1 rendering geometry with relief textures l.baboud x.décoret artis-gravir/imag-inria

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Rendering Geometry withRelief Textures

L.Baboud X.DécoretL.Baboud X.DécoretARTIS-GRAVIR/IMAG-INRIAARTIS-GRAVIR/IMAG-INRIA

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Height-field representationHeight-field representation

What can we represent?What can we represent? How to render it?How to render it?

Fast ?Fast ? Exact?Exact?

Previous workPrevious work Our contributionsOur contributions

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Height-fieldHeight-field

Function from [0,1]2 to [0,1] Represents a surface Sampled in a texture

Memory/GPU efficient

(a) Height texture (b) Reconstructed surface

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Height-fieldHeight-field

Function from [0,1]2 to [0,1] Represents a surface Sampled in a texture

Memory/GPU efficient

Theory: How do you reconstruct?

Practice: Which interpolation for texture lookups?

Refer to the paper for details

(a) nearest

(b) linear

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How to render?How to render?

PolygonalizePolygonalize Simple & naturalSimple & natural Costly, not output sensitiveCostly, not output sensitive Aliasing -> LODAliasing -> LOD

Small coverage

Large coverage

What if the object is not the “main” one? Bump Small objects

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How to render?How to render?

PolygonalizePolygonalize Simple & naturalSimple & natural Costly, not output sensitiveCostly, not output sensitive Aliasing -> LODAliasing -> LOD

Ray-tracingRay-tracing Slow? Feasible on GPU!Slow? Feasible on GPU! Output sensitiveOutput sensitive

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Ray-tracingRay-tracing

Existing solution : VDM Existing solution : VDM [Wang 2003][Wang 2003]

Sampling in all viewing directionsSampling in all viewing directions Memory costly Memory costly (4 Mb compressed for 128x128)(4 Mb compressed for 128x128)

Use GPU capabilities insteadUse GPU capabilities instead

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Principle (1/2)Principle (1/2)

Top view

2D slice

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Principle (2/2)Principle (2/2)

Comparing heightsComparing heights Along rayAlong ray In the heightfieldIn the heightfield

Until we pass belowUntil we pass below

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Policarpo Policarpo [I3D 05][I3D 05]

How many iterations?

Is it correct?

Binarysearch

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Missed intersection

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Fixed sizesteps

Binarysearch

Better but still potentially false

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Fixed sizesteps

Binarysearch

Amounts to vertical slicing

Size of steps along the ray depends on ray tilt

Missedintersection

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Tatarchuk Tatarchuk [I3D06][I3D06]

Varying size steps (between two bounds) Depending on ray tilt

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Conclusion on existing methodsConclusion on existing methods

Advantages : speed Drawbacks : missed intersections

(at grazing angles)

Use it for bump

Policarpo05 Tatarchuk06

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Being exact, what for?Being exact, what for?

Intellectually rewarding Intellectually rewarding Usability large scale geometryUsability large scale geometry

Terrain, buildings, architectural detailsTerrain, buildings, architectural details Objects (cars, etc.)Objects (cars, etc.)

How many polygons ?

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Being exact, what for?Being exact, what for?

Intellectually rewarding Intellectually rewarding Usability large scale geometryUsability large scale geometry

Terrain, buildings, architectural detailsTerrain, buildings, architectural details Objects (cars, etc.)Objects (cars, etc.)

Only 6 quads !

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Being exact, is it hard?Being exact, is it hard?

