Free Form Surface Design with A-Patches·
نویسندگان
چکیده
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 gi ven 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 C l (tangent plane) continuous and single sheeted in each of the tetrahedra. We al so show how to adjust the free parameters of the A-patches to achieve both local and global shape control.
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