Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.
We propose the use of high-order accurate interpolation and approximation schemes alongside high-order accurate time integration methods to enable high-order accurate Particle-in-Cell methods. The key insight is to view the unstructured set of particles as the underlying representation of the continuous fields; the grid used to evaluate integro-differential coupling terms is purely auxiliary. We also include a novel regularization term to avoid the accumulation of noise in the particle samples without harming the convergence rate. We include numerical examples for several model problems: advection-diffusion, shallow water, and incompressible Navier-Stokes in vorticity formulation. The implementation demonstrates fourthorder convergence, shows very low numerical dissipation, and is competitive with high-order accurate Eulerian schemes.
Figure 1: Coarse game-level cloth animation augmented with realistic looking wrinkles in real-time. AbstractDynamic folds and wrinkles are an important visual cue for creating believably dressed characters in virtual environments. Adding these fine details to real-time cloth visualization is challenging, as the low-quality cloth used for real-time applications often has no reference shape, an extremely low triangle count, and poor temporal and spatial coherence. We introduce a novel real-time method for adding dynamic, believable wrinkles to such coarse cloth animation. We trace spatially and temporally coherent wrinkle paths, overcoming the inaccuracies and noise in low-end cloth animation, by employing a two stage stretch tensor estimation process. We first employ a graph-cut segmentation technique to extract spatially and temporally reliable surface motion patterns, detecting consistent compressing, stable, and stretching patches. We then use the detected motion patterns to compute a per-triangle temporally adaptive reference shape and a stretch tensor based on it. We use this tensor to dynamically generate new wrinkle geometry on the coarse cloth mesh by taking advantage of the GPU tessellation unit. Our algorithm produces plausible fine wrinkles on real-world data sets at real-time frame rates, and is suitable for the current generation of consoles and PC graphics cards.
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