Open AccessSimulating deformable objects for computer animation: A numerical perspective
Author(s) -
Uri M. Ascher,
Egor Larionov,
Seung Heon Sheen,
Dinesh K. Pai
Publication year - 2022
Publication title -
journal of computational dynamics
Language(s) - English
Resource type - Journals
eISSN - 2158-2505
pISSN - 2158-2491
DOI - 10.3934/jcd.2021021
Subject(s) - computer science , animation , numerical analysis , variety (cybernetics) , perspective (graphical) , a priori and a posteriori , finite element method , dynamical systems theory , context (archaeology) , ode , computer animation , artificial intelligence , mathematics , computer graphics (images) , mathematical analysis , paleontology , philosophy , physics , epistemology , quantum mechanics , biology , thermodynamics
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.