计算机动画中可变形物体的模拟：数值透视
Simulating deformable objects for computer animation: a numerical perspective
摘要：
我们研究了各种数值方法时出现的考虑动态系统的背景下，基于物理的模拟可变形物体。这些问题出现在各种应用中，包括动画，机器人，控制和制造。适用于这些应用的数值算法的目标和优点不同于动力系统中典型的数值分析研究。在这里，数学模型不是先验固定的，而是必须根据需要进行调整，以捕捉所需的行为，重点是有效地产生具有复杂几何形状的对象的生动动画。结果往往是判断他们似乎观察者的现实程度（通过“眼睛规范”）以及所采用的数值程序的有效性。然而，我们表明，调整后的观点，数值分析和应用数学可以显着有助于适当的方法和它们的分析，在各种领域，包括有限元法，刚性和高振荡常微分方程，模型简化，约束优化的发展。
英文摘要：
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control and fabrication. The goals and merits of suitable numerical algorithms for these applications are different from those of typical numerical analysis research in dynamical systems. Here the mathematical model is not fixed a priori but must be adjusted as necessary to capture the desired behaviour, with an emphasis on effectively producing lively animations of objects with complex geometries. Results are often judged by how realistic they appear to observers (by the "eye-norm") as well as by the efficacy of the numerical procedures employed. And yet, we show that with an adjusted view numerical analysis and applied mathematics can contribute significantly to the development of appropriate methods and their analysis in a variety of areas including finite element methods, stiff and highly oscillatory ODEs, model reduction, and constrained optimization.
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