论文信息 - Modeling with cubic A-patches

Modeling with cubic A-patches

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an A-patch. We present algorithms to build a mesh of cubic A-patches to interpolate a given set of scattered point data in three dimensions, respecting the topology of any surface triangulation T of the given point set. In these algorithms we first specify "normals" on the data points, then build a simplicial hull consisting of tetrahedra surrounding the surface triangulation T and finally construct cubic A-patches within each tetrahedron. The resulting surface constructed is at (tangent plane) continuous and single sheeted in each of the tetrahedra. We also show how to adjust the free parameters of the A-patches to achieve both local and global shape control.

[1] Baining Guo,et al. Modeling arbitrary smooth objects with algebraic surfaces , 1992 .

[2] Thomas W. Sederberg. Piecewise algebraic surface patches , 1985, Comput. Aided Geom. Des..

[3] S. Lodha. Surface approximation by low degree patches with multiple representations , 1993 .

[4] C. Bajaj. The Emergence of Algebraic Curves and Surfaces in Geometric Design , 1992 .

[5] B. Guo,et al. Surface generation using implicit cubics , 1991 .

[6] Helmut Pottmann,et al. Interpolation on surfaces using minimum norm networks , 1992, Comput. Aided Geom. Des..

[7] J. Davenport. Editor , 1960 .

[8] Joe Warren,et al. Approximation of dense scattered data using algebraic surfaces , 1991, Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences.

[9] Gerald Farin,et al. Curves and surfaces for computer aided geometric design , 1990 .

[10] C. Hoffmann. Algebraic curves , 1988 .

[11] Henry P. Moreton. Minimum curvature variation curves, networks, and surfaces for fair free-form shape design , 1993 .

[12] Jörg Peters,et al. Local smooth surface interpolation: a classification , 1990, Comput. Aided Geom. Des..

[13] Insung Ihm,et al. Smoothing polyhedra using implicit algebraic splines , 1992, SIGGRAPH.

[14] Wolfgang Dahmen,et al. Cubicoids: modeling and visualization , 1993, Comput. Aided Geom. Des..

[15] C. Bajaj. Surface fitting using implicit algebraic surface patches , 1992 .