Déformation de courbes et surfaces multirésolution sous contraintes. (Constrained deformation of multiresolution curves and surfaces)

Building intuitive tools for manipulating curves and surfaces is a challenging task in the domains of geometric modelling and computer graphics. First, such tools need an appropriate mathematical model of the geometric objects. In addition, geometric constraints can enhance ergonomics, once they have been integrated into the editing tool. We investigate the integration of non linear constraints into the multiresolution deformation of smooth curves and surfaces : area preserving of closed B-spine curves, volume preserving of B-spline surfaces, volume preserving of surfaces with arbitrary topological type (based on triangular meshes), and length preserving of piecewise linear curves. Thanks to multiresolution schemes based on wavelets one can easily deform complex objects at any scale, while keeping fine details. The geometric constraints are computed using the multiresolution basis. Then they are integrated through an automated constrained optimization step, and they prove to efficiently enhance the realism of deformations. Our methods work in real-time, and can be adapted to a broad range of situations.