Problem with constant stepsProblem with constant steps Can always miss intersectionsCan always miss intersections

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Problem with constant stepsProblem with constant steps Can always miss intersectionsCan always miss intersections Travel slowly above empty spaceTravel slowly above empty space

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Problem with constant stepsProblem with constant steps Can always miss intersectionsCan always miss intersections Travel slowly above empty spaceTravel slowly above empty space

Our contributionsOur contributions Amanatides based approach Amanatides based approach Failsafe approachFailsafe approach

But requires preprocessBut requires preprocess

solves

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Adapted Amanatides traversalAdapted Amanatides traversal

We run along the ray on texel edges

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We run along the ray on texel edges Advantages :

very simple iterations exact intersection

fragment shader main loop

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We run along the ray on texel edges Advantages :

very simple iterations exact intersection

Drawbacks : potentially many iterations texture resolution dependent

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Texture resolution dependentTexture resolution dependent Double resolution Double resolution half speed half speed Ideally should depend on “variations” of Ideally should depend on “variations” of

heightfield, not sampling frequencyheightfield, not sampling frequency Binary search doesn’t have this drawbackBinary search doesn’t have this drawback

Constant number of texture lookupsConstant number of texture lookups

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Analysis of binary searchAnalysis of binary search

At the moment we pass belowAt the moment we pass below At leastAt least one intersection one intersection But potentially severalBut potentially several ?

2D slice

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Analysis of binary searchAnalysis of binary search

At the moment we pass belowAt the moment we pass below At leastAt least one intersection one intersection But potentially severalBut potentially several Ideally : Ideally : at mostat most one intersection one intersection

How can we guarantee this?

Precompute safety radius

2D slice

?

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What is safety radius ?What is safety radius ?

Local informationLocal information

Top view

T

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Which step ?

For any possible viewingray passing above T

Precomputed radius

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Local informationLocal information

Safety radius

Viewing direction

considered texel

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Local informationLocal information In 3D : for each texel :In 3D : for each texel :

Scan every directionScan every direction Keep the minimum radiusKeep the minimum radius

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Failsafe binary searchFailsafe binary search

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Various detailsVarious details

TexturesTextures Can have different resolutionsCan have different resolutions

Normal, color, heightNormal, color, height Can be packed/compressedCan be packed/compressed

Needs recent fragment shaders supporting Needs recent fragment shaders supporting dynamic loopsdynamic loops

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ResultsResults

Fast and exact Height-field regularity dependent Correct interaction with Z-bufferCorrect interaction with Z-buffer Output sensitiveOutput sensitive

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Height-field representationHeight-field representation

What can we represent?What can we represent? How to render it?How to render it?

Fast ?Fast ? Exact?Exact?

Previous workPrevious work Our contributionsOur contributions

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More than bumpMore than bump

Previous methods : small scale bumpPrevious methods : small scale bump Curved surfaces : warping considerationsCurved surfaces : warping considerations

VDM [Wang 03]VDM [Wang 03] [Policarpo05][Policarpo05]

We want to do large scaleWe want to do large scale Problem : limited expressivenessProblem : limited expressiveness

orthogonal height-fieldsorthogonal height-fields

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Expressiveness of heightfieldsExpressiveness of heightfields

Lack of samples on vertical sidesLack of samples on vertical sides

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Projective height-fieldsProjective height-fields

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Similar to “cubist images” Similar to “cubist images” [Hanson 98][Hanson 98]

Projective transforms preserve linesProjective transforms preserve lines Unmodified algorithmUnmodified algorithm

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Wasted fillrateWasted fillrate Many eventually discarded fragmentsMany eventually discarded fragments Easy to solve : clip the bounding boxEasy to solve : clip the bounding box

(a) not clipped (b) clipped

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Multiple height-fieldsMultiple height-fields

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ConclusionConclusion

Remember fast and exact is possible! Efficient representation

Small memory footprint Automatic LOD

Two useful methods (dynamic/static)Two useful methods (dynamic/static)

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FutureFuture

Geometry representable with heightfieldsGeometry representable with heightfields Because we are exactBecause we are exact

Model directly with heightfieldsModel directly with heightfields Photoshop 3D [Mok01]Photoshop 3D [Mok01]

Apply to judicious situationsApply to judicious situations

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FutureFuture

Thank you!Thank you! Questions?Questions?

1 rendering geometry with relief textures l.baboud x.décoret artis-gravir/imag-inria

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