Abstract:Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first‐order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second‐order methods, their use is not widespread. Many of these well‐known methods have significant drawbacks such as severe numerical damping or scene‐dependen… Show more
“…Soft objects, such as the characters that appear in animation movies aimed at young audiences, commonly arise in computer graphics applications. Here, the DIRK methods introduced in Section 3.1, namely TR-BDF2 and SDIRK, have a good record [48,32], even though occasionally an additional stabilization or damping may be required.…”
Section: Siere the Methods Used Inmentioning
confidence: 99%
“…This method performed well in comparative experiments reported in [32]. It has two implicit stages, each requiring the solution of a nonlinear system of size n. S-versions for these are derived directly as before.…”
mentioning
confidence: 93%
“…In this section we mention and discuss several favourite time discretization methods that have seen use in practice. See also the recent [32].…”
mentioning
confidence: 99%
“…Plot of the smoothing function s = s(x; ) for different values of . It is used in (34) through(32) to approximate the Coulomb friction force.…”
<p style='text-indent:20px;'>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 <i>a priori</i> 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.</p>
“…Soft objects, such as the characters that appear in animation movies aimed at young audiences, commonly arise in computer graphics applications. Here, the DIRK methods introduced in Section 3.1, namely TR-BDF2 and SDIRK, have a good record [48,32], even though occasionally an additional stabilization or damping may be required.…”
Section: Siere the Methods Used Inmentioning
confidence: 99%
“…This method performed well in comparative experiments reported in [32]. It has two implicit stages, each requiring the solution of a nonlinear system of size n. S-versions for these are derived directly as before.…”
mentioning
confidence: 93%
“…In this section we mention and discuss several favourite time discretization methods that have seen use in practice. See also the recent [32].…”
mentioning
confidence: 99%
“…Plot of the smoothing function s = s(x; ) for different values of . It is used in (34) through(32) to approximate the Coulomb friction force.…”
<p style='text-indent:20px;'>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 <i>a priori</i> 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.</p>
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.
The emergence of position-based simulation approaches has quickly developed a group of new topics in the computer graphics community. These approaches are popular due to their advantages, including computational efficiency, controllability, stability and robustness for different scenarios, whilst they also have some weaknesses. In this survey, we will introduce the concept of the baseline position based dynamics (PBD) method and review the improvements and applications of PBD since 2018, including extensions for different materials and integrations with other techniques.
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