A new approach towards free-form surfaces control Original Research Article

Deformation of free-form surfaces encounters difficulties because more than one control point must be moved to achieve satisfying results. A new method is described which provides deformation methods involving simultaneous movements of control vertices. The method uses an analogy between the control polyhedron of a surface and the mechanical equilibrium of a bar network. Surface deformation is then carried out through changes of mechanical parameters. Then, surface inflation, tweaking, shrinking, etc. can be achieved. New equilibrium positions of the network match the solution of linear system of equations allowing real time shape modifications. An analytical approach of vertices movements is developed to give further explanations about the methodʹs behaviour and the influence of mechanical parameters changes. Several examples illustrate basic deformation types with various changes of mechanical parameters.