A matrix-based optimization algorithm for shape deformation using parametric curves

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. ∗