Physically based simulation is an indispensable tool for creating realistic and believable virtual environments. By leveraging the power of modern computer systems, and using novel algorithms based on the laws of physics, it takes a huge burden off the shoulders of an artist and allows the creation of highly complex visual effects which would otherwise be unfeasible to animate ‘by hand’, such as crashing ocean waves, snow blizzards and fireball explosions to name a few.
Matterhorn is one of Disney Animation’s proprietary physically based simulators. It was originally developed for creating snow effects in Frozen (2013) . It employs the Material Point Method (MPM) at its core and is highly efficient at simulating large amounts of snow interacting with characters. Recently Matterhorn has been upgraded with more advanced constitutive models to be able to simulate more materials: mud, foam, sand etc.
The Science Behind the Simulator:
What is simulation? Originally, animated movies were created using traditional hand-drawn animation techniques. Teams of animators would draw all characters and the surroundings frame by frame which would be assembled to compose the final film. But there is only so much a person can draw! Things like water, smoke and fire have extreme amounts of richness and degrees of freedom to their composition and movement, which makes them nearly impossible to animate “by hand” in any reasonable amount of time. That is where technology and physically-based algorithms come in: environmental effects like water, smoke and fire are governed by physical equations, so why not let computers do all the heavy computation to solve those equations. The programs that do this computation are called simulators.
Why MPM simulation?
“How do we tell the computer about what something is and how should it be represented internally?” The choice of a particular representation typically depends on the properties of the physical problem to be solved. For example, computations in fluid dynamics are naturally handled using Cartesian grids, so it makes sense to represent fluids as occupying certains parts of such grids and moving through them over time as the simulation progresses. Grains and small rigid bodies are better represented by particles that have position, velocity and other properties. Snow, however, is a complex substance: on one hand it consists of individual grains and snowflakes, but on the other hand they are not that big, so it sometimes behaves like a fluid. The Material Point Method is designed exactly for these kinds of substances. It uses both Cartesian grids and particles to represent the material, and leverages the strengths of each representation.
How does MPM simulation work?
Particles are the primary representation of the material. Each of them has position, velocity, mass, deformation and other properties that determine the look of the snow, such as stiffness, wetness, breaking threshold etc.
Each step of the simulation progresses as follows. Since particles are not a good representation for computing material forces, they are first rasterized to a Cartesian grid, where the force computation is a lot simpler. These material forces act back on the particles, changing their velocities. Finally, the particles are advected with their new velocities, producing the next frame of the simulation.