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Involutions of polynomially parametrized surfaces
, 2014
"... We provide an algorithm for detecting the involutions leaving a polynomially parametrized surface invariant. As a consequence, symmetry axes, symmetry planes or symmetry centers for these surfaces can be determined directly from the parametrization. For this purpose, we show that any involution of t ..."
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We provide an algorithm for detecting the involutions leaving a polynomially parametrized surface invariant. As a consequence, symmetry axes, symmetry planes or symmetry centers for these surfaces can be determined directly from the parametrization. For this purpose, we show that any involution
Parametric Surfaces With Displacement And Deformation
"... Parametric surfaces are widely used for modeling in CAD systems. However, they pose problems when representing complex macrogeometric features. In order to solve these problems we introduce an extension to parametric surface models that incorporates displacements and deformations. Our extended model ..."
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Parametric surfaces are widely used for modeling in CAD systems. However, they pose problems when representing complex macrogeometric features. In order to solve these problems we introduce an extension to parametric surface models that incorporates displacements and deformations. Our extended
Parametric Surface Rendering
"... Parametric surface [Fari02] is a surface defined by a tensorproduct of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computeraided geometric design and objec ..."
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Parametric surface [Fari02] is a surface defined by a tensorproduct of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computeraided geometric design
Rendering Parametric Surfaces in Pen and Ink
, 1996
"... This paper presents new algorithms and techniques for rendering parametric freeform surfaces in pen and ink. In particular, we introduce the idea of “controlleddensity hatching ” for conveying tone, texture, and shape. The fine control over tone this method provides allows the use of traditional t ..."
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Cited by 81 (3 self)
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This paper presents new algorithms and techniques for rendering parametric freeform surfaces in pen and ink. In particular, we introduce the idea of “controlleddensity hatching ” for conveying tone, texture, and shape. The fine control over tone this method provides allows the use of traditional
Multivariate Visualization on Parametric Surfaces
"... Attribute Blocks are the basis of a multivariate visualization scheme that has been shown to be effective for twodimensional data sets such as those common in Geographical Information System (GIS) applications. In this paper, we present an extension of this technique into three dimensions. Specific ..."
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. Specifically, we show how the variation of multiple attributes defined continuously across a parametric surface can be explored using the Attribute Block technique. Any combination of geometric and/or nongeometric attributes can be visualized in this way. We present the method and illustrate it with a few
Implicit Representation of Rational Parametric Surfaces
 J. SYMBOLIC COMPUTATION
, 1992
"... this paper we present algorithms to implicitize rational parametric surfaces with and without base points. One of the strength of the algorithms lies in the fact that we do not use multivariate factorization. The base points blow up to rational curves on the surface and we present techniques to comp ..."
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Cited by 27 (6 self)
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this paper we present algorithms to implicitize rational parametric surfaces with and without base points. One of the strength of the algorithms lies in the fact that we do not use multivariate factorization. The base points blow up to rational curves on the surface and we present techniques
Geodesic Curvature Flow on Parametric Surfaces
 In Curve and Surface Design: SaintMalo 2002
, 2002
"... The motion of curves and images in IR has been researched extensively. The curvature ow, which is a geometric heat equation for planar curves, is among the classical ones. In this paper we present a numerical scheme to extend the planar curvature ow to the geodesic curvature ow on parametric ..."
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Cited by 6 (2 self)
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surfaces. The ow is implemented by back projecting the ow on the parametric surface to the parameterization plane, calculating the ow on the plane by the level sets method and then mapping it back to the manifold. This approach enables a more general and ecient solution of the problem than previous
Implicitization of Rational Parametric Surfaces
, 1996
"... A generalized projective implicitization theorem is presented that can be used to solve the implicitization of rational parametric curves and surfaces in an affine space. The Groebner bases technique is used to implement the algorithm. The algorithm has the advantages that it can handle base points ..."
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Cited by 2 (0 self)
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A generalized projective implicitization theorem is presented that can be used to solve the implicitization of rational parametric curves and surfaces in an affine space. The Groebner bases technique is used to implement the algorithm. The algorithm has the advantages that it can handle base points
Hierarchical modeling with parametric surfaces
"... We present a hierarchical triangular surface of arbitrary topology and its application to adaptive surface fitting. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plan ..."
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We present a hierarchical triangular surface of arbitrary topology and its application to adaptive surface fitting. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent
Parametric surface denoising
"... Three dimensional (3D) surfaces can be sampled parametrically in the form of range image data. Smoothing/denoising of such raw data is usually accomplished by adapting techniques developed for intensity image processing, since both range and intensity images comprise parametrically sampled geometry ..."
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Three dimensional (3D) surfaces can be sampled parametrically in the form of range image data. Smoothing/denoising of such raw data is usually accomplished by adapting techniques developed for intensity image processing, since both range and intensity images comprise parametrically sampled geometry
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