Intersection of offsets of parametric surfaces
Computer Aided Geometric Design
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Curve offsetting based on Legendre series
Computer Aided Geometric Design
Contour machining of free-form surfaces with real-time PH curve CNC interpolators
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
Mathematical Methods for Curves and Surfaces
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Problem Reduction to Parameter Space
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
The convex hull of freeform surfaces
Computing - Geometric modelling dagstuhl 2002
Contouring 1- and 2-Manifolds in Arbitrary Dimensions
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Intersecting a freeform surface with a general swept surface
Computer-Aided Design
Geometric computations in parameter space
Proceedings of the 21st spring conference on Computer graphics
Sliding windows algorithm for B-spline multiplication
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Self-intersection detection and elimination in freeform curves and surfaces
Computer-Aided Design
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Voronoi diagram computations for planar NURBS curves
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Good global behavior of offsets to plane algebraic curves
Journal of Symbolic Computation
Equivolumetric offset surfaces
Computer Aided Geometric Design
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
Computing surface offsets and bisectors using a sampled constraint solver
Proceedings of Graphics Interface 2009
Solving global geometric constraints on free-form curves
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Offsetting operations on non-manifold topological models
Computer-Aided Design
Surface self-intersection computation via algebraic decomposition
Computer-Aided Design
Computer aided design of ventilation tubes for customized hearing aid devices
Computer-Aided Design
Critical point analysis using domain lifting for fast geometry queries
Computer-Aided Design
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
A surface blending approach for displacement features on freeform surfaces
Computer-Aided Design
Efficient offset trimming for planar rational curves using biarc trees
Computer Aided Geometric Design
Discrete geometric modeling of thick pelvic organs with a medial axis
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
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A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented. Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset. By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected. The zero-set of polynomial equation(s) corresponds to the self-intersection regions. These regions are trimmed by projecting the zero-set into an appropriate parameter space. The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient. Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces. The effectiveness of our approach is demonstrated using several experimental results.