Relevant bibliographies by topics / Bézier triangles

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Bézier triangles'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Bézier triangles"

1

Goldman, Ronald N., and Daniel J. Filip. "Conversion from Bézier rectangles to Bézier triangles." Computer-Aided Design 19, no. 1 (1987): 25–27. http://dx.doi.org/10.1016/0010-4485(87)90149-7.

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Prautzsch, H. "On convex Bézier triangles." ESAIM: Mathematical Modelling and Numerical Analysis 26, no. 1 (1992): 23–36. http://dx.doi.org/10.1051/m2an/1992260100231.

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Lee, Chang-Ki, Hae-Do Hwang, and Seung-Hyun Yoon. "Bézier Triangles with G2 Continuity across Boundaries." Symmetry 8, no. 3 (2016): 13. http://dx.doi.org/10.3390/sym8030013.

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Yan, Lanlan. "Construction Method of Shape Adjustable Bézier Triangles." Chinese Journal of Electronics 28, no. 3 (2019): 610–17. http://dx.doi.org/10.1049/cje.2019.03.016.

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Gregory, John A., and Jianwei Zhou. "Convexity of Bézier nets on sub-triangles." Computer Aided Geometric Design 8, no. 3 (1991): 207–11. http://dx.doi.org/10.1016/0167-8396(91)90003-t.

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Feng, Yu-Yu. "Rates of convergence of Bézier net over triangles." Computer Aided Geometric Design 4, no. 3 (1987): 245–49. http://dx.doi.org/10.1016/0167-8396(87)90016-1.

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Belbis, Bertrand, Lionel Garnier, and Sebti Foufou. "Construction of 3D Triangles on Dupin Cyclides." International Journal of Computer Vision and Image Processing 1, no. 2 (2011): 42–57. http://dx.doi.org/10.4018/ijcvip.2011040104.

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This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, pa
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Walz, Guido. "Trigonometric Bézier and Stancu polynomials over intervals and triangles." Computer Aided Geometric Design 14, no. 4 (1997): 393–97. http://dx.doi.org/10.1016/s0167-8396(96)00061-1.

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Filip, Daniel J. "Adaptive subdivision algorithms for a set of Bézier triangles." Computer-Aided Design 18, no. 2 (1986): 74–78. http://dx.doi.org/10.1016/0010-4485(86)90153-3.

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Hermes, Danny. "Helper for Bézier Curves, Triangles, and Higher Order Objects." Journal of Open Source Software 2, no. 16 (2017): 267. http://dx.doi.org/10.21105/joss.00267.

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Dissertations / Theses on the topic "Bézier triangles"

1

BOSCHIROLI, MARIA ALESSANDRA. "Local parametric bézier interpolants for triangular meshes: from polynomial to rational schemes." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2011. http://hdl.handle.net/10281/27853.

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Problems of "Reverse Engineering" type are recurrent in Computer Aided (Geometric) Design (CA(G)D) and in computer graphics, in general. They consist in the reconstruction of objects from point clouds. In computer graphics, for visualisation purposes, for example, the existing solutions consist in triangulating the point data and then fitting them with planar triangles. The object is thus approximated by a piecewise linear surface, which is only C0 continuous. In order to obtain a smooth aspect a huge amount of triangles is necessary. Triangular meshes are widely used because they are suffici
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Ubach, de Fuentes Pere-Andreu. "BEST : Bézier-Enhanced Shell Triangle : a new rotation-free thin shell finite element." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/670369.

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A new thin shell finite element is presented. This new element doesn’ t have rotational degrees of freedom. Instead, in order to overcome the C1 continuity requirement across elements, the author resorts to enhance the geometric description of the flat triangles of a mesh made out of linear triangles, by means of Bernstein polynomials and triangular Bernstein-Bézier patches. The author estimates the surface normals at the nodes of a mesh of triangles, in order to use them to define the Bernstein-Bézier patches. Ubach, Estruch and García-Espinosa performed a comprehensive statistical compari
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Morávek, Andrej. "Geomorfologická interpolace vrstevnic nad nepravidelnou trojúhelníkovou sítí." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-306708.

