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TopIntroduction
Simulation of rigid body deformation has been profusely studied by the computer graphics community. Realistic deformation models have immediate and obvious applications in many areas, such as virtual reality, surgery simulation or virtual sculpting. Since 1984, when Sederberg and Parry presented the Free Form Deformation method (Serderberg & Parry, 1986), a vast collection of works have aimed to create efficient and realistic methods to create the illusion of elasticity or plasticity.
However, and similarly to any other physical simulation, realism and efficiency are confronted. On the one side, physically based simulations require many resources and computation time, which consequently limits the size of the model involved. On the other side, simplified or heuristic deformations are easier to compute, but obviously produce less robust results.
The proposed method tries to find an equilibrium between these two approaches. A natural tactile experience is generated using physical principles, whereas simplifications are made in the deformation model – the huge number of elements required by volumetric models would be hard to handle otherwise.
First of all in this document a review of the most notable research produced in the area is presented. Afterwards the volumetric domain shall be introduced, for it will be of use when explaining the developed techniques. Next, the force generation algorithm and the visual feedback will be respectively described. Finally, the results will be shown in a series of images illustrating the effects produced with the here described techniques.
Contribution
The main contribution of this work is a deformation technique which allows interactive deformation of volumetric images. User experience is furthermore enhanced with the addition of a realistic, physically plausible haptic feedback. Model deformation, collision detection and force calculation are computed independently at high frame rates, ensuring a soft, continuous and natural tactile sensation. Since a wrapping Free Form Deformation structure is used, the deformation rates are independent from the size of the volume being deformed.
Previous Works
A number of methods have been presented aiming to create both ad-hoc and general solutions to the elastic problem. In this section a selection of them will be referenced, providing an interesting overview of the state of the art on deformable models and haptic interaction.
Complex models with a large number of nodes usually require some kind of simplification in the deformation algorithms to achieve interactive response times. This is the case of spring-mass based solutions, which have been widely used to calculate deformations on human tissues or elastic materials (Delingette, 1998). Despite of the simplifications done, works such as those of Choi et al. (2003) and McDonnell et al. (2001) have shown satisfactory results when they are combined with haptic interaction. Usually, spring-mass models require the addition of heuristic knowledge to acquire physical reality (Natsupakpong & Cenk, 2010).
The Chain-Mail Algorithm, developed by Frisken-Gibson (1999), makes use of a volumetric structure to compute both elastic deformations and haptic responses. The proposed structure is a 3D point matrix where every element admits a certain displacement within its original position. When the voxel reaches its maximum offset, the displacement is chained to the neighbors. The result is a linked volume which accepts geometrical deformations.
Dewaele and Cani (2004) presented a method that made possible the global plastic deformation of a volumetric structure. Displacements fields were computed directly on the grid, using two or more contact points.