Physics-Based Modeling Ming C. Lin Department of Computer Science University of North Carolina lin...
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![Page 1: Physics-Based Modeling Ming C. Lin Department of Computer Science University of North Carolina lin geom lin@cs.unc.edu.](https://reader037.fdocuments.in/reader037/viewer/2022110207/56649d3f5503460f94a19471/html5/thumbnails/1.jpg)
Physics-Based Modeling
Ming C. Lin Department of Computer Science
University of North Carolinahttp://www.cs.unc.edu/~lin
http://www.cs.unc.edu/[email protected]
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New Needs
Add more realistic and higher fidelity simulations, especially for urban simulations/scenarios.
Physics-based computations: weather effects, explosions, entity simulation, spatialized sound effects, shadows, environmental effects, etc.
Require modeling/simulation of civilians: “heterogeneous crowds”
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Some Issues
Performance vs. FidelityValidation and VerificationAssessment & Evaluation
– “Correct training”– Performance enhancement– Cost saving
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Speed vs. Fidelity/Accuracy
Multiresolution framework Perception-basedData driven + Physics + New Math
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High Energy Fluid-Elastic Interaction
Fluid phenomena everywhere in real worldSource of interesting phenomena – from
interaction and fluid itself
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Introduction
Fluid notoriously difficult to simulate– Mathematically:
• Nonlinear• Characteristics travel with high or infinite
speed
– Computationally:• Volume discretization• Stability problems• Resists paralleization
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Introduction
Fluid-solid interaction difficult:– Fluid typically Eulerian– Solid objects typically Lagrangian
Interaction introduces severe meshing problems
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Our Approach
We want to simulate interaction of fluids & solids– Do it at high fluid energy levels– “Solid” bodies enter elastic regime
We want a method that is fast and capable of handling high-energy fluids
We need to handle meshing issues
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Our Approach
Fast -> parallel– Parallel means local operators
Residual distribution schemes (RDS)– A technique developed in aeronautical
community for simulating the Euler equations. [Roe '81]
Very simple, local stencils based on wave models of problem equation.
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Residual Distribution Schemes
Consider simple 1D passive advection:
t1
t0
ut=au
x
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Residual Distribution Schemes
Each discrete cell moves along a characteristic
Think of the characteristic as a “signal” that is
sent to the next cell
At each timestep, each cell sends a portion of
its value to the next cell
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Residual Distribution SchemesIn RDS, each signal is derived from the residual
(or fluctuation) of the equation over each cell.
This example is very simple – we have
constant-speed advection
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Burger's Equation
Nonlinear extension to linear advection– Characteristics depend on unknowns
ut=uu
x
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RDS Procedure
For each cell:– Compute fluctuation, decompose into
waves– Distribute waves to incident nodes
• Accumulate updates
For each node:– Time-integrate updates
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RDS Procedure
Lends itself to parallelization:– Perform cell computation in parallel
• Atomic node accumulation
– Barrier– Perform node integration in parallel– Barrier
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Elasticity
We use a standard FEM model of linear elasticity for solid objects.
Iterative solve (conjugate gradient) for new displacements– Parts of CG amenable to parallelization
RDS-based elasticity (in progress)
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Mesh Wrangling
Elastic solve does not take fluid domain mesh into account– Elastic deformations likely to invert fluid
tetrahedra. We use a weakly stiff elasticity on the
fluid tetrahedra to enforce postive volumes
Practical and cheap
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Mesh Refinement
Semi-regular refinement splits tets into 8 children– 4 similar– 4 others
Currently only static in use – Suitable for multigrid, etc.
Dynamic in progress
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Results
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Results
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Results
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Results - Timing
Interactive fluid solution speeds.Finite element method elasticity
bottleneck
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Results - Scaling
RDS very scalable - residuals can be computed and distributed independently.
Multi-core scaling
of RDS solve for
skyscraper scene
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Ongoing/Future Efforts
RDS for elasticity solves – clean solution, parallelizable.
GPU implementation of RDS.More advanced mesh management
for topological changes in domain.
