Surface representations using blossoms and buds
Shape representations using polynomials in computer-aided geometric design (CAGD) and computer graphics are ubiquitous. This paper shows that any bivariate polynomial p(t,u) of total degree d les n can be represented in the form of a blossom of another bivariate polynomial b(t, u) of total degree d...
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| Published in: | 2008 IEEE International Conference on Shape Modeling and Applications pp. 139 - 145 |
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| Main Author: | |
| Format: | Conference Proceeding |
| Language: | English |
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IEEE
01.06.2008
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| ISBN: | 9781424422609, 1424422604 |
| Online Access: | Get full text |
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| Abstract | Shape representations using polynomials in computer-aided geometric design (CAGD) and computer graphics are ubiquitous. This paper shows that any bivariate polynomial p(t,u) of total degree d les n can be represented in the form of a blossom of another bivariate polynomial b(t, u) of total degree d evaluated off the diagonal at the linear function pairs (Xj(t),Yj(u)), j = 1,... ,n, chosen under some conditions expressed in terms of symmetric functions. The bivariate polynomial b(t,u) is called a bud of the bivariate polynomial p(t,u). An algorithm for finding a bud b(t,u) of a given bivariate polynomial p(t,u) is presented. Successively, a bud of b(t, u) can be computed and so on, to form a sequence of representations. The information represented by the original bivariate polynomial is preserved in its buds. This scheme can be used for encoding/decoding geometric design information. The objects in the encoding/decoding sequence can be rendered graphically and manipulated geometrically like the usual parametric representations. Examples concerning triangular Bezier patches are provided as illustrations. |
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| AbstractList | Shape representations using polynomials in computer-aided geometric design (CAGD) and computer graphics are ubiquitous. This paper shows that any bivariate polynomial p(t,u) of total degree d les n can be represented in the form of a blossom of another bivariate polynomial b(t, u) of total degree d evaluated off the diagonal at the linear function pairs (Xj(t),Yj(u)), j = 1,... ,n, chosen under some conditions expressed in terms of symmetric functions. The bivariate polynomial b(t,u) is called a bud of the bivariate polynomial p(t,u). An algorithm for finding a bud b(t,u) of a given bivariate polynomial p(t,u) is presented. Successively, a bud of b(t, u) can be computed and so on, to form a sequence of representations. The information represented by the original bivariate polynomial is preserved in its buds. This scheme can be used for encoding/decoding geometric design information. The objects in the encoding/decoding sequence can be rendered graphically and manipulated geometrically like the usual parametric representations. Examples concerning triangular Bezier patches are provided as illustrations. |
| Author | Yohanes, S.L. |
| Author_xml | – sequence: 1 givenname: S.L. surname: Yohanes fullname: Yohanes, S.L. organization: Fac. of Comput. Sci., Univ. of Indonesia, Depok |
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| Snippet | Shape representations using polynomials in computer-aided geometric design (CAGD) and computer graphics are ubiquitous. This paper shows that any bivariate... |
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| StartPage | 139 |
| SubjectTerms | algorithm Algorithm design and analysis and Object Representations bivariate polynomial blossom of a bivariate polynomial bud of a bivariate polynomial Computer applications Computer graphics Computer science Decoding Encoding encoding-decoding geometric design Hierarchy and Geometric Transformations I.1.2 [Symbolic and Algebraic Manipulation]: Algorithms-Algebraic Algorithms I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve J.6 [Computer Applications]: Computer-Aided Engineering-Computer-Aided Design (CAD) Pervasive computing Polynomials Rendering (computer graphics) sequence of representations Shape shape representation Solid Surface surface representation triangular Bézier patch |
| Title | Surface representations using blossoms and buds |
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