Tensor product Bézier surfaces on triangle Bézier surfaces

Lasser, Dieter

doi:10.1016/s0167-8396(02)00145-0

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…Hu et al [21] studied the continuity conditions between generalized Bézier-like surfaces with multiple shape parameters and also discuss some properties and applications of the smooth continuity by providing the modeling examples. Lasser [22] proposed an algorithm for converting a rectangular patch of a triangular Bézier surface into a tensor product Bézier representation and also discuss the corner problem of a surface. The curves and surfaces in [1][2][3][4][5][6][7][8][9][10][18][19][20][21] have several specific advantages such as they inherit the positive properties of the classical Bézier curves and surfaces.…”

Section: Introductionmentioning

confidence: 99%

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Ammad

Misro

2020

Symmetry

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Based on quintic trigonometric Bézier like basis functions, the biquintic Bézier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bézier surface but also have exceptional shape adjustment. In order to construct Bézier like curves with shape parameters, we present a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surface. In addition to the application of the proposed method, we also discuss the shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries). However, the modeling examples shows that the suggested approach is efficient and easy to implement.

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Section: Introductionmentioning

confidence: 99%

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Ammad

Misro

2020

Symmetry

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“…However, the algorithm for the control points of the compositions is not sufficiently efficient in practice. Lasser [15,16] studied the composition of TP over TB, and the composition of TB over TP. Explicit formulas are provided for the control points of the compositions.…”

Section: Introductionmentioning

confidence: 99%

“…Lasser [15,16] formulated the control points of the composition as the linear combinations of some intermediate points called the construction points. However, the number of the construction points is huge and many of them actually have the same positions.…”

Section: Introductionmentioning

confidence: 99%

Triangular Bézier sub-surfaces on a triangular Bézier surface

Chen

Zheng

et al. 2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch.

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“…Neste capítulo, apresentamos fórmulas para conversão entre estas duas representações de polinômios multivariados. Estes resultados generalizam, para dimensão arbitrária, a conversão de retalhos retangulares para triangulares de Goldmann [11], Hu [14] e Lasser [18], e a conversão de retalhos triangulares para retangulares de Brueckner [3], Hu [13] [14]e Lasser [17].…”

Section: Conversão Tensorial/simplicialunclassified

Modelagem geológica por simplóides de Bézier

Freitas¹,

Jorge²

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ResumoA exploração e monitoramento de um reservatório de petróleo ou gás natural exige conhecimento bastante detalhado das estruturas geológicas da região de interesse. A representação matemática e computacional desse conhecimento é um modelo geofísico.Nesta tese descrevemos um sistema geral para modelagem geofísica baseado em elementos finitos polinomiais de graus arbitrários. Adotamos uma abordagem comum na indústria, em que a geometria e as propriedades das formações geológicas são representadas por funções definidas por partes, ou splines, que consistem da justaposição de tais elementos. Neste contexto, apresentamos contribuições teóricas e computacionais.A principal contribuição teórica é uma teoria unificada dos elementos simploidais de Bézier, que incluem os tipos de elementos finitos mais comuns na modelagem por malhastais como arcos de Bézier, retalhos de Bézier triangulares e retangulares, blocos de Bézier tetraédricos, prismáticos e hexaédricos, e suas generalizações para dimensões arbitrárias, com graus independentes em cada eixo e cada componente. Como parte testa teoria, desenvolvemos fórmulas genéricas explícitas para conversão entre estes vários tipos de blocos, bem como diferenciação, reparametrização afim e elevação de grau.As contribuições computacionais desta tese incluem a implementação dessa teoria na forma de uma biblioteca (BezEl) que permite a representação e manipulação eficiente de malhas de elementos de Bézier simplodais com dimensões e graus arbitrários. Outra contribuição original desta tese é uma metodologia para realizar o traçado eficiente de raios em malhas de elementos simploidais.

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Tensor product Bézier surfaces on triangle Bézier surfaces

Cited by 8 publications

References 15 publications

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Triangular Bézier sub-surfaces on a triangular Bézier surface

Modelagem geológica por simplóides de Bézier

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