G¹ SMOOTHING SOLID OBJECTS BY BICUBIC BEZIER PATCHES

A general and unified method is presented for generating a wide range of 3-D objects by smoothing the vertices and edges of a given polyhedron with arbitrary topology using bicubic Bezier patches. The common solution to the compatibility equations of G¹ geometric continuity between two Bezier patche...

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Bibliographic Details
Published in:Journal of computational mathematics 1991-07, Vol.9 (3), p.198-210
Main Authors: You-dong, Liang, Xiu-zi, Ye, Xiao-fen, Fang
Format: Article
Language:English
Subjects:
Data smoothing
Geometric shapes
Mathematical surfaces
Mathematical vectors
Polyhedrons
Tangents
Topological spaces
Topology
Umbrellas
Vertices
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Summary:A general and unified method is presented for generating a wide range of 3-D objects by smoothing the vertices and edges of a given polyhedron with arbitrary topology using bicubic Bezier patches. The common solution to the compatibility equations of G¹ geometric continuity between two Bezier patches is obtained and employed as the foundation of this new method such that this new solid and surface model is reliable and compatible with the solid modeling and surface modeling systems in the most common use. The new method has been embeded in an algorithm supported by our newly developed solid modeling system MESSAGE. The performance and implementation of this new algorithm show that it is efficient, flexible and easy to manipulate.
ISSN:0254-9409
1991-7139