Hemispherical Rasterization for SelfShadowing of Dynamic Objects

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Hemispherical Rasterization for Self-Shadowing of
Dynamic Objects

• COMP238 Class Presentation, November 22, 2004
• Nico Galoppo von Borries

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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer
• Dynamic Transfer Vectors
• An Efficient Hemispherical Rasterizer
• Results and Optimizations
• Properties and Issues

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Self shadowing in the past

• Traditionally, real-time rendering has only used
  point light sources or area lights for shading a
  scene
• Unrealistic, hard shadow boundaries
• Environment maps
• Provides realistic and dynamic spherical incident
  lighting, but doesnt account for shadowing
  effects

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Self shadowing in the past

• Ambient Occlusion
• Precompute visibility function
• Heres how it works
• Shoot rays over hemisphere (with importance
  sampling) at point p and store the fraction that
  doesnt hit other geometry
• Produces nice soft shadows
• For static geometry only!

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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer

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Precomputed Radiance Transfer

• The basic idea is to extend dynamic environment
  mapping with soft shadows
• We want to compute the exitant radiance Lout,p(v)
  from a point p into direction v

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Precomputed Radiance Transfer

• Transfer function Vp(s,v) is independent of p,
  we can precompute it!

(static geometry diffuse BRDF)
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Efficient Radiance Transfer

• Heres a cool trick to do the hemisphere
  integration efficiently
• Project Lin(s) and Vp(s,v) into the orthonormal
  basis B with basis functions bi(s)
• This yields coefficient vectors Lin and Vp(v)
• Now, the integration is simply a dot product
  Lout,p (v) Lin Vp(v)
• Vp(v) is the transfer vector
• Advantages
• With the right basis, only limited number of
  coefficients needed for good accuracy
• Integral evaluation reduced to a simple dot
  product operation

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Static Transfer Vectors

• Lout,p (v) Lin Vp(v), assume
• Static models
• Diffuse BRDF
• Then the transfer vectors Vp(v) are constants
  and can be precomputed
• Lighting is projected into basis B at run time
• Enables shading of static objects in
  time-varying, spherical lighting environments
  with soft shadows
• Non-diffuse BRDF is possible but requires
  transfer matrix instead of transfer vectors

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Which Basis B ?

• Spherical Harmonics (SH)
• Good for low-frequency lighting environments,
  only few coefficients needed
• Wavelets
• Preferable for higher-frequency lighting
• Coefficients that carry most energy is unknown at
  preprocessing, thus the preprocess needs to
  account for all basis functions

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What about animated scenes?

• One approach PCA reduction
• Compute transfer vectors for sparse set of frames
• Perform PCA and interpolate solutions for
  intermediate frames in low-dimensional PCA basis
• Still, precomputation is extremely long
• This paper addresses self-shadowing of dynamic
  scenes in real-time

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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer
• Dynamic Transfer Vectors

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Dynamic Transfer Vectors

• Main contribution of this paper
• Basic idea compute transfer coefficients
  Vp,i(v) on the fly (project into basis B)
• Requires evaluation of the integral
• Represent Vp(s) as a discrete binary image, the
  visibility mask

This is the only non-trivial term!
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Whats this visibility mask?

• Its a 1 bit framebuffer that holds the image of
  blocker triangles, rendered by a spherical
  rasterizer (by hemispherical projection)
• Its a regular grid inside the unit disk
• Black blocked, White environment visible from p

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Advantage of Dynamic Transfer Vectors

• Why not just integrate lighting Lout,p(v)
  directly, using this visibility mask?
• SH basis function integration requires lower
  resolution visibility mask to suppress aliasing
  artifacts
• If model with diffuse BRDF is static in some
  frames, the coefficients can be reused

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Heres the Rendering Pipeline

• For all vertices p to be shaded, what is
  Lout,p(v) ?
• Visibility rasterization ? Visibility mask
• Compute transfer vector Vp(v)
• ?i
• This is all done in the same discrete 2D domain
  as the visibility mask, just discrete sum of
  multiples
• Integrate over hemisphere by dot product Lout,p
  (v) Lin Vp(v)
• Pass Lout,p (v) to GPU for rendering

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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer
• Dynamic Transfer Vectors
• An Efficient Hemispherical Rasterizer

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Visibility Rasterization

• The domain of the visibility mask is a regular
  grid inside the unit disk
• Domain of the visibility function Vp(v) is the
  unit hemisphere just drop the z coordinate to
  get to domain of visibility mask
• Compared to single plane sampling
• This reparameterization perfectly importance
  samples the hemisphere according to cosine
  distribution (Nussel analog)
• Occluders near horizon arent missed
• Compared to hemicube sampling
• Only requires 1 pass (vs. 5)
• No depth sorting required (visibility function
  is binary function)

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Now make it efficient!

