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953
Functional Compositions via Shifting Operators for Bézier Patches and Their Applications
, 1999
"... There are two kinds of Bezier patches which are represented by different base functions, namely the triangular Bezier patch and the rectangular Bezier patch. In this paper, two results about these patches are obtained by employing functional compositions via shifting operators. One is the compositio ..."
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There are two kinds of Bezier patches which are represented by different base functions, namely the triangular Bezier patch and the rectangular Bezier patch. In this paper, two results about these patches are obtained by employing functional compositions via shifting operators. One
n with control points Ti,j,k is defined by
, 2000
"... This paper presents an explicit formula that converts a triangular Bézier patch of degree n to a degenerate rectangular Bézier patch of degree n × n by reparametrization. Based on this formula, we develop a method for approximating a degenerate rectangular Bézier patch by three nondegenerate Bézier ..."
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This paper presents an explicit formula that converts a triangular Bézier patch of degree n to a degenerate rectangular Bézier patch of degree n × n by reparametrization. Based on this formula, we develop a method for approximating a degenerate rectangular Bézier patch by three nondegenerate Bézier
BSPatch: Constrained Bezier Parametric Patch
"... Abstract: Bezier parametric patches are used in engineering practice quite often, especially in CAD/CAM systems oriented to mechanical design. In many cases quadrilateral meshes are used for tessellation of parameters domain. We propose a new modification of the Bezier cubic rectangular patch, the ..."
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Cited by 2 (2 self)
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Abstract: Bezier parametric patches are used in engineering practice quite often, especially in CAD/CAM systems oriented to mechanical design. In many cases quadrilateral meshes are used for tessellation of parameters domain. We propose a new modification of the Bezier cubic rectangular patch
A Geometric Algorithm for Ray/Bézier Surfaces Intersection using Quasiinterpolating Control Net
"... In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bézier patch. The novelty of our approach resides in the use of bounds of the difference between a Bézier patch and its quasiinterpolating control net. The quasiinterpolating polygon of ..."
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In this paper, we present a new geometric algorithm to compute the intersection between a ray and a rectangular Bézier patch. The novelty of our approach resides in the use of bounds of the difference between a Bézier patch and its quasiinterpolating control net. The quasiinterpolating polygon
Mean value Bézier surfaces
 IN MATHEMATICS OF SURFACES XII
, 2007
"... Bézier surfaces are an important design tool in Computer Aided Design. They are parameterized surfaces where the parameterization can be represented as a homogeneous polynomial in barycentric coordinates. Usually, Wachspress coordinates are used to obtain tensor product Bézier surfaces over rectan ..."
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Cited by 2 (1 self)
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rectangular domains. Recently, Floater introduced mean value coordinates as an alternative to Wachspress coordinates. When used to construct Bézier patches, they offer additional control points without raising the polynomial degree. We investigate the potential of mean value coordinates to design mean value
Surface Fitting with Hierarchical Splines
 ACM Transactions on Graphics
, 1995
"... We consider the fitting of tensor product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor product splines are used with gridded data, the surface fitting problem decomposes into a sequence of curve fitting processes, making the c ..."
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Cited by 57 (1 self)
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approach is compared to multiresolution analysis and the use of wavelets. 1 Introduction In [9] an adaptive process was presented for fitting surface data with a geometrically continuous collection of rectangular Bezier patches. The adaptivity resulted from fitting a portion of the data with a patch
Toric degenerations of Bézier patches
, 2011
"... Parametric Bézier curves and surfaces are widely used to represent geometric objects in a computer for design and manufacturing. While classical, they were rediscovered in 1959/62 by De Casteljau (Citroën) and Bézier (Renault) for automotive design. Used in animation software such as Adobe flash. Yo ..."
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Cited by 2 (2 self)
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Parametric Bézier curves and surfaces are widely used to represent geometric objects in a computer for design and manufacturing. While classical, they were rediscovered in 1959/62 by De Casteljau (Citroën) and Bézier (Renault) for automotive design. Used in animation software such as Adobe flash
Simple Methods For Drawing Rational Surfaces as Four or Six Bézier Patches
 University of Pennsylvania
, 1999
"... . In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several B'ezier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real projective plane RP 2 into four and six triangles respecti ..."
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Cited by 2 (2 self)
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. In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several B'ezier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real projective plane RP 2 into four and six triangles
Continuity of Bézier patches
"... The paper is concerned about the question of smooth glueing of triangular B'ezier patches. In the begining polar forms are briefly explained. After that they are applied on parametric continuity. We'll obtain a geometric interpretation of C 1 and C 2 smoothly joined B'ezier patche ..."
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The paper is concerned about the question of smooth glueing of triangular B'ezier patches. In the begining polar forms are briefly explained. After that they are applied on parametric continuity. We'll obtain a geometric interpretation of C 1 and C 2 smoothly joined B
Intersecting biquadratic Bézier surface patches
 IN BERT JUETLLER AND RAGNI PIENE, EDITORS, COMPUTATIONAL METHODS FOR ALGEBRAIC SPLINE SURFACES
, 2007
"... We present three symbolic–numeric techniques for computing the intersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods. ..."
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Cited by 1 (0 self)
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We present three symbolic–numeric techniques for computing the intersection and self–intersection curve(s) of two Bézier surface patches of bidegree (2,2). In particular, we discuss algorithms, implementation, illustrative examples and provide a comparison of the methods.
Results 1  10
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953