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The aim of this master thesis is to create an application to generate smooth contours with the method of non-linear, so-called geomorphological interpolation over triangulated irregular network using patch technique. The introductory part consists of the state of art in the field of patch modelling and description of georelief in the form of digital terrain models. The core of the work comprises the mathematical background of Bézier triangle patches using barycentric coordinates and interpolation techniques with definition of continuity. The main contribution is a proper algorithm of balanced
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Books on the topic "Bézier triangles"

1

Reiter, Jesse Chain. Textured surface modeling using Bézier triangles. National Library of Canada, 1996.

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Book chapters on the topic "Bézier triangles"

1

Farin, Gerald. "Bézier Triangles." In Curves and Surfaces for CAGD. Elsevier, 2002. http://dx.doi.org/10.1016/b978-155860737-8/50017-x.

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2

Farin, Gerald. "Bézier Triangles." In Curves and Surfaces for Computer-Aided Geometric Design. Elsevier, 1993. http://dx.doi.org/10.1016/b978-0-12-249052-1.50023-4.

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Farin, Gerald. "Practical Aspects of Bézier Triangles." In Curves and Surfaces for CAGD. Elsevier, 2002. http://dx.doi.org/10.1016/b978-155860737-8/50018-1.

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4

Lischinski, Dani. "Converting Rectangular Patches into Bézier Triangles." In Graphics Gems. Elsevier, 1994. http://dx.doi.org/10.1016/b978-0-12-336156-1.50037-9.

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Lischinski, Dani. "CONVERTING BÉZIER TRIANGLES INTO RECTANGULAR PATCHES." In Graphics Gems III (IBM Version). Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-08-050755-2.50058-0.

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6

Belbis, Bertrand, Lionel Garnier, and Sebti Foufou. "Construction of 3D Triangles on Dupin Cyclides." In Intelligent Computer Vision and Image Processing. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-3906-5.ch009.

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This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, pa
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7

Seidel, H. P. "A General Subdivision Theorem for Bézier Triangles." In Mathematical Methods in Computer Aided Geometric Design. Elsevier, 1989. http://dx.doi.org/10.1016/b978-0-12-460515-2.50046-9.

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Lischinski, Dani. "CONVERTING BÉZIER TRIANGLES INTO RECTANGULAR PATCHES: (page 256)." In Graphics Gems III (IBM Version). Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-08-050755-2.50117-2.

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Foley, Thomas A., and Karsten Opitz. "Hybrid Cubic Bézier Triangle Patches." In Mathematical Methods in Computer Aided Geometric Design II. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-12-460510-7.50024-0.

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Conference papers on the topic "Bézier triangles"

1

Wang, Cunfu, Songtao Xia, Xilu Wang, and Xiaoping Qian. "Isogeometric Shape Optimization on Triangulations." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59611.

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The paper presents an isogeometric shape optimization method that is based on Bézier triangles. Bézier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, triangular Bézier parameterization can be automatically generated. This shape optimization method is thus applicable to structures of complex topology. Due to the use of B-spline parameterization of the boundary, the optimized shape can be compactly represented with a relatively small number of optimization variables. In order to ensure mesh validity during shape op
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Morera, Dimas Martínez, Paulo Cezar Carvalho, and Luiz Velho. "Geodesic Bézier curves on triangle meshes." In ACM SIGGRAPH 2006 Research posters. ACM Press, 2006. http://dx.doi.org/10.1145/1179622.1179723.

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Song, Yang, and Elaine Cohen. "Making Trimmed B-Spline B-Reps Watertight With a Hybrid Representation." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97485.

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Abstract Watertightness is an important property for CAD models, yet it is not generally available in commercial systems. This paper introduces watertight hybrid B-spline based B-reps that maintain the original parameterization and representation except in narrow regions around trimming curves, where Bézier triangle type regions seal the model. The new representation matches the model space trimming curve exactly. It can be discretized for analysis and fabrication in a straightforward manner without requiring any post modeling repair operations. We apply this representation to mechanical model
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