Ray Space Factorization for From-Region Visibility

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Ray Space Factorization for From-Region Visibility

• Tommer Leyvand
• Olga Sorkine
• Daniel Cohen-Or
• Tel-Aviv University, Israel

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From-Region Visibility
Problem of identifying which parts are visible
from a region (viewcell)
Visibility Set Valid from within the viewcell
Entire Model
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Dimensionality ofFrom-Region Visibility

• From-Region visibility is 4D
• A ray exists the viewcell through a 2D surface
  and enters the target region through a 2D surface

viewcell
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From-Region Occluder Fusion

• Wonka et.al. EGRW 2000
• Koltun et.al. EGRW 2000
• Schaufler et.al. SIGGRAPH 2000
• Durand et.al. SIGGRAPH 2000

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A Ray Space Technique
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Primary Space
Ray Parameter Space
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A Ray Space Technique(Cont.)

• Appropriate for 2D from-region visibility
• Exact (up to discretization)
• Can be realized with common graphics hardware
• Can be used to accelerate 2.5D from-region
  visibility
• Koltun et.al. EGRW 2001
• Bittner et.al. PG2001

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Our Factorization
We factor the 4D visibility problem into
horizontal and vertical components
Ray Space Approach
Umbra Merging Approach
Horizontal direction
Vertical direction
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Lumigraph/Light Field
A 2D grid of 2D images
Light field
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Vertical Slice
The visibility is solved within each vertical
slice
A vertical slice
Within a vertical slice
Horizontal direction
Vertical direction
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Our Main Contribution

• A factorization that
• Exploits vertical coherence
• Maps to the graphics card

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Algorithm Overview

• Per object
• Parameterization of vertical slices
• Umbra encoding

Vertical umbra
footprint
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Algorithm Overview(Cont.)

• Parameterization of vertical slices
• Umbra encoding and visibility test
• Merging umbrae

Vertical umbra
footprint
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Horizontal Parameterization

• Produces a 2D polygonal footprint of scene
  objects
• Project scene objects onto the ground plane
• Maps planes slicing both the viewcell and some
  object into points in parameter space

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Building the footprint

• Our parameterization maps a 3D triangle into
  several 2D polygons
• Each point in the resulting footprint represents
  a plane that slices both the viewcell and the
  segment

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Umbra Encoding
Encode directional umbra using supporting and
separating lines
Vertical slice P(s,t)
v
directional umbra
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(s,t)
Intersection of some scene object with slice
viewcell
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Parameter Space
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Global Occlusion Map

• Stores the directional accumulated umbra for all
  directions
• Encoded by sets of supporting and separating
  angles
• Each set encodes a single umbra
• Traverse the scene top-down front-to-back, and
• Bounding boxes are tested for visibility
• Objects in visible leafs augment the map

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Testing Visibility

• Within a slice
• Test occlusion by comparing supporting angles
• Performed in parallel on all (s,t) slices

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Merging Umbrae

• Increase the current accumulated umbra in the
  occlusion map
• Augment if directional umbra intersects

viewcell
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Merging Umbrae

• Increase the current accumulated umbra in the
  occlusion map
• Augment if directional umbra intersects
• Otherwise create another umbra entry
• In case there are too many entries, discard

viewcell
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Implementation

• Cg implementation
• 4x32bit floating point PBuffers
• Used to store a single set global occlusion map
• Fragment programs for testing occlusion and
  merging umbra
• Calculates less conservative values
• Previous generation hardware implementation
• Using occlusion query and OpenGL

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Results
Procedural Urban Model
Box Field Model
Vienna 2000 Model
3D-e
2.5De
2.5D
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Video
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Thanks

• Israel Science Foundation
• Israeli Ministry of Science
• Reviewers

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The End
Before
After
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Procedural City

• XML configured city generation engine
• Simple building blocks
• 3D boxes and pyramids
• Rotation and scaling operators
• Texture groups
• Instantiation parameters within user defined
  random limits
• Exports city to VRML 2.0

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Conservativeness
Piecewise constant approximation of the rational
umbra function at each slice
Each vertical plane is not infinitesimal - it has
some width