Efficient and Stable Simulation of Inextensible Cosserat Rods by a Compact Representation
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Piecewise linear inextensible Cosserat rods are usually represented by Cartesian coordinates of vertices and quaternions on the segments. Such representations use excessive degrees of freedom (DOFs), and need many additional constraints, which causes unnecessary numerical difficulties and computational burden for simulation. We propose a simple yet compact representation that exactly matches the intrinsic DOFs and naturally satisfies all such constraints. Specifically, viewing a rod as a chain of rigid segments, we encode its shape as the Cartesian coordinates of its root vertex, and use axis-angle representation for the material frame on each segment. Under our representation, the Hessian of the implicit time-stepping has special non-zero patterns. Exploiting such specialties, we can solve the associated linear equations in nearly linear complexity. Furthermore, we carefully designed a preconditioner, which is proved to be always symmetric positive-definite and accelerates the PCG solver in one or two orders of magnitude compared with the widely used block-diagonal one. Compared with other technical choices including Super-Helices, a specially designed compact representation for inextensible Cosserat rods, our method achieves better performance and stability, and can simulate an inextensible Cosserat rod with hundreds of vertices and tens of collisions in real time under relatively large time steps.
Description
CCS Concepts: Computing methodologies --> Physical simulation; Animation --> Animation with Constraints
@article{10.1111:cgf.14701,
journal = {Computer Graphics Forum},
title = {{Efficient and Stable Simulation of Inextensible Cosserat Rods by a Compact Representation}},
author = {Zhao, Chongyao and Lin, Jinkeng and Wang, Tianyu and Bao, Hujun and Huang, Jin},
year = {2022},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14701}
}