Abstract
This paper describes an algorithm for generating piecewise parametric curved surfaces from arbitrary topological meshes. The algorithm is developed by extending and modifying Riesenfeld's constructive method for determining points on B-spline curves. The surfaces produced near extraordinary points are shown to be slope continuous and compatible with bi-quadratic B-spline surfaces generated from adjacent rectangular regions. In fact, applying this algorithm to rectangular meshes gives bi-quadratic B-spline surfaces. The implementation of this algorithm is simple and the evaluation of position vectors, tangent vectors and normal vectors of points on the surfaces is straightforward.
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