A Finite Element Method on Convex Polyhedra

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dc.contributor.authorWicke, Martinen_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.authorGross, Markusen_US
dc.date.accessioned2015-02-21T15:41:35Z
dc.date.available2015-02-21T15:41:35Z
dc.date.issued2007en_US
dc.description.abstractWe present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping.This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.en_US
dc.description.number3en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume26en_US
dc.identifier.doi10.1111/j.1467-8659.2007.01058.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages355-364en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2007.01058.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleA Finite Element Method on Convex Polyhedraen_US
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