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Modeling of Soft Articulated Bodies in Contact Using Dynamic Deformation Textures
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Motivation
Global deformations Detailed deformations
Müller et al. ‘05Barbič & James ‘05 Ours
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Motivation
Dynamic simulation of deformable solids Highly detailed surface geometry Large contact area: objects bounce, roll, slide,…
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Layered Models Motivation
Detailed, small-scale deformationsGlobal (skeletal) deformationsDynamic interplay between skeletal
motion and surface deformation during contact
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Layered Models
Overview– Dynamic Deformation Textures
Fast Coupled Layered DynamicsFast Condensed Skeleton Dynamics
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Layered Models
Overview– Dynamic Deformation Textures
Fast Coupled Layered DynamicsFast Condensed Skeleton Dynamics
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Layered Models
S
C
S
C
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Layered ModelsDynamic Deformation Textures
Dynamic DeformationTexture
S
C
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Layered Models
Overview– Dynamic Deformation Textures
Fast Coupled Layered DynamicsFast Condensed Skeleton Dynamics
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Fast Coupled Layered Dynamics
Generalized Lagrangian frameworkLinear elasticity in moving frame of
reference [Terzopoulos&Witkin’88]
FEM discretizationImplicit integrationPhysically based approximations
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Dynamic FormulationDecoupled Solution
1. Project surface forces to update core velocity
2. Distribute core velocity to update surface velocities
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Motion interaction Heterogeneous material
Cylinder: 161K tetrahedra
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Fast & Responsive Contact
Hierarchical Collision Queries– Texture-based Collision Detection
Responsive Contact HandlingFast Coupled Contact Response
– Skeleton Response Anticipation
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Texture-based Collision Detection
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Texture-based Collision DetectionStage 1: Low-resolution
Fast proximity tests between proxiesContact plane D per contact region
D
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Surface projection onto contact plane DIdentify contacts in D from separation
distances
D
Texture-based Collision DetectionStage 2: Detailed Surface Interference
D
GPU-based
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Texture-based Collision DetectionCollision Information Transfer
Contact response in dynamic deformation texture
Transfer collision information
D
DGPU Texture Mapping
T
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Hierarchical Pruning
Exploit skeletal nature of deformation– Locality
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Robust 2-stage collision detection
Gear: 173K tetrahedra Cylinder: 161K tetrahedra
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Articulated Contact Response
Snake: 3,102 surface points 16 bones
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Highly detailed, dynamic deformations
Head: 240K tetrahedra 40K vertices
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Highly detailed, dynamic deformations
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Exploiting Parallelism
All surface-related computations on GPUCommunication between core and
surface computations minimizedDynamic deformation textures for
immediate rendering
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Fast Contact Modeling for Soft Characters
Deer: 2,755 surface points 34 bones 10 FPS
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Sound in Nature
Collisions lead to surface vibrationsVibrations create pressure waves in airPressure waves are sensed by ear
Vibration Pressure Wave Perception
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Physically Based Sound Synthesis
Aim: Generate Sounds directly from physical principles
Current: Recorded SoundsProblems with recorded sounds:
– Difficult, expensive or dangerous to record (eg. Explosions)
– Repetitiveness
* Image taken from: http://www.marblehead.net/foley/index.html
A typical foley studio*
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Perceptually Based Acceleration
Brute force physical simulation infeasible Use analytical solution for surface dynamics Exploit human auditory perception
– Mode Compression– Mode Truncation– Quality Scaling
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Key Characteristics
Discretized physically-based representation Simplicity of formulation and ease of
implementation; No assumptions about the input mesh topology
– Surface meshes used for physics can be used directly for sound
Capable of yielding both impact and rolling sounds Enables rich environments consisting of numerous
sounding objects, with insignificant difference in the overall audio quality
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System Demonstration
Video
[Raghuvanshi & Lin; I3D 2006]
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Motivation: Acoustics
The acoustics of a scene contribute a lot to the immersion and realism
More generally, wave propagation has applications in diverse areas:
- Radio waves (Electromagnetic)
- Sonar
- Seismic Waves (Earthquakes)
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Problem Statement
Given: An arbitrary scene in 3D, the locations and sounds for many moving sound sources and the location of the listener (dynamic)
Evaluate the sound heard by the listener as efficiently as possible
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Challenges
Need full time-domain solutionMultiple reflections (>10) are
perceptually relevantAudible sounds (20-22000 Hz) have
wavelengths ~cm: Diffraction is important
Sound is coherent: Interference is also important
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Approaches
Mainly two types of approaches:– Ray/Beam-based–Wave-based
Ray-based approaches motivated from light simulation– Trace sound rays/packets of rays/beams– Compute-intensive for higher order reflections– Integrating diffraction accurately is tough
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Approaches (contd..)
Wave-based approaches directly solve the underlying physical equations
Discretize the equations using an FEM/FDM based approach
Capture reflection, interference and diffraction accurately
Computationally Intractable, especially for high frequencies– Most current methods limited to ~100 Hz
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Our approach
Wave-based approach: Solve the Wave Equation:
is the laplacian operator in 3D = 340m/s is the speed of sound is the pressure field to solve for
The RHS is the forcing term, corrsponding to sound sources in the scene
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Our approach (contd..)
We discretize the Laplacian Operator using an FDM-based approach, giving a discrete set of equations in time:
Observation: This set of equations can be solved analytically by diagonalizing the Discrete Laplacian Matrix, K
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Our approach (contd..)
Main Computational Challenge: Diagonalization has complexity O(n3)
For a typical scene in 3D:
n ~ (lvmax/c)3
l: Diameter of the scene, vmax: Maximum simulated frequency, c: speed of sound
That is, the running time:
T ~ (lvmax/c)9 !!
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Our approach (contd..)
Divide and conquer Divide the scene into many partitions Employ analytical solution within
partitions (very efficient at runtime) Apply perceptually based optimizations to
further increase performance Use a simple explicit scheme between
partitions
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Performance Benchmark
A typical training environmentRuns at near-real-time performance Simulation frequencies upto 1KHzSystem: Intel Core 2 Duo 2.33 GHz, 2
GB RAM, Nvidia 7950 GTX Graphics
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Demo
Visualization of the sound field on the same game environment
The pressure amplitude is color-codedThe input sound is a 200 Hz sine pulseNote the heavy amount of diffraction,
interference and reflection in the simulation
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Ongoing/Future Efforts
Increase efficiency to handle 3D scenes in real time– Exploit recent advances in
many-core/parallel hardwareEmploy perceptually based techniques
to make approach more scalableExtend approach to handle dynamic
scenes
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Hardware Acceleration
Programmable GPUMany-Core Architecture
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Portable Simulation in a Box
Integrate physics-based simulation and develop embedded systems– e.g. On a 30GB flash card, squeeze all
simulation technologies into it and integrated with applications.
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The End
Questions?