Month: June 2016

SCA 2016 papers

Simulation-related papers from Symposium on Computer Animation 2016:

ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models

Rahul Narain, Matthew Overby, George E. Brown

We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general-purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We demonstrate these benefits on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity.

ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models

Hierarchical hp-Adaptive Signed Distance Fields

Dan Koschier, Crispin Deul, Jan Bender

In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell’s polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.

Hierarchical hp-Adaptive Signed Distance Fields

Hele-Shaw Flow Simulation with Interactive Control using Complex Barycentric Coordinates

Aviv Segall, Orestis Vantzos, Mirela Ben-Chen

Hele-Shaw flow describes the slow flow of a viscous liquid between two parallel plates separated by a small gap. In some configurations such a flow generates instabilities known as Saffman-Taylor fingers, which form intricate visual patterns. While these patterns have been an inspiration for artists, as well as thoroughly analyzed by mathematicians, efficiently simulating them remains challenging. The main difficulty involves efficiently computing a harmonic function on a time-varying planar domain, a problem which has been recently addressed in the shape deformation literature using a complex-variable formulation of generalized barycentric coordinates. We propose to leverage similar machinery, and show how the model equations for the Hele-Shaw flow can be formulated in this framework. This allows us to efficiently simulate the flow, while allowing interactive user control of the behavior of the fingers. We additionally show that complex barycentric coordinates are applicable to the exterior domain, and use them to simulate two-phase flow, yielding a variety of interesting patterns.

Hele-Shaw Flow Simulation with Interactive Control using Complex Barycentric Coordinates