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Ray Space Factorization for From-Region Visibility. Tommer Leyvand Olga Sorkine Daniel Cohen-Or Tel-Aviv University, Israel. 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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Ray Space Factorization for From-Region Visibility


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ray space factorization for from region visibility

Ray Space Factorization for From-Region Visibility

Tommer Leyvand

Olga Sorkine

Daniel Cohen-Or

Tel-Aviv University, Israel

slide2

From-Region Visibility

Problem of identifying which parts are visible from a region (viewcell)

Visibility Set

Valid from within the viewcell

Entire Model

slide3

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

slide4

From-Region Occluder Fusion

  • Wonka et.al. EGRW 2000
  • Koltun et.al. EGRW 2000
  • Schaufler et.al. SIGGRAPH 2000
  • Durand et.al. SIGGRAPH 2000
slide5

A Ray Space Technique

t=0

1/4

t

s=0

1/4

3/4

1/2

3/4

1/2

s

0

1/2

3/4

1

1/4

Primary Space

Ray Parameter Space

slide6

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
slide7

Our Factorization

We factor the 4D visibility problem into horizontal and vertical components

Ray Space Approach

Umbra Merging Approach

Horizontal direction

Vertical direction

slide8

v

u

Lumigraph/Light Field

A 2D grid of 2D images

Light field

slide9

Vertical Slice

The visibility is solved within each vertical slice

A vertical slice

Within a vertical slice

Horizontal direction

Vertical direction

slide10

Our Main Contribution

A factorization that

  • Exploits vertical coherence
  • Maps to the graphics card
slide11

Vertical slice

v

R

t

R

t

s

s

Parameter Space

Horizontal direction

Algorithm Overview

Per object:

  • Parameterization of vertical slices
  • Umbra encoding

Vertical umbra

footprint

slide12

Vertical direction

v

R

t

R

t

s

Horizontal direction

s

Parameter Space

Algorithm Overview(Cont.)

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

Vertical umbra

footprint

slide13

t

s

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

t=0

1/4

s=0

1/4

3/4

1/2

3/4

1/2

slide14

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

t

1/4

t=0

q

s=0

1/4

3/4

1/2

s

3/4

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0

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slide15

Umbra Encoding

Encode directional umbra using

supporting and separating lines

Vertical slice P(s,t)

v

directional

umbra

t

(s,t)

Intersection of

some scene object

with slice

viewcell

s

Parameter Space

slide16

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
slide17

Vertical slice P(s,t)

Directional

accumulated

umbra

viewcell

Testing Visibility

Within a slice:

  • Test occlusion by comparing supporting angles

Performed in parallel on all (s,t) slices

slide18

Merging Umbrae

Increase the current accumulated umbra in the occlusion map

  • Augment if directional umbra intersects

viewcell

slide19

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

slide20

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
slide21

Results

Procedural Urban Model

Box Field Model

Vienna 2000 Model

3D-ε

2.5D+ε

2.5D

slide23

Thanks

  • Israel Science Foundation
  • Israeli Ministry of Science
  • Reviewers
slide24

The End

Before

After

slide25

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
slide26

viewcell

outer

square

Conservativeness

Piecewise constant approximation

of the rational umbra function at each slice

Each vertical plane is not infinitesimal - it has some width