A control of smooth deformations with topological change on a polyhedral mesh based on curves and loops

We propose a method to model and control topological changes by a smooth deformation of a polyhedral mesh using curves and loops. As changing the genus of a surface is not a continuous transformation, the topological change is made when an intermediate shape between the two topologies has been obtained. The creation and the deletion of holes are studied. The deletion of a hole uses non null-homotopic loops to designate the hole to be deleted. A method computing two independent loops associated to a hole is presented.