Loop detection in surface patch intersections
Computer Aided Geometric Design
Improved test for closed loops in surface intersections
Computer-Aided Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Intersection of offsets of parametric surfaces
Computer Aided Geometric Design
Exploiting topological and geometric properties for selective subdivision
SCG '85 Proceedings of the first annual symposium on Computational geometry
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Mathematical Methods for Curves and Surfaces
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Global curve analysis via a dimensionality lifting scheme
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Surface self-intersection computation via algebraic decomposition
Computer-Aided Design
Hausdorff and minimal distances between parametric freeforms in R2and R3
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
A surface blending approach for displacement features on freeform surfaces
Computer-Aided Design
Computer Aided Geometric Design
Computer Aided Geometric Design
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We present several algorithms for self-intersection detection, and possible elimination, in freeform planar curves and surfaces. Both local and global self-intersections are eliminated using a binormal-line criterion and a simple direct algebraic elimination procedure that enables the direct solution of the algebraic (self-)intersection constraints. All algorithms have been fully implemented and tested. Examples are presented for applications in self-intersection detection, self-intersection-free metamorphosis of curves, and proper trimming of self-intersections in offset curves.