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.

翻译：计算机辅助几何建模中一个理论上引人入胜的问题源于张量积贝塞尔曲面片的拼接问题。当这些曲面片共享一个奇异顶点时，无法沿从该奇异顶点出发的边实现C1或G1连续性。遗憾的是，这一问题无法通过采用更高次或有理多项式来解决。本文提出了一种改进的de Casteljau细分算法，为该问题提供解决方案。我们的改进de Casteljau细分方法与拓扑建模相结合，为任意拓扑分段光滑流形网格的交互式实时建模提供了框架。该改进细分的主要优势在于：给定边界边上的C1连续性不依赖于其他边界边上控制点的位置。改进细分使我们能够沿从奇异顶点出发的边获得所需的C1连续性，同时在奇异顶点处获得所需的G1连续性。