Ray Space Factorization for From-Region VisibilityRay Space Factorization for From-Region Visibility

Tommer LeyvandOlga SorkineDaniel Cohen-Or

Tel-Aviv University, Israel

From-Region VisibilityFrom-Region VisibilityFrom-Region VisibilityFrom-Region Visibility

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

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

Entire Model Visibility SetValid from within the viewcell

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

and enters the target region through a 2D surface

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

and enters the target region through a 2D surface

Dimensionality ofDimensionality ofFrom-Region VisibilityFrom-Region VisibilityDimensionality ofDimensionality ofFrom-Region VisibilityFrom-Region Visibility

viewcell

From-Region Occluder From-Region Occluder FusionFusionFrom-Region Occluder From-Region Occluder FusionFusion

• Wonka et.al. EGRW 2000

• Koltun et.al. EGRW 2000

• Schaufler et.al. SIGGRAPH 2000

• Durand et.al. SIGGRAPH 2000

• Wonka et.al. EGRW 2000

• Koltun et.al. EGRW 2000

• Schaufler et.al. SIGGRAPH 2000

• Durand et.al. SIGGRAPH 2000

A Ray Space TechniqueA Ray Space TechniqueA Ray Space TechniqueA Ray Space Technique

s=0

t=0

1/4

1/2

1/23/4

1/4

3/4

1/4 1/2 3/4 10s

t

Primary Space Ray Parameter Space

A Ray Space TechniqueA Ray Space Technique(Cont.)(Cont.)A Ray Space TechniqueA Ray Space Technique(Cont.)(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

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

Our FactorizationOur FactorizationOur FactorizationOur Factorization

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

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

Horizontal direction Vertical direction

Ray Space ApproachRay Space Approach Umbra Merging ApproachUmbra Merging Approach

Lumigraph/Light FieldLumigraph/Light FieldLumigraph/Light FieldLumigraph/Light Field

A 2D grid of 2D imagesA 2D grid of 2D images

v

u

Light field

Vertical SliceVertical SliceVertical SliceVertical Slice

The visibility is solved within each vertical slice

The visibility is solved within each vertical slice

Horizontal direction Vertical direction

A vertical sliceA vertical slice Within a vertical sliceWithin a vertical slice

Our Main ContributionOur Main ContributionOur Main ContributionOur Main Contribution

A factorization that

•Exploits vertical coherence

•Maps to the graphics card

A factorization that

•Exploits vertical coherence

•Maps to the graphics card

Algorithm OverviewAlgorithm OverviewAlgorithm OverviewAlgorithm Overview

s t

R

R ‘

Horizontal direction

Vertical slice

Per object:• Parameterization of vertical slices

• Umbra encoding

Per object:• Parameterization of vertical slices

• Umbra encoding

v

s

t

Parameter Space

footprint

Vertical umbra

Algorithm OverviewAlgorithm Overview(Cont.)(Cont.)Algorithm OverviewAlgorithm Overview(Cont.)(Cont.)

• Parameterization of vertical slices

• Umbra encoding and visibility test

• Merging umbrae

• Parameterization of vertical slices

• Umbra encoding and visibility test

• Merging umbrae

s t

R

R ‘

Horizontal direction

Vertical directionv

s

t

Parameter Space

footprint

Vertical umbra

Horizontal Horizontal ParameterizationParameterizationHorizontal Horizontal ParameterizationParameterization

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

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

s

ts=0

t=0

1/4

1/2

1/23/4

1/4

3/4

Building the footprintBuilding the footprintBuilding the footprintBuilding 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

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

s=0

1/4

1/4 q

1/23/4

1/4 1/2 3/4 1

)4/1(qt

)2/1(qt

)4/1(qt

)2/1(qt

0s

t

t=0

1/23/4

Umbra EncodingUmbra EncodingUmbra EncodingUmbra Encoding

v

s

t

Encode directional umbra usingsupporting and separating linesEncode directional umbra usingsupporting and separating lines

Parameter Space

viewcell

directi

onal

umbra

Intersection ofsome scene objectwith slice

Vertical slice P(s,t)

(s,t)

top

bottom

top

bottom

topbottom

top bottom

Global Occlusion MapGlobal Occlusion MapGlobal Occlusion MapGlobal 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

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

Testing VisibilityTesting VisibilityTesting VisibilityTesting Visibility

Within a slice:• Test occlusion by

comparing supporting angles

Performed in parallel on all (s,t) slices

Within a slice:• Test occlusion by

comparing supporting angles

Performed in parallel on all (s,t) slices

viewcell

Directionalaccumulatedumbra

Vertical slice P(s,t)

t

b

t

b

Merging UmbraeMerging UmbraeMerging UmbraeMerging Umbrae

Increase the current accumulated umbra in the occlusion map

• Augment if directional umbra intersects

Increase the current accumulated umbra in the occlusion map

• Augment if directional umbra intersects

viewcell

Merging UmbraeMerging UmbraeMerging UmbraeMerging 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

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

ImplementationImplementationImplementationImplementation

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

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

ResultsResultsResultsResultsProcedural Urban Model Box Field Model Vienna 2000 Model

2.5D+ε 3D-ε 2.5D

VideoVideoVideoVideo

ThanksThanksThanksThanks

• Israel Science Foundation

• Israeli Ministry of Science

•Reviewers

• Israel Science Foundation

• Israeli Ministry of Science

•Reviewers

The EndThe EndThe EndThe End

Before After

Procedural CityProcedural CityProcedural CityProcedural 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

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

ConservativenessConservativenessConservativenessConservativeness

viewcell

outersquare

Piecewise constant approximationof the rational umbra function at each slice

Each vertical plane is not infinitesimal - it has some width