Efficient and Stable Simulation of Inextensible Cosserat Rods by a Compact Representation

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dc.contributor.authorZhao, Chongyaoen_US
dc.contributor.authorLin, Jinkengen_US
dc.contributor.authorWang, Tianyuen_US
dc.contributor.authorBao, Hujunen_US
dc.contributor.authorHuang, Jinen_US
dc.contributor.editorUmetani, Nobuyukien_US
dc.contributor.editorWojtan, Chrisen_US
dc.contributor.editorVouga, Etienneen_US
dc.date.accessioned2022-10-04T06:41:54Z
dc.date.available2022-10-04T06:41:54Z
dc.date.issued2022
dc.description.abstractPiecewise 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.en_US
dc.description.number7
dc.description.sectionheadersPhysics Simulation and Optimization
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume41
dc.identifier.doi10.1111/cgf.14701
dc.identifier.issn1467-8659
dc.identifier.pages567-578
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14701
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14701
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies --> Physical simulation; Animation --> Animation with Constraints
dc.subjectComputing methodologies
dc.subjectPhysical simulation
dc.subjectAnimation
dc.subjectAnimation with Constraints
dc.titleEfficient and Stable Simulation of Inextensible Cosserat Rods by a Compact Representationen_US
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