Blending Pipe Surfaces with Piecewise Algebraic Surfaces

This paper derives a geometric continuity condition for algebraic surface patch complexes meeting at a common vertex. Based on the geometric continuity condition, a new scheme is presented to blend three cylinders with piecewise cubic algebraic surfaces. The algorithm starts with a suitable space partition for the defining domains of the piecewise algebraic surface patches. Then the piecewise algebraic surface is constructed by solving a linear system of equations. An intuitive and geometric means of controlling the shape of the blending surface is also discussed based on the Bernstein Bezier(B B) representation of algebraic surface patches. The results suggest that modeling with piecewise algebraic surfaces has two main advantages: (1) The degree of the algebraic surface patches is comparatively low; (2) The control over the shapes of the piecewise algebraic surfaces is much more intuitive and efficient.