A G1 triangular spline surface of arbitrary topological type

doi:10.1016/0167-8396(94)90005-1

Computer Aided Geometric Design

Volume 11, Issue 3, June 1994, Pages 303-330

https://doi.org/10.1016/0167-8396(94)90005-1 Get rights and content

Abstract

A piecewise G¹ spline surface composed of sextic triangular Bézier patches in one-to-one correspondence with the faces of a triangular control mesh is presented. Surfaces of arbitrary topological type are created by approximating any mesh that represents a triangulated 2-manifold. The surface has local support and is affine invariant. A set of shape parameters are available for additional local control over the shape of the surface. If some local regularities are present in the structure of the control mesh, then the corresponding patches may be parametrized as quintic or even quartic Bézier triangles. In the case of a regular triangulation (with appropriate shape parameters), the surface generated by this method is equivalent to a quartic C² triangular B-spline.

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^★: Work done while the author was at the University of Washington.

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A G1 triangular spline surface of arbitrary topological type

Abstract

Computer-Aided Design

Computer Aided Geometric Design

Computer Aided Geometric Design

J. Approx. Theory

Comput. Graphics Image Processing

Computer-Aided Design

Computer Aided Geometric Design

Computer-Aided Design

Smoothing polyhedra using implicit algebraic splines

Comput. Graphics

The de Boor algorithm for triangular splines

Generating the Bézier points of triangular splines

Design of solids with free-form surfaces

Computer Graphics

B-splines from parallelepipeds

J. Anal. Math.

Geometric Continuity: A Parametrization Independent Measure of Continuity for Computer Aided Geometric Design

Ph.D. thesis

A subdivision algorithm for smoothing down irregularly shaped polyhedrons

Proc. on Interactive Techniques in Computer Aided Design

Smooth interpolation to scattered 3D data

A G¹ triangular spline surface of arbitrary topological type