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首页> 外文学位 >Multiresolution Green's function methods for interactive simulation of large-scale elastostatic objects and other physical systems in equilibrium.
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Multiresolution Green's function methods for interactive simulation of large-scale elastostatic objects and other physical systems in equilibrium.

机译：多分辨率格林函数方法，用于在平衡状态下交互式仿真大型弹性物体和其他物理系统。

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摘要

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 second-generation 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.
机译：本文为线性弹性静力学模型及与线性椭圆偏微分方程有关的其他系统的低延迟交互仿真提供了一个框架。这种方法使得交互式地模拟大型物理模型成为可能。通过根据格林函数（GFs）公式化边界值问题（BVP）解决方案来开发线性度，可以对格林函数（GFs）进行预先计算以提供快速且廉价的查找操作。使用基于Sherman-Morrison-Woodbury公式的电容矩阵算法（CMA）集合来解决运行时BVP。时间一致性是通过缓存和重用以及依次更新以前的电容矩阵逆来利用的。多分辨率增强功能使仿真和存储非常大的模型变得切实可行。使用在表面上定义的第二代小波可以获得预先计算的GF的有效压缩表示。快速逆小波变换允许使用快速求和方法来加速运行时BVP解决方案。小波GF压缩因子直接与交互式仿真加速相关，并且在适度误差水平下提供了数百倍改进的示例。此外，使用分层基础函数定义分层约束，然后使用相关的分层GF来构建分层CMA。这种直接解决方案的方法适用于硬实时仿真，因为它提供了一种可以优雅地降级为较粗分辨率近似值的机制，并且小波表示允许运行时自适应多分辨率渲染。这些GF CMA非常适合交互式触觉应用，因为GF允许随机访问解决方案组件，并且电容矩阵是用于高逼真力反馈渲染的接触柔量。提供了分布式和点状交互的示例。还考虑了预先计算的多区域运动学GF模型，并提供了用于计算机图形中角色动画的示例。最后，我们简要讨论了使用数值预计算方法或基于现实的机器人测量方法生成多分辨率GF模型的方法。

著录项

  • 作者

    James, Douglas Leonard.;

  • 作者单位

    The University of British Columbia (Canada).;

  • 授予单位 The University of British Columbia (Canada).;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 154 p.
  • 总页数 154
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

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