Disney Enterprises, Inc.

Alexey Stomakhin

Joseph M Teran

Andrew Selle

Rasmus Tamstorf

Lawrence Chai

Andrew Milne

Rajsekhar Setaluri

Mark McLaughlin

The disclosure provides an approach for simulating three-dimensional (3D) virtual environments using generalized collision objects. In one aspect, the generalized collision object includes a shape specifying the boundary of the generalized collision object, a shape velocity specifying how the generalized collision object moves and evolves through space, and a material velocity specifying how the material being simulated moves at the boundary of the generalized collision object. Taking the shape, shape velocity, and material velocity as inputs, a simulation application determines source and sink boundary conditions to apply in a simulation based on a difference between components of the shape velocity and the material velocity that are normal to the boundary of the generalized collision object. The simulation application then performs the simulation of the 3D virtual environment while enforcing velocity boundary conditions using the material velocity and the determined source and sink boundary conditions.

Guided simulation with generalized collision objects

An adaptive material point method for simulating and rendering of solid materials is disclosed. During each time step, a simulation application splits and/or merges particles according to a resolution of a grid and assigns properties to the split/merged particles. The simulation application then rasterizes particle information, including masses and velocities, to the grid, on which forces and/or collisions are computed to obtain updated velocities. Grid information, including the updated velocities, is then transferred back to the particles. The transfer from particles to grid and back from grid to particles may employ different transfer functions. In particular, a quadratic transfer function may be used to transfer information from the particles to the grid, while a linear transfer function may be used elsewhere, including to transfer information back from the grid to the particles. After updated velocities are transferred to the particles, the simulation application advects the particles using the updated velocities.

Adaptive material point method

The disclosure provides an approach for reducing information loss when transferring from particles to grid and vice versa in a hybrid Lagrangian/Eulerian simulation, while also preserving stability. In one aspect, referred to as the rigid particle-in-cell (RPIC) method, a simulation application stores a sampling of local angular momentum for each particle, helping to preserve the angular momentum that would otherwise be lost in the transfer from grid to particles. In another aspect that is more generally applicable and referred to herein as the rigid and shearing particle-in-cell (RSPIC) method, the simulation application stores, for each particle, a matrix with rotational and shearing information. The RSPIC method effectively reduces dissipation, preserves angular momentum exactly, and prevents instabilities. Further, the RSPIC method is applicable to both incompressible liquids and material point method (MPM) simulations of materials such as solids.

Particle-in-cell methods preserving shearing and rotation

The disclosure provides an approach for simulating and rendering materials across different states and undergoing phase transitions. In one configuration, a simulation application generates video frames depicting a material phenomenon using an augmented material point method (MPM). Traditional MPM does not handle incompressible materials such as fluids. Techniques disclosed herein augment the MPM with a Chorin-style projection technique to enable simulation of arbitrarily incompressible materials. In one configuration, this is achieved with a marker-and-cell (MAC) grid based MPM solver, a splitting of stress used in the simulation into elastic and dilational parts, a projection-like implicit treatment of the Eulerian evolution of the dilational part of the stress, and particular techniques for rasterizing and updating quantities on the MAC grid. In addition, a heat model may be coupled to the MPM solver, allowing material changes to be driven with temperature and phase changes.

Augmented material point method for simulating phase changes and varied materials

The disclosure provides an approach for simulating and rendering granular materials. A simulation application generates video frames depicting a granular material phenomenon using a strain based elasto-plastic constitutive model integrated with a hybrid Eulerian/Lagrangian material point method (MPM). The elasto-plastic constitutive model includes physical equation(s) which dictate forces that affect the granular material during the simulation. In particular, the constitutive model may include user-controllable parameters defining threshold(s) to start plastic deformation, as well as a hardening parameter which controls how fast the granular material packs under compression. The MPM is a procedure in which particles of the granular material and a background grid are coupled, with the grid being used to assist in computing forces dictated by the physical equation(s) of the elasto-plastic constitutive model. In one configuration, the grid may further be rendered with volumetric rendering to generate video frames depicting the granular material.

Material point method for simulation of granular materials

A method and system for simulation of deformation of elastic materials are disclosed herein. A matrix-free geometric multigrid method utilizing a direct coarse grid discretization is presented for the solution of linear systems resulting from an octree discretization of the equations of corotational linear elasticity. The diagonal component of the stiffness matrix needed for the multigrid smoother is calculated without generating the stiffness matrix. The use of an incomplete linear octree data structure supports the efficient simulation of objects with complicated boundaries. Furthermore, the method is robust to large deformations, making it suitable for character skinning applications in computer animation.

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Studio City, CA, United States of America

Alexey Stomakhin