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CS-C3100 Computer Graphics Jaakko Lehtinen

9.1 Intro to Dynamical Simulation

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In This Video

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• A tour of physically-inspired animation techniques

Types of Animation

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• Keyframing • Procedural • Physically-based

– Particle Systems • Smoke, water, fire, sparks, etc. • Usually heuristic as opposed to simulation, but not always • Mass-Spring Models (Cloth)

– Continuum Mechanics (fluids, etc.), finite elements • Not in this class

– Rigid body simulation • Not in this class

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Types of Animation: Physically-Based

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• Assign physical properties to objects – Masses, forces, etc.

• Also procedural forces (like wind) • Simulate physics by solving equations of motion

– Rigid bodies, fluids, plastic deformation, etc. • Realistic but difficult to control

Control (Buster Keaton)

5Steamboat Bill, Jr. (1928)

“Directable Simulation”

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• Aim to produce simulations that obey user-specified constraints – Add as-small-as-possible fictitious forces to simulation to

nudge it towards artist/TD needs • Lots of cool stuff!

• See e.g. http://www.cs.huji.ac.il/labs/cglab/projects/tdsmoke/

Modern: Let the AI Drive

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• Ma et al., SIGGRAHP 2018, Fluid directed rigid body control using deep reinforcement learning

Types of dynamics

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• Point

Types of dynamics

Animation by Mark Carlson 9

• Point

• Rigid body

Types of dynamics

Mark Carlson 10

• Point

• Rigid body

• Deformable body (include clothes, fluids, smoke, etc.)

We Focus on Point Dynamics

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• Lots of points! • “Particle systems”

– Borderline between procedural and physically-based

Can Model Everything using Particles!

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• Unified Particle Physics for Real-Time Applications (Chantanez et al. SIGGRAPH 2014) – video

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Real-Time Particles Demo (3DMark03)

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• 3DMark03 by Futuremark Corp. – Explosions, vapor trails, muzzle flashes are particles

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Generalizations (later)

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• Mass-spring and deformable surface dynamics – surface represented as a set of points – forces between neighbors keep the surface coherent

Take-Home Message

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• Particle-based methods can range from pure heuristics (hacks that happen to look good) to “real” simulation

• Basics are the same: Things always boil down to integrating ODEs! – Also in the case of

grids/computational meshes

Andrew Selle et al.

Further reading

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Cloth Video

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Generalizations

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• It’s not all hacks: Smoothed Particle Hydrodynamics (SPH) – A family of “real” particle-based

fluid simulation techniques.

– Fluid flow is described by the Navier-Stokes Equations, a nonlinear partial differential equation (PDE)

• SPH discretizes the fluid as small packets (particles!), and evaluates pressures and forces based on them.

Jos Stam

Müller et al. 2005

SPH Example

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Predictive-Corrective Incompressible SPH. Barbara Solenthaler, Renato Pajarola. ACM Transactions on Graphics (SIGGRAPH), 2009

Meshless Techniques

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• Most simulation techniques work on either regular grids or meshes constructed from triangles/tets

• PDEs defined on space are discretized on the grid.

Regular 3D grid Irregular 2D grid

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Meshless Techniques

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• Most simulation techniques work on either regular grids or meshes constructed from triangles/tets

• In contrast, so-called meshless methods do not require the underlying space to be discretized – Instead, represent things using points (particles!) – They can still be “well-founded”: SPH is an example. – Another example: Point-Based

Animation of Elastic, Plastic and Melting Objects (Müller, Keiser, Nealen, Pauly, Gross, Alexa, SCA 2004)

Müller et al.

That’s all!

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• Next time: particle systems