• Whats the image of a blocker triangle in the
  visibility mask?
• Define 3 planes for each triangle
• Formed by v and each edge of the triangle

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Pixel inside triangle test

• Pixel belongs to the image of the triangle if
  point on the hemisphere that corresponds to that
  pixel is above all 3 planes defined by the edges

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Use Lookup Tables

• Precompute set of bitmasks for a discrete set of
  planes
• An edge normal from the set defines a particular
  bitmask, stored in the lookup table
• Triangle mask 3 edge bitmasks ANDed together
• Visibility mask Vp for point p by ORing all
  blocker triangle images together

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Indexing the Lookup Table

• Cubemap the normal vectors defining the edge
  planes
• 6 x 128 x 128 cubemap
• For 32 x 32 bitmasks, results in 12 Mb of data
• This resolution provides visually accurate
  results with good efficiency

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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer
• Dynamic Transfer Vectors
• An Efficient Hemispherical Rasterizer
• Results and Optimizations

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Demo (and probably a better explanation)
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Reduce of triangles to be rasterized

• Mesh Hierarchy
• Use a 2-level mesh hierarchy
• Assume smooth lighting conditions
• Far-away blocker triangles cast soft shadows
• Use the low-res mesh
• Close-by blocker triangles (one or two-ring) cast
  sharp shadows
• Use the high-res mesh

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Reduce of triangles to be rasterized

• Hierarchical Culling
• Group triangles together
• Update their bounding box during animation
• Test bounding box against tangent plane
• Only rasterize those groups above the tangent
  plane

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Reduce of triangles to be rasterized

• Potentially Visible Sets
• If some prior information of the animation is
  known, construct PVS for each vertex
• Can be static or time-dependent
• Example
• Bottom of feet will never be visible to vertices
  on the top of the head
• If you dont buy that, please give a demo right
  here!

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Results

• Tests performed on pretty high-end system Dual
  3Ghz P4 Xeon

To be rasterized for visibility mask
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Overview

• Self Shadowing Previous Work
• Precomputed Radiance Transfer
• Dynamic Transfer Vectors
• An Efficient Hemispherical Rasterizer
• Results and Optimizations
• Properties and Issues

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Properties and Issues

• Scalability
• Complexity is proportional to
• Avg. Triangles vertices of the object
• Assuming that the low-res mesh remains fixed, the
  cost of increasing the resolution of the high-res
  mesh is linear.
• This means you can compute lighting for extra
  vertices at linear cost
• But inter-object shadows increase complexity
  quadratically
• Project approximation of other shadow casting
  objects onto the environment maps of the
  receiving objects

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Properties and Issues

• Per-vertex Sampling
• Shadow artifacts
• Creep due to undersampling
• This problem is inherent to per vertex sampling
  and common to other techniques (such as
  per-vertex Monte-Carlo integration, radiosity, )
• Sacrifice quality for speed

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Properties and Issues

• Accuracy of the local geometry
• 2-level hierarchical culling introduces shadow
  artifacts
• 3D distance between triangles small
• Distance along surface is larger than 2-ring
• They propose a more complex spatial data
  structure, but dont specify
• Does anyone have any suggestions?

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Properties and Issues

• They compare to a GPU hemispherical rasterizer
• We need to subdivide the triangles to render
  curved triangle edges in the hemispherical
  projection
• 16 times as many triangles need to be rasterized
  much slower (only 0.76 FPS)
• You dont want to do it anyway, because the GPU
  is busy rendering background geometry anyway,
  while the CPU is computes self-shadowing

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Conclusion

• Main contributions
• Dynamic transfer vectors (based on static
  transfer vectors)
• The SH basis transform gives visually accurate
  results for fairly low-res visibility masks which
  allows efficient integration
• Efficient hemispherical rasterizer

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Conclusion

• Render dynamic objects with softself-shadows in
  time-varying lighting environments
• No prior information on the animation is needed,
  although such information can be used for
  optimization

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References

• Hemispherical Rasterization for Self-Shadowing of
  Dynamic Objects 
• Jan Kautz, J. Lehtinen, T. Aila
• Proceedings of the Eurographics Symposium on
  Rendering 2004
• Precomputed Radiance Transfer for Real-Time
  Rendering in Dynamic, Low-Frequency Lighting
  Environments
• Peter-Pike Sloan, Jan Kautz, and John Snyder
  SIGGRAPH 2002,July, 2002

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Thanks! Questions?