Variational r-Adaptive Cloth Simulation
Jiahao Wen, Zhen Chen, Jernej Barbič, Danny M. Kaufman
cs.GR
2026-08-18
The first r-adaptive method for frictionally contacting cloth works inside modern IPC pipelines: a degeneracy-activated MIPS quality regularization kills both local-minimum traps and collapse-to-cheat-energy failures at once, and a coherence-exploiting solver adds 3-6X speedup over prior ITR.
Cloth's visual payoff (wrinkles, folds, buckling) demands high spatial resolution, and uniform refinement under implicit integration is unaffordable. Adaptive simulation offers three levers: h-adaptivity adds vertices, p-adaptivity raises interpolation order, and r-adaptivity keeps connectivity fixed and moves vertices of the reference mesh (the undeformed 2D material coordinates) to reallocate resolution. For cloth, r-adaptivity has a structural edge: vertices can snap precisely onto sharp contact features like table edges.
Prior r-adaptive work covered volumetric solids only. Moving it to thin shells, the Adobe team hit two failure modes that had gone unanalyzed:
First, the discretized incremental potential (IP) is nonconvex and hosts nonequivalent local minima: not physically valid alternative wrinkle patterns, but discretization artifacts sitting at higher energy. Newton-type solvers cannot climb back out, and the mesh tangles progressively.
Second, a subtler cheat: with low-order linear elements, once element shapes degrade the finite element approximation locally breaks down and the IP value stops measuring physical quality. The solver discovers that shrinking an element's rest area toward zero scales its elastic restoring force down while gravity stays constant; the cloth sags a bit more and the IP drops. So the optimizer happily collapses elements, a gain with zero physical content. In a 0.2K-vertex draping demo, unregularized r-adaptivity converged to -1.21e-4, below even a 25.5x-finer fixed-mesh benchmark of 5.1K vertices. Pure cheating, undetected by the objective.
One prescription for both diseases: a degeneracy-activated quality regularizer. It must stay inactive where elements are healthy (healthy anisotropy is r-adaptivity's whole point) and brake hard only near degeneracy.
The construction uses MIPS energy: for each triangle, take the singular values of the map from initial to current reference configuration and compute the ratio sum, minimum 2 at conformal. The quality energy is
Equality = max((MIPS - 2.5)^3, 0)
The same term cures the first disease: suboptimal minima correlate strongly with degraded element quality, so lifting the energy around low-quality basins fills in the trap while leaving the global minimum untouched (verified by exhaustive enumeration on a 1D rod: the suboptimal minimum disappears, the global one does not move). A cloth-specific failure the authors name element bunching, where elements pile up and collapse as cloth slides across a sharp edge, also disappears.
The second contribution is solver speed, targeting two bottlenecks of the bi-level optimization:
| Experiment | Comparison | Result |
| Solver ablation (Fig. 5) | vs Wen et al. 2025 r-ITR | 5x volumetric, 3x cloth speedup; strategies independently composable |
| 3D masticator | vs baseline | 6x over the full sequence, Hausdorff distance to fine-mesh benchmark up only 1% |
| Two-point draping (Fig. 6) | fixed mesh, 26K vertices | 7.8K vertices (3.3x fewer) reproduces its buckling behavior at lower energy and less time |
| Draping cheat demo (Fig. 3) | fixed mesh, 5.1K vertices | No quality term: -1.21e-4 (below physical); with it: -1.13e-4, matching the fine benchmark |
| Cube draping (two thicknesses) | equal-vertex fixed mesh | consistently lower energy; fixed mesh shows non-monotonic energy jumps (locking signature), ours none |
| Dress on dancing mannequin (14K vertices) | equal-budget fixed mesh | fixed mesh membrane-locks with aliased wrinkles; ours resolves smooth wrinkle flows and multi-layer folds |
The evaluation protocol deserves note: contacting thin shells have no unique ground truth, since different resolutions produce physically valid but different wrinkles. The paper evaluates along three axes (equal-budget energy reduction, conforming contact adaptation, locking artifact reduction) instead of against a reference configuration.
This is the first r-adaptive cloth method that plugs into modern IPC pipelines (the current standard for intersection- and inversion-free frictional contact), and both contributions transfer independently. The quality-regularizer idea is metric-agnostic (MIPS can be swapped for ODT, minimum angle, aspect ratio) and applies to any variational r-adaptivity; the tolerance scheduling and derivative caching also work for volumetric ITR, verified at 6x there. For cloth practitioners, one extra notch of wrinkle detail at equal vertex budget is a concrete win. All experiments ran on a MacBook Pro with an M3 Pro and 18GB of memory, so the entry bar is low.