An algorithmic approach to degree reduction of B'ezier curves is presented. The algorithm is based on the matrix representations of the degree elevation and degree reduction processes. The control points of the approximation are obtained by the generalized least square method. The computations are carried out by minimizing the L 2 and discrete l 2 distance between the twocurves. 1.

. This paper provides four alternative sufficient condition-sets, ensuring that a patch of a parametric tensor-product B-spline surface is locally convex. These conditions are at most tri-quadratic with respect to the control points of the surface. Keywords: Convexity, B-spline surface, Tensor-Product 1 Introduction. The most frequently occuring shape constraint in the Computer- Aided Geometric Design (CAGD) of surfaces is that of the local convexity (concavity) of a surface, over a user-specified two-dimensional subdomain of its parametric domain of definition. It is thus desirable to possess sufficient and, if possible, necessary conditions, which secure the convexity (concavity) of the surface under construction and, moreover, are handy from the computational point of view. It is easily understood that these conditions should, first of all, be of discrete character, i.e., independent of u and v, although the local-convexity (-concavity) requirement applies on a two-dimensional com...

CAD systems are usually based on a tensor product representation of free form surfaces. In this case, trimmed patches are used for modeling non rectangular zones. Trimmed patches provide a reasonable solution for the representation of general topologies, provided that the gap between equivalent trimming curves in the euclidean space is small enough. Several commercial CAD systems, however, represent certain non rectangular surface regions through degenerate rectangular patches. Degenerate patches produce rendering artifacts and can lead to malfunctions in the subsequent geometric operations. In the present paper, two algorithms for converting degenerate tensor-product patches into triangular and trimmed rectangular patches are presented. The algorithms are based on specific degree reduction algorithms for B'ezier curves. In both algorithms, the final surface approximates the initial one in a quadratic sense while inheriting its boundary curves. In the second one, " \Gamma G 1 cont...