Splatting

1
Splatting

• Josh Anon
• Advanced Graphics 1/29/02

2
Types of Rendering Algorithms

• Backward mapping
• Image plane mapped into data
• Ray casting
• Forward mapping
• Map data onto image plane
• Accumulate image front-back, back-front
• Image complete when every data point displayed or
  pixel full

3
Backward Mapping Problems

• Basic parallel solns require volume be duplicated
  at each node
• Input values often not right on ray, so
  interpolated
• Requires anti-aliasing to correct for tri-linear
  interpolation

4
Goal of Splatting

• Avoid artifacts from convential volume rendering
• Simplify computation
• Parallelize, lookup tables, etc.
• Be fast!

5
Enter Forward Mapping Algo

• Treat each data point in isolation so avoid
  replicating volume
• Since working in 2D with a footprint function,
  dont have to interpolate
• Footprint area of pixels a voxel affects
• Uses tables as often as possible

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Basic Algorithm

• Input mapped to screen space
• Density, gradient strength/direction, and screen
  coordinates
• Packet then shaded
• Splatted
• Composited

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Screen mapping

• DDA

Dx Dy Dz
dx/di dx/dj dx/dk dy/di dy/dj dy/dk dz/di dz/dj d
z/dk
Di Dj Dk

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Shading

• 4 tables
• Emitted color
• Reflected color
• Opacity
• Table to modulate opacity
• Also use gradient vector for each sample
  (generated during pre-processing)

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Calculations

• Iemit Tableemitindexemit
• Idiff Tablereflindexrefl dot(l, g)
• Ispec Tablereflindexrefl dot(h, g)n
• L light vector, g gradient, h vector half-way
  between eye and light, n specular power
• Ifin Iemit Idiff Ispec

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Opacity

• Afin Tableopacindexopac Tablemodindexmod
• Colors in table are opaque color, so color
  attenuated by opacity during combining phase

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Reconstruction

• Backward mapping associates pixel w/ n samples
• Forward mapping associates a sample w/ n pixels
• Reconstruct image-space voxels by using a filter

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Reconstruction

• Vol reconstruction eqn
• i ranges over input samples in kernel centered _at_
  (x,y,z)
• Effect _at_ point(x,y,z) from sample i is

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Combining Samples

• Old integrate brightness along view direction
• New footprint function that lets you compute the
  weight of a pixel affected by a sample

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Using Tables

• Footprint independent spatial position, so store
  in a table
• When rendering, multiple RGBA by table value and
  add to buffer
• Splatting process of table lookup, weighting,
  and combining

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Sample front-back traversal

• Io Ic ((1-Ac) (InAn))
• Ao Ac ((1-Ac) An)
• I intensity, A opacity, o output, c whats in
  image buffer, n point

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Results

• 96x128x113 CT scan rendered at full res in lt 3
  minutes (low-res at 3 seconds)
• (Except for a Sun-3/60M w/ 8MB memory)
• Certainly faster on todays machines, esp if
  using hardware

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Time to draw in sec (clockwise, upper left)
3,9,65,165