PerPixel Evaluation of Parametric Surfaces on GPU

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Per-Pixel Evaluation of Parametric Surfaces on GPU
Takashi Kanai
Yusuke Yasui
Keio University SFC
ASTOM Inc.
ACM Workshop on General Purpose Computing on
Graphics Processors Los Angeles, USA, 7-8
August, 2004
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Per-Pixel Evaluation of Parametric Surfaces on GPU
Takashi Kanai
Yusuke Yasui
Keio University SFC
ASTOM Inc.
ACM SIGGRAPH 2004 Poster Los Angeles, USA, 8-12
August, 2004
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Surface Rendering

• In the rendering of parametric surfaces, in
  general, we often use a polygon to draw the
  approximation of its original surface. However,
  such rendering of a polygon does not represent
  its original surface exactly. This occurs notably
  in the case that a polygon is coarse or that a
  view position becomes closer to a surface.

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Our Contribution

• Use of GPU (Programmable Graphics Hardware)
• Fragment-based evaluation (position, derivatives)
  of parametric surfaces on GPU
• Robust and high-quality evaluation
• Interactive computation

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Parametric Surfaces on GPU

• Linear form of parametric surfaces
• (Bezier, B-spline, Coons, )
• Control points
• stored to texture(s)
• Basis functions
• directly provided in a fragment
  program

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Parametric Form of Subdivision Surface Stam98
Subdivision Surface on GPU 1

• u,v n,k (n subdivision level, k
  domain id)
• 1st derivatives of both u, v directions can also
  be computed

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Implementation on GPU
Subdivision Surface on GPU 2

• computed in advance
• Computed for all patterns of n, k
• (n 115, k 1, 2, 3. 45 patterns)
• ? stored in a texture
• In the fragment program,
• Fetch 16 control points from a texture by n, k
• Basis functions
• directly computed in FP
• Linear combination of basis functions and control
  points

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Texture Storage
Subdivision Surface on GPU 3
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Texture Storage (Close-up View)
Subdivision Surface on GPU 3
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Algorithm Overview
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Application Reflection LinesYasui and Kanai,
SMI 2004

• For each fragment,
• Compute a reflection vector
• Compute an intersection point
• Assign a color to a fragment
• A line on a surface
• with different color
• a reflection line

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Results
wireframe
polygon-based
fragment-based
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Polygon-based
Pixel-based
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Discussion

• Position of a fragment
• Position of parametric surface
• computed on GPU
• Current solution
• input polygon better approximation of a surface
• run fragment program with bigger size of image

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Conclusion and Future Work

• Conclusion
• Fragment-based evaluation of parametric surfaces
  on GPU
• Robust computation
• High-quality even for low polygons
• Interactive computation
• Future Work
• The number of instruction sets in a fragment
  program
• 1,024 (GF 5x00) ? 65,000 (GF 6x00)
• Processing on a single fragment program
  will be possible
• (cuurrently two FPs) in the near future.

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Contact References

• Takashi Kanai
• Keio University SFC
• E-mail kanai_at_sfc.keio.ac.jp
• Web http//www.sfc.keio.ac.jp/kanai/
• References
• Yusuke Yasui and Takashi Kanai,
• "Surface Quality Assessment of Subdivision
  Surfaces on Programmable Graphics Hardware",
• Proc. International Conference on Shape Modeling
  and Applications 2004 (Genova, Italy, 7-9 June
  2004), pp.129-136, 2004.