Simulating deformable objects for computer animation: a numerical perspective

TL;DR

This paper reviews numerical methods for simulating deformable objects in computer animation, emphasizing their practical effectiveness in producing realistic visuals and their mathematical analysis.

Contribution

It highlights the importance of tailored numerical algorithms for physics-based animation, bridging numerical analysis with practical animation needs.

Findings

Numerical methods can be adapted to produce realistic animations.

Analysis of methods improves their stability and efficiency.

Application to complex geometries enhances visual realism.

Abstract

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.