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Codimensional Incremental Potential Contact
Extends IPC to shells, rods, and particles coupled seamlessly, enabling unified interpenetration-free simulation of cloth, hair, and volumetric bodies together.
Abstract
We extend the incremental potential contact (IPC) model [Li et al. 2020a] for contacting elastodynamics to resolve systems composed of codimensional degrees-of-freedoms in arbitrary combination. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending the IPC model to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C 2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically-consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend the IPC model to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (respectively mid-lines) of shells (respectively rods) will not move closer than applied thickness values, even as these thicknesses become characteristically small.
How to read this
- Category
- Method: unified codimensional contact simulation (C-IPC)
- Contributions
- Extends IPC to couple codimension-0,1,2,3 geometries (volumes, shells, rods, particles) seamlessly with frictional contact, interpenetration-free
- A C2 constitutive barrier model enforcing strain limiting as an energy potential while preserving rest state (isotropic and anisotropic)
- Distance-offset enforcement so codimensional mid-surfaces and mid-lines keep a strict geometric thickness during collision
- Context
- Directly extends Incremental Potential Contact (IPC) from volumetric elastodynamics to thin and reduced-dimension structures, enabling cloth, hair, and bodies in one solver.Builds on: Incremental Potential Contact: Intersection- and Inversion-free Large-Deformation Dynamics
- Correctness
- Built on the IPC guarantee of intersection- and inversion-free dynamics extended to shells/rods/particles; strict guarantees come at the cost of barrier-based optimization that is computationally heavy, so interactive use is not the target.
- Clarity
- Dense and math-heavy; a first pass gives the unification claim, but the formulation needs careful second and third passes.
- How to read it
- First pass for what codimensions are unified and the three contributions; reserve a second/third pass for the barrier model and strain-limiting derivations only if you implement or modify a contact solver.
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