A tensor optimization algorithm for Bézier Shape Deformation

Abstract

In this paper we propose a tensor based description of the Bézier Shape Deformation (BSD) algorithm, denoted 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 shown, 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.

High-Performance Computation of Bézier Surfaces on Parallel and Heterogeneous Platforms

“…Due to their simplicity and mathematical properties, Bézier surfaces have been employed in applications such as surface reconstruction from clouds of points [3], modeling of free-form deformations [4,5], interactive manipulation of three-dimensional meshes and rendering [6][7][8], bio-mechanical modeling [9], hybrid volumetric object representation [10], registration in medical imaging [11,12], and computer games [13] among others.…”

Mathematical modeling and computational methods

“…Respect to the first item, L. Hilario et al [21] present a use of tensors which reduces the computational time of the BSD (Bezier Shape Deformation) algorithm. The result is a tensorial method called T-BSD (Tensor Bezier Shape Deformation) which enjoys the same properties of the former method including a key advantage: its low computational time and real-time performance.…”