A tool for analytical simulation of B-splines surface deformation

A non-planar surface deformation model based on B-splines as finite elements is presented here. The model includes the variational formulation, the system of ordinary differential equations derived from it and its analytical solution. The model has been checked for a variety of surfaces such as tiles, half spheres, planes, etc. Furthermore, we are able to solve the system analytically by only moving a reduced number of control points to deform the surface. This makes the method faster, since numerical methods are no longer necessary.

► A model surface deformation based on B-splines is developed.
► To achieve “realistic” deformations using finite elements based on B-splines.
► Energy functional of a surface is defined.
► Using the Euler–Lagrange equations, an equation of the surface is found.
► Analytical solution using variational and corresponding differential.