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Easy going vector

graphics as textures onthe GPU

Gustavo Patow

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Like playing games?

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Typical problem withtextures

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However, vector graphics

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!ain i"ea

If vector graphics

preserve quality overresolution, why don’t weuse them?

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#hat to expect

Bitmaps have constant evaluation cost

Vector graphics (eps, pdf, …)

have a clear dependency over the number of objects

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#here?

Point-wise evaluation in thefragment shaders, lie

regular te!tures"

(Problem# power $%& 'P)

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How to evaluate

o point-in-polygon is betterthan

*(log(n)) n + number ofedges

If we have m polygons, wedhave

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Evaluation solution $%&

Image  regular grid ofcells

≅ hash for the vectordrawing"

te!el

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Evaluation solution $%%&

•or each te!el we should build aneasy evaluation structure

•./P trees seem easy enough•*verlapping polygons

• $hen the evaluation of the upper poly

gives“outside

”, join with ne!t poly• $hen evaluation gives inside, return

the polygon’s color

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out

colorout

'ata (tructure

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color

color   Back-groun

d

Linking

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) couple o* optimi+ations

If a top polygon fully covers ate!el

• /tore a color instead of apointer

If a deeper polygon covers thefull te!el

• store its color instead of a

subtree

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eal time evaluation

Pi!el/hader (0oat1 te!coord) # color0oat2 colour + %ead 34/3 te!ture with te!coord

if  (is a pointer(colour))

0oat pos + compute pos from colour

while (pos 5 676)0oat inde! + -pos 8 19

0oat2 (segment, dest) + %ead bspodes te!ture withInde!

0oat sign + sign*fPoint$%&:ine( segment7!,

segment7y,  segment7;, segment7w,

  te!coord7!, te!coord7y)9

pos + (sign < 6)? dest7!# dest7y9

colour + mae colour from pos

return colour9

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!agni*ication

/imply super-sample the te!elarea"

• &ae several samples on ate!ture area de=ned by theprojected are of the currentpi!el (++current hardwareimplementations)

• If samples can be grouped, tryto re-use evaluations

• &his was not im lemented in our

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!ini*ication

4t a distance from the observerwe switch to a regular raster

texture with mip-mappingenabled

• &his distance can be de=ned

absolutely or depending on thepi!el projected area

%esults are e>cientl anti-

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'iscussion

*ur algorithm is pi!el- bound#most worload on the fragment

shaders• :arger si;e on screen +< moreevaluations

'omputational cost*(p ln(n))

n number of primitives

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%n*luence o* the gri" si+e

• 3ash resolution only in0uences the amountof detail contained within each te!el

• :arger resolutions correspond to less detail

@arA1B• .ounded from below

• C7g7, at cells where polygon boundaries overlap,we need to store the intersection itself

• Increasing grid resolution +< fewerevaluations at each sample +< more speed"

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Possible improvement

•/ort the root elements in theodes &e!ture following a Dorton

line @arA1B•'urrently, cells are sored in rasterorder

•%egular te!ture access patternsshow that Dorton encoding bene=tscoalesced memory access

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!ore -uture #ork

4dd gradient evaluations anddiEusion curves, much in theline of /un et al7 /FGHA1B

• &his implies solving comple!

computations +

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Easy going vector graphics as textures on

the GPU

Questions?

Thanks.

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