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The Distance For The Bezier Curves And Degree Reduction
 Bull. Australian Math. Soc
, 1997
"... 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 c ..."
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Cited by 8 (3 self)
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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.
Convexity Conditions for Parametric TensorProduct Bspline Surfaces
, 1998
"... . This paper provides four alternative sufficient conditionsets, ensuring that a patch of a parametric tensorproduct Bspline surface is locally convex. These conditions are at most triquadratic with respect to the control points of the surface. Keywords: Convexity, Bspline surface, TensorProd ..."
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Cited by 3 (1 self)
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. This paper provides four alternative sufficient conditionsets, ensuring that a patch of a parametric tensorproduct Bspline surface is locally convex. These conditions are at most triquadratic with respect to the control points of the surface. Keywords: Convexity, Bspline surface, TensorProduct 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 userspecified twodimensional 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 localconvexity (concavity) requirement applies on a twodimensional com...
From Degenerate Patches to Triangular and Trimmed Patches
 CURVES AND SURFACES
, 1997
"... 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 trim ..."
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Cited by 1 (1 self)
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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 tensorproduct 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...