An efficient bivariate basis for triangular patch modeling
Journal article
Authors/Editors
Strategic Research Themes
No matching items found.
Publication Details
Author list: Dejdumrong N.
Publisher: American Scientific Publishers
Publication year: 2013
Journal: Advanced Science Letters (1936-6612)
Volume number: 19
Issue number: 5
Start page: 1500
End page: 1505
Number of pages: 6
ISSN: 1936-6612
eISSN: 1936-7317
Languages: English-Great Britain (EN-GB)
Abstract
A new bivariate basis for triangular patches is expressed by recurrence formulae. This patch can be constructed by a recursive formula that is proven to be the most efficient algorithm compared to any existing triangular surface models. Extended from the author's univariate blending functions, evaluating a point on the basis's curve can be efficiently calculated in linear computations by either its iterative or recursive algorithms. The computational time for this surface's recursive algorithm is of quadratic complexity, 0(n2). Several essential geometric properties for the curves and tensor-product surfaces using this basis are identified, for example, the boundary point interpolation, the affine invariance, the partition of unity, the convex hull properties, and the symmetry. Moreover, the transformations between the B้zier triangular patches and the proposed surfaces can be performed using the monomial form approach. Finally, the degree elevation formula is derived. ฉ 2013 American Scientific Publishers All rights reserved. All rights reserved.
Keywords
Conversion formulae, Recurrence formulae, Recursive algorithm, Triangular B้zier surface
ติดต่อสอบถามเพิ่มเติมได้ที่