design
Minimum area enclosure and alpha hull of a set of freeform planar closed curves
Computer-Aided Design
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We present an efficient real-time algorithm for computing the precise convex hulls of planar freeform curves. For this purpose, the planar curves are initially approximated with G^1-biarcs within a given error bound @e in a preprocessing step. The algorithm is based on an efficient construction of approximate convex hulls using circular arcs. The majority of redundant curve segments can be eliminated using simple geometric tests on circular arcs. In several experimental results, we demonstrate the effectiveness of the proposed approach, which shows the performance improvement in the range of 200-300 times speed up compared with the previous results (Elber et al., 2001) [8].