Surface Representations for High Performance Processing

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Surface Representations for High Performance
Processing

• Nathan A. Carr
• University of Illinois Urbana-Champaign
• Feb. 13, 2005

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Modern Processor Design (Pessimism and Optimism)
cache

• CPU (pessimism)
• Designed for the worst case
• Assumes programs are single threaded,
  synchronous, with data dependencies
• Lots of cache
• GPU (optimism)
• Designed for the best case
• Assumes programs are massively multi-threaded
  with little/no communication between threads.
• Little/no data dependencies
• Less cache more chip space dedicated to ALUs

AMD Athlon 64 FX die
Nvidia GeForce 6800 Ultra die
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Performance and Possibility

• NV40 (Geforce 6)
• 225 million xtors
• 450mhz
• Pentium 4 EE chip
• 175 million xtors
• 3.2 Ghz

Stream Programming Environments Hanrahan,
2004
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Ray-Engine (2002) A Hybrid Approach

• Idea Use GPU as a SIMD stream processor to
  perform ray cast queries.
• Paralleled work done at Stanford.(Purcell et al.
  S02)
• Approach Let CPU do what it does best, and the
  GPU do what it does best

Monte-Carlo
Monte-Carlo Photon Mapping
Carr Hart. The Ray Engine Graphics Hardware
2002.
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Idea Build a Compiler

• Transform old source code into programs that
  execute in this hybrid processor environment.
• Not and easy task transformations are too complex
  for compilers alone!
• Need compiler, language, and programmer support!
• Requires Programmer Support
• Re-write code to extract parallelism
• Re-design algorithms to be parallel
• Develop new constructs that ease this
  transformation for a wide range of applications.

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We know how to work with 2D images..

• Compression
• jpg, png, wavelets, etc..
• progressive transmission
• Memory Layout
• row order, tiled, Hilbert curve, etc..
• Filtering
• smoothing, sharpening, blur, emboss, edge
  detection, etc..
• Numerical Simulation
• Solve PDEs on regular grid
• Use finite differencing to derive stencils to
  solve PDEs
• Graphics Hardware Support
• GPUs are specifically designed for working with
  images.

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What about 3D surfaces ??
3D Surface Painting
Stable Fluids Simulation
Laplacian Smoothing
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A Reduction From Surfaces To Images

• Surface Parameterization

O??2
?3
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Challenges of Surface Parametrization
Authalic
Conformal
Mean-value
L2 single-chart
L2 multi-chart
Area Distortion Metric
oversampled
undersampled
0.5
2.0
1.0
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Geometry Images

• Store geometric information (x,y,z coordinates)
  into a set of images
• Original triangle mesh is no longer needed
• Connectivity is implicit
• Use conventional image processing toolbox for
• Compression
• Progressive Transmission
• Filtering
• GPU processing

Single-chart Geometry Images Gu et al. (SIGGRAPH
02)
Multi-chart Geometry Images Sander et al. (SGP
04)
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Images are Square/Rectangular

• Objective Decompose mesh into a set of face
  clusters such that each face cluster
• Is homeomorphic to a disc ( e.g. can be flattened
  without fold-over)
• Flattens with low distortion
• Forms a (nearly) rectangular shape when flattened

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Lloyds Algorithm and K-means Clustering
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The Growth Process
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Clipping, Centering, and Re-orientation
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Global Parametrization

• Visit each patch
• Assign discrete texel lengths to each shared
  boundary segments

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10
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8
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Global Parametrization

• Choose patch aspect ratio
• Select four corners, and divide boundary segment
  intervals

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4
4
10
6
8
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Forcing Continuity

• Assign patch vertices to the boundary
• Force Patch into perfect rectangle
• Linear solve
• Guarantees and embedding with no fold-over

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4
10
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Optimization
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Seamless Square Patches Meshes
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Compression and Storage

• Rectangular Multi-Chart Geometry Images

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Whats This Stuff Good For

• Texture Mapping
• Procedural Solid Texturing
• Compression
• Progressive Transmission
• Subsurface Scattering (Light Transport)
• Fluid Simulation
• 3D Surface Painting
• GPU Acceleration

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3D Mesh Filtering on Graphics Hardware

• Filters (think PhotoShop)
• Smoothing ( Laplacian ), Sharpening, etc..
• Parametrized patch images provide a regular grid
  over the surface
• Just apply stencils to regular grid
• Use differential geometry to bias stencil weights
  accounting for surface distortion. (Taubin,
  Eurographics STAR 00, Meyer et al. VisMath 02)

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GPU Stable Fluid Simulation

• Fluid flow over surfaces
• Numerical solutions to PDEs derived from finite
  difference equations
• Most solvers require a regular grid
• Problem solved on arbitrary surfaces CPU
• Stam (SIGGRAPH 99)
• One Motivation fluid flow essential for
  simulating natural media
• Oil paint, watercolor, etc..

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Texture Atlas Generation

• Each flattened patch forms a chart
• For convenience, charts can be packed into a
  single image
• Trade-off Between
• Continuity
• Full texture space ultilization

chart
Texture Atlas
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Chart PackingMulti-Resolution Meshed Atlas (MMA)
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Step 3 Chart PackingMulti-Resolution Meshed
Atlas (MMA)
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Step 3 Chart PackingMulti-Resolution Meshed
Atlas (MMA)
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Surface Signal Balancing

• Optimize Texture Atlas for the signal being
  stored
• Balance MMA tree based on surface signal
  importance
• Optimize local charts parametrization

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3D Painting Dynamic Re-Parametrization
Dynamic MMA Atlas
Static Atlas (Conformal)
Carr Hart. Painting Detail SIGGRAPH 04.
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GPU Painting
GPU
CPU
Model
Stroke Buffer
Depth Map
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Real-Time Subsurface Scattering
Links -uv offset -lod -scale factor
Carr et al. GPU Algorithms for Radiosity and
Subsurface Scattering, GH 2003.
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Limitations

• Quality of results are tied to the tessellation
  of the input mesh
• Low tessellation models
• Limited opportunity to choose parameterization to
  better distribute surface samples.
• Irregularly tessellation models
• Methods may fail to find clusters that
  parameterize well into square/rectangular regions

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Thanks!
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A Call for Action!

• Need New Compiler Technology
• Need Language Designers
• Need New Parallel Algorithms
• Need Better Developer tools
• Need to get the word out
• Apply computational model to other problems
  outside of graphics
• Bio-informatics, computational biology
• Numerical Simulation and Computation