We resolve the longstanding problem of simulating the contact-mediated interaction of cloth and sharp geometric features by introducing an Eulerian-on-Lagrangian (EOL) approach to cloth simulation. Unlike traditional Lagrangian approaches to cloth simulation, our EOL approach permits bending exactly at and sliding over sharp edges, avoiding parasitic locking caused by over-constraining contact constraints. Wherever the cloth is in contact with sharp features, we insert EOL vertices into the cloth, while the rest of the cloth is simulated in the standard Lagrangian fashion. Our algorithm manifests as new equations of motion for EOL vertices, a contact-conforming remesher, and a set of simple constraint assignment rules, all of which can be incorporated into existing state-of-the-art cloth simulators to enable smooth, inequality-constrained contact between cloth and objects in the world.
Eulerian on Lagrangian Cloth Simulation Kyle PiddingtonThis thesis introduces a novel Eulerian-on-Lagrangian (EoL) approach for simulating cloth. This approach allows for the simulation of traditionally difficult cloth scenarios, such as draping and sliding cloth over sharp features like the edge of a table.A traditional Lagrangian approach models a cloth as a series of connected nodes.These nodes are free to move in 3d space, but have difficulty with sliding over hard edges. The cloth cannot always bend smoothly around these edges, as motion can only occur at existing nodes.An EoL approach adds additional flexibility to a Lagrangian approach by constructing special Eulerian on Lagrangian nodes (EoL Nodes), where cloth material can pass through a fixed point. On contact with the edge of a box, EoL nodes are introduced directly on the edge. These nodes allow the cloth to bend exactly at the edge, and pass smoothly over the area while sliding.Using this 'Eulerian-on-Lagrangian' discretization, a set of rules for introducing and constraining EoL Nodes, and an adaptive remesher, This simulator allows cloth to move in a sliding motion over sharp edges. The current implementation is limited to cloth collision with static boxes, but the method presented can be expanded to include contact with more complicated meshes and dynamic rigid bodies.iv ACKNOWLEDGMENTS Thanks to:
We present a new, Eulerian-on-Lagrangian approach for modeling cloth. When a cloth modeled using the traditional Lagrangian approach is moved around an object with sharp corners, such as the edge of a table, the cloth cannot always bend smoothly around the object because it can bend only at its nodes. With our method, these constraints are built into the discretization of the cloth, giving us an equation of motion that directly honors these constraints. This allows the cloth to bend and move smoothly around such constraints. We show how our method can efficiently handle challenging simulations, such as pulling a table cloth from under wine glasses without knocking them over.
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