Multiresolution green's function methods for interactive simulation of large-scale elastostatic objects

Abstract

This thesis presents a framework for low-latency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate large-scale physical models.Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green's functions (GFs) which may be precomputed to provide speed and cheap lookup operations. Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the Sherman-Morrison-Woodbury formula. Temporal coherence is exploited by caching and reusing, as well as sequentially updating, previous capacitance matrix inverses.Multiresolution enhancements make it practical to simulate and store very large models. Efficient compressed representations of precomputed GFs are obtained using secondgeneration wavelets defined on surfaces. Fast inverse wavelet transforms allow fast summation methods to be used to accelerate runtime BVP solution. Wavelet GF compression factors are directly related to interactive simulation speedup, and examples are provided with hundredfold improvements at modest error levels. Furthermore, hierarchical constraints are defined using hierarchical basis functions, and related hierarchical GFs are then used to construct an hierarchical CMA. This direct solution approach is suitable for hard real time simulation since it provides a mechanism for gracefully degrading to coarser resolution approximations, and the wavelet representations allow for runtime adaptive multiresolution rendering.These GF CMAs are well-suited to interactive haptic applications since GFs allow random access to solution components and the capacitance matrix is the contact compliance used for high-fidelity force feedback rendering. Examples are provided for distributed and point-like interactions.Precomputed multizone kinematic GF models are also considered, with examples provided for character animation in computer graphics.Finally, we briefly discuss the generation of multiresolution GF models using either numerical precomputation methods or reality-based robotic measurement.ii

Eigenmode compression for modal sound models

“…Seo et al [2011] considered the problem of compressing blend shapes for animation, however their method exploits the sparsity of deformation fields which does not apply to global eigenmodes. Second-generation wavelets [Schröder and Sweldens 1995;Kolarov and Lynch 1997] offer another approach to compressing surface displacement field operators, such as for "spiky" Green's function displacement fields to support fast wavelet summation [James and Pai 2003], and have been used to compress parametrically coherent mesh animations [Guskov and Khodakovsky 2004]. However, they are less ideal for compressing pseudo-band-limited eigenmodes with sparse random access, especially when mode-specific mesh patches are needed to exploit symmetry.…”

A Survey of Haptics in Serious Gaming

“…The time complexity of haptic rendering algorithms increases with the more complicated scenarios, which designed to simulate Six or higher DOFs and deformable or viscous object/environment [69]. Although the computing techniques and hardware have been improved significantly these days, it is still not good enough for haptic rendering of complicated virtual environment interaction, nor are the existing physical models efficient enough to compensate computational delay [70][71][72][73]. Trade-off still exists between computational resources and real-time performance.…”

Frame-Based Interactive Simulation of Complex Deformable Objects

“…For simplicity, linearized strain has been applied assuming small displacements in rotated frames [29]. Precomputed deformations modes have been used to interactively deform large structures [18,6,22]. Using deformation modes rather than point-like nodes as DOFs allows to easily tradeoff accuracy for speed.…”