An implementation of triangular B-spline surfaces over arbitrary triangulations

doi:10.1016/0167-8396(93)90041-Z

Computer Aided Geometric Design

Volume 10, Issues 3–4, August 1993, Pages 267-275

https://doi.org/10.1016/0167-8396(93)90041-Z Get rights and content

Abstract

A new multivariate B-spline scheme based on blending functions and control vertices has recently been developed by Dahmen, Micchelli, and Seidel (1992). This surface scheme allows us to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C_k−1-continuous everywhere. The scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Any piecewise polynomial can be represented by the new scheme [Seidel '92]. This paper illustrates some of the algorithms underlying the new scheme by means of examples from a first test implementation [Fong '92].

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An implementation of triangular B-spline surfaces over arbitrary triangulations

Abstract

Computer Aided Geometric Design

Approximation and geometric modeling with simplex B-splines associated with irregular triangles

Computer Aided Geometric Design

On the linear independence of multivariate B-splines I. Triangulations of simploids

SIAM J. Numer. Anal.

Recent progress in multivariate splines

Blossoming begets B-splines built better by B-patches

Math. Comp.

Shape control for B-splines over arbitrary triangulations