Hybrid Cubic Bézier Triangle Patches

Abstract With two additional control points, we modify the cubic Bezier triangle patch to obtain a compact representation for some procedurally defined triangular patches. The hybrid form can be evaluated with the de Casteljau algorithm, and with a slight variation we can easily compute first order derivatives. A C1 interpolant to scattered data with cubic precision is given that is significantly smoother than when linear cross boundary derivatives are used.

[1]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[2]  H. B. Said,et al.  A C1 triangular interpolant suitable for scattered data interpolation , 1991 .

[3]  Gerald E. Farin,et al.  A modified Clough-Tocher interpolant , 1985, Comput. Aided Geom. Des..

[4]  S. Stead.  Estimation of gradients from scattered data , 1984 .

[5]  Hiroaki Chiyokura,et al.  Design of solids with free-form surfaces , 1983, SIGGRAPH.

[6]  G. Nielson.  A method for interpolating scattered data based upon a minimum norm network , 1983 .

[7]  W. J. Gordon,et al.  Smooth interpolation in triangles , 1973 .

[8]  L. Schumaker.  Fitting surfaces to scattered data , 1976 .

[9]  Nira Dyn,et al.  Algorithms for the construction of data dependent triangulations , 1990 .

[10]  Helmut Pottmann,et al.  Scattered data interpolation based upon generalized minimum norm networks , 1991 .

[11]  Gary Herron.  A Characterization of Certain $C^1 $ Discrete Triangular Interpolants , 1985 .

[12]  Richard Franke,et al.  Recent Advances in the Approximation of surfaces from scattered Data , 1987, Topics in Multivariate Approximation.

[13]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[14]  Gregory M. Nielson,et al.  Scattered Data Interpolation and Applications: A Tutorial and Survey , 1991 .

[15]  Hans Hagen,et al.  Methods for surface interrogation , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[16]  G. Nielson.  The side-vertex method for interpolation in triangles☆ , 1979 .