Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Intersection of offsets of parametric surfaces
Computer Aided Geometric Design
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Mathematical Methods for Curves and Surfaces
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Self-intersection detection and elimination in freeform curves and surfaces
Computer-Aided Design
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
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This work draws upon a recent result (Pekerman et al., 2008) [3] on self-intersection detection and elimination for planar curves, which attempted to eliminate redundant algebraic components. We extend this result to surfaces and bivariate functions. An algebraic decomposition is presented that reformulates the surface self-intersection problem using an alternative set of constraints, while removing the redundant components. Extensions to higher dimensions are also briefly discussed.