Modeling with cubic A-patches
Chandrajit Bajaj, Jindon Chen, Guoliang Xu · ACM Transactions on Graphics · 1995
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 tbe topology of any surface triangulation T of the given point set.In these algorithms we first specify "normals" an the data points, then build a simplicial hull consisting of tetrahedral surrounding the surface triangulation 2', and finally construct cubic A-patches within each tetrahedron.The resulting surface constructed is C' (tangent plane) continuous and single sheeted in each of the tetrahedral.We also show how to adjust the free parameters of the A-patches to achieve both local and global shape control.