Resumen de On some interactive mesh deformations
María Dels Àngels Cerveró Abelló
Techniques devoted to deform 3D models are an important research field in Computer Graphics. They can be used in differentstages: the modelling phase, the animation process and also during some special simulations. Additionally, some applications may require the manipulation of 3D models under certain restrictions to preserve the volume of the modified object. Hence, thepresent PhD Dissertation explores new algorithms to perform flexible, robust and efficient 3D deformations. Apart from this, it also researches on a new methodology to restrict these deformations so that the volume of the manipulated model remains constant. Some of the most used methods to achieve smooth deformations are those included in the Cage-Based Deformation paradigm. Cage-based deformations enclose the model to be deformed in a coarse polyhedron, the cage. Then, they usually rely on Generalized Barycentric Coordinates to relate the model with the vertices, and other geometric elements, of this cage, which are the control points or the deformation handles. Finally, every time that one of these handles is dragged, the model is deformed accordingly. Although this paradigm is simple, elegant and performs efficient deformations, some cage-free space deformation techniques have recently appeared. They increase the flexibility of the deformation handles, which do not need to be connected, and define powerful tools that make the deformation process more versatile and intuitive. In this context, the Dissertation introduces new Generalized Barycentric Coordinate systems specially designed to be used in a cage-free environment. Any user who wants to use the presented schemes only needs to locate a set of control points in the vicinity of the model that he or she wants to deform. These handles can be placed wherever he or she considers mode suitable and the only requirement is that the model has to be enclosed in their convex hull. Up to now, there are few techniques to produce volume-preserving space deformations. However, in recent years there has been a growing interest in performing constrained deformations due to their more realistic and physically plausible results. Our contribution to this research line consists in a deformation framework that preserves the volume of the 3D models by means of its gradient and a control surface to restrict the movement of the handles. Moreover, the proposed methodology is not restricted to the cage-based schemes, but it can also be used in a cage-free environment. Finally, our research can be specially useful for spatial deformations of biological and medical models. This kind of models represent real organs and tissues, which are often soft and lack an internal rigid structure. In addition, they are elastic and incompressible. Any application designed to deal with this group of models and to train or assist doctors must be flexible, robust, efficient and user-friendly. The combination of the proposed cage-free systems with the presented volume-preserving deformation framework satisfies
