A tensor optimization algorithm for Bézier Shape Deformation

In this paper we propose a tensor based description of the Bézier Shape Deformation (BSD) algorithm, denoted as T-BSD. The BSD algorithm is a well-known technique, based on the deformation of a Bézier curve through a field of vectors. A critical point in the use of real-time applications is the cost...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-01, Vol.291, p.264-280
Main Authors: Hilario, L., Falcó, A., Montés, N., Mora, M.C.
Format: Article
Language:English
Subjects:
Algorithms
Bezier
Bézier curves
Computational efficiency
Deformation
Evolutionary algorithms
Mathematical analysis
Mathematical models
Parametric curve deformation
Tensor product
Tensors
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Summary:In this paper we propose a tensor based description of the Bézier Shape Deformation (BSD) algorithm, denoted as T-BSD. The BSD algorithm is a well-known technique, based on the deformation of a Bézier curve through a field of vectors. A critical point in the use of real-time applications is the cost in computational time. Recently, the use of tensors in numerical methods has been increasing because they drastically reduce computational costs. Our formulation based in tensors T-BSD provides an efficient reformulation of the BSD algorithm. More precisely, the evolution of the execution time with respect to the number of curves of the BSD algorithm is an exponentially increasing curve. As the numerical experiments show, the T-BSD algorithm transforms this evolution into a linear one. This fact allows to compute the deformation of a Bézier with a much lower computational cost.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.02.035