Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
The NURBS book
Triangular NURBS and their dynamic generalizations
Computer Aided Geometric Design
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
P3DMA: A Physical 3D Deformable Modelling and Animation System
AMDO '02 Proceedings of the Second International Workshop on Articulated Motion and Deformable Objects
Analytical simulation of non-planar B-spline surfaces deformation
AMDO'10 Proceedings of the 6th international conference on Articulated motion and deformable objects
A tool for analytical simulation of B-splines surface deformation
Computer-Aided Design
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In this paper an analytic solution of an evolution model is proposed in order to deform B-splines parametric surfaces. The deformation model is based on an associated energy functional to one surface and its variational formulation is introduced. After some simplifications including assumptions regarding the mass and damping matrices and taking into account the properties of B-splines when are used as finite elements, a second order differential equations is obtained which can be solved analytically. The spatial discretization where these finite elements are defined and computed appears as a reduced number of control points and is deformed instead of all the surface points, obtaining an efficient and fast method in order to simulate surface deformations.