Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by one’s favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.
Month: June 2007
Arbitrary Cutting of Deformable Tetrahedralized Objects
We propose a flexible geometric algorithm for placing arbitrary cracks and incisions on tetrahedralized deformable objects. Although techniques based on remeshing can also accommodate arbitrary fracture patterns, this flexibility comes at the risk of creating sliver elements leading to models that are inappropriate for subsequent simulation. Furthermore, interactive applications such as virtual surgery simulation require both a relatively low resolution mesh for efficient simulation of elastic deformation and highly detailed surface geometry to facilitate accurate manipulation and cut placement. Thus, we embed a high resolution material boundary mesh into a coarser tetrahedral mesh using our cutting algorithm as a meshing tool, obtaining meshes that can be efficiently simulated while preserving surface detail. Our algorithm is similar to the virtual node algorithm in that we avoid sliver elements and their associated stringent timestep restrictions, but it is significantly more general allowing for the arbitrary cutting of existing cuts, sub-tetrahedron resolution (e.g. we cut a single tetrahedron into over a thousand pieces), progressive introduction of cuts while the object is deforming, and moreover the ability to accurately cut the high resolution embedded mesh.
Adaptive Deformations with Fast Tight Bounds
“Simulation of deformations and collision detection are two highly intertwined problems that are often treated separately. This is especially true in existing elegant adaptive simulation techniques, where standard collision detection algorithms cannot leverage the adaptively selected degrees of freedom.We propose a seamless integration of multi-grid algorithms and collision detection that identifies boundary conditions while inherently exploiting adaptivity. We realize this integration through multiscale bounding hierarchies, a novel unified hierarchical representation, together with an adaptive multigrid algorithm for irregular meshes and an adaptivity-aware hierarchical collision detection algorithm. Our solution produces detailed deformations with adapted computational cost, but it also enables robust interactive simulation of self-colliding deformable objects with high-resolution surfaces.”