A Robust Approach to Interactive Virtual Cutting: Geometry and Color

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Interactive simulation of deformable bodies has attracted growing interest in the course of the last decade and, while for a long time it has been limited to applicative domains such as virtual surgery, it is nowadays a fundamental part of almost every game engine. The reasons of this evolution may be found both in the continuous effort of the scientific community and in the technological improvement of computers performance that allowed to sustain such a calculation-intensive task even on commodity computers.The simulation of a deforming object requires a physical model of the object behavior and an efficient and stable algorithm to simulate it.Generally speaking, the physical model must consider the phenomenon at the right scale (e.g. a ball will not be modeled as the interaction of its atoms) and capture the aspects of the simulation we are interested in (e.g. do not include the temperature when computing the bouncing of the ball). Concerning the algorithm, it must be able to update the state of the system in real-time and it must be stable. The latter is particularly critical because simulation includes resolution of Partial Differential Equations (PDEs) which easily could easily diverge if not handled with care.Although many consolidated results in this field exist, there are still problems that need further investigation, for example how to model the cutting (or fracturing) of deformable objects.A cut on a deformable object has two major implications: it changes its boundary by adding a new portion of surface ( the part that is revealed by the cut) which means that the geometric description must be updated on-the-fly; new information (e.g. the color) is needed to render the newly generated surface portion; finally, it changes the physical behavior of the object, which translates in updating the boundary conditions of the physical model.The contribution of this thesis to the problem stated above is twofold:A new algorithm to model interactive cuts or fractures on deforming objects, named Splitting Cubes. The Splitting Cubes can be considered as a tessellation algorithm for deformable surfaces. It is independent from the underlying physical model which defines the deformation functions. For the particular case of mesh-free methods for the physical simulation, we also describe a practical GPU-friendly method to introduce discontinuities of the deformation, the Extended Visibility criterion.Due to its stability and efficiency, the Splitting Cubes is particularly suitable for interactive simulations, including virtual surgery and games.A new algorithm to derive the color of the interior of an object from few cross sections. To address this problem we propose a new appearance-modeling paradigm for synthesizing the internal structure of a 3D model from photographs of a few cross-sections of a real object. In our approach colors attributes (textures) of the surface are synthesized on demand during the simulation. We will demonstrate that our modeling paradigm reveal highly realistic internal surfaces in a variety of artistic flavors. Due to its efficiency, our approach is suitable for real-time simulations.We finally present two collateral results that emerged during the research carried out in these years: a robust model for real-time simulation of knot-tying which is certainly useful in endoscopic surgical simulator; a technique for building a virtual model of a human head, developed in the framework of the approximation of individual Head Related Transfer Functions (HRTF) for the realistic binaural rendering of three-dimensional sound.