Loop detection in surface patch intersections
Computer Aided Geometric Design
Evaluation and properties of the derivative of a NURBS curve
Mathematical methods in computer aided geometric design II
Robust and efficient surface intersection for solid modeling
Robust and efficient surface intersection for solid modeling
Hodographs and normals of rational curves and surfaces
Computer Aided Geometric Design
The NURBS book
Tangent, normal, and visibility cones on Be´zier surfaces
Computer Aided Geometric Design
A counterexample to a corollary of Kim et al.
Computer Aided Geometric Design
A note on degenerate normal vectors
Computer Aided Geometric Design
Partial derivatives of rational Be´zier surfaces
Computer Aided Geometric Design
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Computing normal vector Bézier patches
Computer Aided Geometric Design - Pierre Bézier
Mathematical Methods for Curves and Surfaces
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Solving systems of algebraic equations
Machine Graphics & Vision International Journal
Surface-surface intersection: loop destruction using bezier clipping and pyramidal bounds
Surface-surface intersection: loop destruction using bezier clipping and pyramidal bounds
Implementation of a divide-and-conquer method for intersection of parametric surfaces
Computer Aided Geometric Design
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This paper considers tangent cones for NURBS surfaces. The first part gives new bounds for the tangent field, which extends the results of [Wang, G.-J., Sederberg, T.W., Saito, T., 1997. Partial derivatives of rational Bezier surfaces. Computer Aided Geometric Design 14, 377-381] to NURBS surfaces. In particular, if the weights of the NURBS surface have a tensor product structure, the tangent cones are spanned by the differences of the control points in one direction. The second part revisits uniqueness criteria for intersections between curves and surfaces and non-existence criteria for self-intersections, which are based on tangent cones. Using a unified proof, we reprove known theorems and deduce new criteria, e.g. for the non-existence of self-intersections.