1:303:15 Advanced Features

1
130-315 Advanced Features

• 130-200 Volume Rendering (Shirley)
• 200-230 Massive Models (Slusallek)
• 230-300 Hardware Support
• GPU ray tracing demo (Foley)
• Ray processing unit (RPU) (Slusallek)
• Future challenges (Mark)
• 315-330 Break

2
Overview

• Isosurfacing done implicitly at every pixel
• Care is needed for data layout, but otherwise is
  brute force
• Direct volume rendering harder but possible

3
Isosurfacing for Analytic Functions

• f(x,y,z)0
• ray tracing via root finding (e.g. Kalra and Barr
  89)
• explicit polygonalization (e.g. Stander and Hart
  97)

4
Trilinear Cells are Easier
5
Isosurfacing for a Trilinear Cell

• Marching Cubes
• Lorensen and Cline (87)
• Wyvill and Wyvill (86)

6
Why Not Always Use Marching Cubes?

• Marching cubes can generate millions of polygons
• Reduce by decimation (e.g. Shekhar et. al 96)
• Reduce by culling (e.g. Livnat and Hansen 98)

7
Isosurfacing for a Trilinear Cell
8
Isosurfacing for a Piecewise Linear Cell
marching cubes
ray tracing
9
Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Effects of Direct Cubic Solution
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Isosurfacing for a grid of cells
ray
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(No Transcript)
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Previous Ray Tracing for Isosurfaces

• Marschner and Lobb (94)
• Lin and Ching (96)

21
Feature Comparison

• Ray Tracing
• Implicit geometry
• Software shading

• Marching Cubes
• Explicit geometry
• Hardware shading

22
Shadows
without
with
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Transparency
24
3D textures
25
Optimizations

• Parallelism
• Hierarchical data representation
• Data layout for better locality

26
Hierarchical Data Representation

• Skip over cells which do not contain an
  isosurface - Wilhelms and van Gelder (90)
• Keep macrocells which contain the min/max
  values for contained cells

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Two Level Representation
ray
ray
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Two Level Representation
ray
ray
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Two Level Representation
ray
ray
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Two Level Representation
ray
ray
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Two Level Representation
ray
ray
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Two Level Representation
ray
ray
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Two Level Representation
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Two Level Representation
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Number of Hierarchy Levels

• Traversal from cell to cell is cheaper than
  moving up and down levels
• Would like to skip large empty regions
• We use 3 or 4 levels in practice

36
Data Layout (Bricking)

• Optimizing for memory locality
• Two levels (bricks and metabricks)
• Common trick (e.g. Cox and Ellsworth 97)

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Brick
Metabrick
1 2 3 10 11 12 4 5 6 13 14 15 7 8 9 16
17 18
144...
153...
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Data Layout (Bricking)

• Brick sizes (Cache line and page sized cubes)
• 16 bit data
• 32 bit data

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Combining Hierarchy and Bricking

• Requirements of hierarchy are different than
  the brick sizes
• Traversal at finest level of hierarchy can cross
  brick boundaries
• Must compute indices into bricked array

40
Indexing

• Consider 6x6x6 bricks of 3x3x3 bricks
• index (x/3/6)666333nynz
  (y/3/6)666333nz (z/3/6)666333
  (x/36)66333 (y/36)6333
  (z/36)333 (x3)33 (y3)3 (z3)
• Very expensive
• Integer division and modulus

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What about that function?

• index (x/3/6)666333nynz
  (y/3/6)666333nz (z/3/6)666333
  (x/36)66333 (y/36)6333
  (z/36)333 (x3)33 (y3)3 (z3)
• index fx(x) fy(y) fz(z)

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Optimization Results
.
0
6
.
8
1
.
5
B
o
n
e


f
r
o
m

f
e
e
t

5
0
.
9
1
1
.
3
1
.
2
Relative times
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Where time is spent
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Unstructured data
Mike Parker
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• 128 CPU altix (1.3GHz Itanium 2),
• 1M pixels
• 10Gb model, 170 timesteps 82x82x332 plus 1.1
  million particles 15-20 fps

James Bigler
46
(No Transcript)
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Questions

• What data structure is best for uniform grids?
• Faster Isosurface Ray Tracing using Implicit
  KD-Trees, Wald, Friedrich, Marmitt, Slusallek and
  Seidel, IEEE TVCG
• What is best for unstructured grids?
• Faster direct volume rendering?
• Custom hardware? (SUNY SB)

48

• Thanks to
• Steve Parker
• Mike Parker
• James Bigler
• SGI