Necessary and sufficient conditions for tangent plane continuity of Be´zier surfaces
Computer Aided Geometric Design
A technique for constructing developable surfaces
GI '96 Proceedings of the conference on Graphics interface '96
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Existence conditions for Coons patches interpolating geodesic boundary curves
Computer Aided Geometric Design
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Geodesic-like curves on parametric surfaces
Computer Aided Geometric Design
Construction and smoothing of triangular Coons patches with geodesic boundary curves
Computer Aided Geometric Design
A note of boundary geodesic problem on regular surfaces
ECC'11 Proceedings of the 5th European conference on European computing conference
The general orthogonal projection on a regular surface
ECC'11 Proceedings of the 5th European conference on European computing conference
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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We consider patches that contain any given 3D polynomial curve as a pregeodesic (i.e. geodesic up to reparametrization). A curve is a pregeodesic if and only if its rectifying plane coincides with the tangent plane to the surface, we use this fact to construct ruled cubic patches through pregeodesics and bicubic patches through pairs of pregeodesics. We also discuss the G^1 connection of (1,k) patches with abutting pregeodesics.