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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Bibliographic Details
Published in:2008 IEEE International Conference on Shape Modeling and Applications pp. 139 - 145
Main Author: Yohanes, S.L.
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2008
Subjects:
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
ISBN:9781424422609, 1424422604
Online Access:Get full text
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Summary: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.
ISBN:9781424422609
1424422604
DOI:10.1109/SMI.2008.4547960