CONSTRUCTION OF SMOOTH BICUBIC SURF ACES DEFINED OVER ARBITRARY QUADRILATERAL MESHES
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Date
2001-11
Authors
ABD MANAF, FADZILAH
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Abstract
Two methods of modelling closed smooth precewrse bicubic surfaces on
polyhedral mesh are described.
The first method deals with the construction of bicubic B-spline basis functions.
These functions are constructed on simple quadrilateral meshes, that is a closed
polyhedral mesh in which every face has four edges and every vertex is the joint of
three or four edges. These functions are used to model smooth closed surfaces from
control polyhedron with quadrilateral faces. Geometric continuity is ensured at the
extraordinary vertices and parametric continuity elsewhere. Surface splitting algorithm
is applied in order to plot the surfaces.
The second uses a subdivision approach to construct the surface. An algorithm to
subdivide the surface recursively is proposed. By repeated subdivision, the surface is
made to satisfy geometric continuity G1 around the extraordinary vertices and C1
elsewhere.
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CONSTRUCTION OF SMOOTH BICUBIC SURF ACES DEFINED OVER