Meshless methods for physics-based modeling and simulation of deformable models

As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects' size, geometry, and topology. As a consequence, point-sampled geometry is becoming ubiquitous in graphics and geometric information processing, and poses new challenges which have not been fully resolved by the state-of-art graphical techniques. In this paper, we address the challenges by proposing a meshless computational framework for dynamic modeling and simulation of solids and thin-shells represented as point samples. Our meshless framework can directly compute the elastic deformation and fracture propagation for any scanned point geometry, without the need of converting them to polygonal meshes or higher order spline representations. We address the necessary computational techniques, such as Moving Least Squares, Hierarchical Discretization, and Modal Warping, to effectively and efficiently compute the physical simulation in real-time. This meshless computational framework aims to bridge the gap between the point-sampled geometry with physics-based modeling and simulation governed by partial differential equations.