Month: May 2012

Discrete Viscous Sheets

Christopher Batty, Andres Uribe, Basile Audoly, Eitan Grinspun

We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.

Discrete Viscous Sheets

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Changsoo Je, Min Tang, Youngeun Lee, Minkyoung Lee, Young J. Kim

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Stress Relief: Improving Structural Strength of 3D Printable Objects

Ondrej Stava, Juraj Vanek, Bedrich Benes, Nathan Carr, Radomir Mech

3D printing is a rapidly maturing area that has shown great progress over the past couple of years. It is now possible to produce 3D printed objects with exceptionally high fidelity and precision. However, while the quality of 3D printing has gone up, both the time to print and material costs have remained high. Moreover, there is no guarantee that a printed model is structurally sound. Many times, the printed product does not survive cleaning, transportation, or handling, or it even collapses under its own weight. We present a system that addresses this issue by providing automatic detection and correction of the problematic cases. The structural problems are detected by combining a lightweight structure analysis solver with 3D medial axis approximations. After areas with high structural stress are found, the model is corrected by combining three approaches: hollowing, thickening, and strut insertion. This detection and correction repeats until all problematic cases are corrected. Our process is designed to create a model that is visually similar to the original model, while possessing greater structural integrity

Stress Relief: Improving Structural Strength of 3D Printable Objects

Underwater Rigid Body Dynamics

Steffen Weissman, Ulrich Pinkall

We show that the motion of rigid bodies under water can be realistically simulated by replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This allows us to model fluid-body interaction without simulating the surrounding fluid at all. We explain some of the phenomena that arise and compare our results against real experiments. It turns out that many real scenarios (sinking bodies, balloons) can be matched using a single, hand-tuned scaling parameter. We describe how to integrate our method into an existing physics engine, which makes underwater rigid body dynamics run in real time.

Underwater Rigid Body Dynamics

Lagrangian Vortex Sheets for Animating Fluids

Tobias Pfaff, Nils Thuerey, Markus Gross

Buoyant turbulent smoke plumes with a sharp smoke-air interface, such as volcanic plumes, are notoriously hard to simulate. The surface clearly shows small-scale turbulent structures which are costly to resolve. In addition, the turbulence onset is directly visible at the interface, and is not captured by commonly used turbulence models. We present a novel approach that employs a triangle mesh as a high-resolution surface representation combined with a coarse Eulerian solver. On the mesh, we solve the interfacial vortex sheet equations, which allows us to accurately simulate buoyancy induced turbulence. For complex boundary conditions we propose an orthogonal turbulence model that handles vortices caused by obstacle interaction. In addition, we demonstrate a re-sampling scheme to remove surfaces that are hidden inside the bulk volume. In this way we are able to achieve highly detailed simulations of turbulent plumes efficiently.

Lagrangian Vortex Sheets for Animating Fluids

Ghost SPH for Animating Water

Hagit Schechter, Robert Bridson

We propose a new ghost fluid approach for free surface and solid boundary conditions in Smoothed Particle Hydrodynamics (SPH) liquid simulations. Prior methods either suffer from a spurious numerical surface tension artifact or drift away from the mass conservation constraint, and do not capture realistic cohesion of liquid to solids. Our Ghost SPH scheme resolves this with a new particle sampling algorithm to create a narrow layer of ghost particles in the surrounding air and solid, with careful extrapolation and treatment of fluid variables to reflect the boundary conditions. We also provide a new, simpler form of artificial viscosity based on XSPH. Examples demonstrate how the new approach captures real liquid behaviour previously unattainable by SPH with very little extra cost.

Ghost SPH for Animating Water