  One of the theoretically intriguing problems in computer-aided geometric
modeling comes from the stitching of the tensor product Bezier patches. When
they share an extraordinary vertex, it is not possible to obtain continuity C1
or G1 along the edges emanating from that extraordinary vertex. Unfortunately,
this stitching problem cannot be solved by using higher degree or rational
polynomials. In this paper, we present a modified de Casteljau subdivision
algorithm that can provide a solution to this problem. Our modified de
Casteljau subdivision, when combined with topological modeling, provides a
framework for interactive real-time modeling of piecewise smooth manifold
meshes with arbitrary topology. The main advantage of the modified subdivision
is that the continuity C1 on a given boundary edge does not depend on the
positions of the control points on other boundary edges. The modified
subdivision allows us to obtain the desired C1 continuity along the edges
emanating from the extraordinary vertices along with the desired G1 continuity
in the extraordinary vertices.
