Packing Square Tiles Packing Square Tiles into One Textureinto One Texture

Eurographics 2004Eurographics 2004

Philippe Decaudin Fabrice NeyretPhilippe Decaudin Fabrice Neyret GRAVIR/IMAG-INRIA, Grenoble, FranceGRAVIR/IMAG-INRIA, Grenoble, France

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2 Packing Square Tiles into One Texture EG ’04

IntroductionIntroduction

AimAim Pack square texture tiles of the same size into 1 texturePack square texture tiles of the same size into 1 texture Reduce space lossReduce space loss

Packing is importantPacking is important Graphic context switching Graphic context switching performance penalty performance penalty Easier to manage one texture instead of a setEasier to manage one texture instead of a set

10tiles

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Introduction (Introduction (contcont.).)

Why packing Why packing NN tiles with no space loss is difficult ? tiles with no space loss is difficult ? Texture size is constrainedTexture size is constrained

ww // h = 2h = 2 ii w and h are bounded (w and h are bounded (<<

4096)4096)

For others For others NN, efficient schemes are not obvious…, efficient schemes are not obvious…

Trivial packing with no space loss: Trivial packing with no space loss: NN == 22nn and and NN == nn22

N = 20 21 22 23 24 … N = 22 32 …

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Packing an arbitrary number of tilesPacking an arbitrary number of tiles

Space loss can be substantialSpace loss can be substantial E.g.,E.g., packing 5 tiles packing 5 tiles

10 tiles 17 tiles

Best known packingsBest known packings [Jennings’95, Fridman’98][Jennings’95, Fridman’98] Complex schemesComplex schemes And still space lostAnd still space lost

37% unused 55% unused

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Our packing schemeOur packing scheme

We propose a packing scheme with no loss for many We propose a packing scheme with no loss for many NN Ranges of uncovered numbers are smallRanges of uncovered numbers are small

loss greatly reduced for other values of loss greatly reduced for other values of NN

The trick: texture space has special propertiesThe trick: texture space has special properties Torus topologyTorus topology texture addresses wrap texture addresses wrap

((GL_REPEATGL_REPEAT or or D3DADDRESS_WRAPD3DADDRESS_WRAP))

Can be rotatedCan be rotated

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Using these properties, 2 tiles can be packed into 1 square textureUsing these properties, 2 tiles can be packed into 1 square texture

Basic exampleBasic example

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2, 2, 22nn and and nn22 packing schemes packing schemes

22nn scheme scheme nn22 scheme scheme 2 scheme2 scheme

2 4 8

Packing schemes can be combinedPacking schemes can be combined E.g.,E.g.,

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GeneralizationGeneralization

We can define We can define ((nn22 + + kk22) …) …

First, let consider the packing of 5 tiles (2First, let consider the packing of 5 tiles (222 ++ 1122))

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here,n=3k=2

n

k

nk

The The ((nn22 + + kk22) packing scheme, with ) packing scheme, with kk nn

nn nn square subdivided by 2 sets of parallel slanted lines square subdivided by 2 sets of parallel slanted lines

13 tiles(n2+k2)

This construction results in This construction results in nn22 ++ kk22 square tiles square tiles Proof is in the paperProof is in the paper

k=1 10 tiles

k=0 9 tiles

k=3 18 tiles

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Reachable numbersReachable numbers

((nn22 + + kk22) schemes provide a dense set of reachable ) schemes provide a dense set of reachable NN with no loss with no loss

By combining these schemes, any tiles number By combining these schemes, any tiles number

of the form can be reached (of the form can be reached (kki i < < nnii , , ppii positive int.) positive int.) i

pii

ikn )( 22

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ConclusionConclusion

We have shown that We have shown that NN tiles can be packed into 1 texture tiles can be packed into 1 texture

with no space loss for all with no space loss for all NN of the form of the form i

pii

ikn )( 22

Allows many more possible schemes for no loss packing than Allows many more possible schemes for no loss packing than the common schemesthe common schemes

Could be extended to 3D textures for cubic tilesCould be extended to 3D textures for cubic tiles

space saved for volume data could be consequentialspace saved for volume data could be consequential[Kraus-Ertl’02, Lefebvre-Neyret’03][Kraus-Ertl’02, Lefebvre-Neyret’03]

For an arbitrary For an arbitrary NN, it provides a packing with little loss, it provides a packing with little loss

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Thanks…Thanks…

http://www-imagis.imag.fr/Publications/2004/DN04bhttp://www-imagis.imag.fr/Publications/2004/DN04b

Questions ?

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Reachable numbers (Reachable numbers (cont.cont.))

Similarities with prime factor decomposition, with some gaps.Similarities with prime factor decomposition, with some gaps.

Some primes missing: 3, 7, 11, 19, 23,…Some primes missing: 3, 7, 11, 19, 23,…