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Computer Graphics & Visualization

Lecture 3Anti-Aliasing

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Overview

Antialiasing Techniques

Supersampling

Areasampling

- unweighted

- weighted

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Antialiasing

Aliasing, jagged edges or staircasingcan be reduced by:

Higherscreenresolution

- Needahugeframebuffer

Antialiasingtechniques

- Varypixelintensitiesalongboundariestosmooththeedge.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Antialiasing Techniques

Computeintensitiesatsub-pixelgridpositionsandcombinetheresultstoobtainthepixelintensity.

Findpixelintensitybycalculatingtheareasofoverlapofeachpixelwithintheobjectstobedisplayed.

Pixelintensityisproportionaltotheamountofareacovered.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Antialiasing Techniques

Defineaweightingfunctionthatdeterminestheinfluenceontheintensityofthepixel.

Linesaresmoothedbymovingtheelectronbeamtoacloserapproximateofthemathematicalline.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Supersampling(zero line width)

Example:astraightlineonagrayscaledisplay

Divideeachpixelintosub-pixels.

Thenumberofintensitiesarethemaxnumberofsub-pixelsselectedonthelinesegmentwithinapixel.

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PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Supersamling(finite line width)

Theintensitylevelforeachpixelis

proportionaltothenumberofsub-pixelsinsidethepolygonrepresentingthelinearea.

Lineintensityisdistributedovermorepixels.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Supersamling(finite line width)

Disadvantages

Morecalculationsinvolvedtoidentifyinteriorpixels.

Positioningofthelinedependsontheslopeoftheline.

- 45 - linecenteredinpolygon

- Horizontalorverticallineline pathonpolygonboundary

- |m|1linepathclosertoupperboundary

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Unweigted Area Sampling

Theintensityofapixeldecreasesasthedistancebetweenthepixelcentreandtheedgeincreases.

Theprimitivemustintersectthepixeltohave

someeffect. Equalareascontributeequallytothepixelintensity.

Intensityofapixelisproportionaltoitsareacoveredbytheline

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Weighted Area Sampling

Equalareascancontributetounequalintensity.

(Wechangeproperty3)

Circularpixelgeometry.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Weighting (Filter) Function

DeterminestheinfluenceontheintensityofapixelofagivensmallareadA ofaprimitive.

Thisfunctionisconstantforunweightedanddecreaseswithincreasingdistanceforweighted.

Totalintensityistheintegraloftheweighting(filter)functionovertheareaofoverlap.

Wsisthevolume(alwaysbetween0and1)

I = Imax

Ws

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Unweighted Area Sampling

Box Filter:

Wsisawedgeofthebox.

Heightoftheboxnormalizesto1(boxvolume=1)

Athicklinecoveringtheentirepixelhasintensity:

I = Imax

1 = Imax

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PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Weighted Area Sampling

Cone Filter: Acircularcone,wherethebaseistheradiusoftheunitdistanceoftheintegergrid.

Rotationalsymmetry.

Lineardecreaseofthefunctionwithradialdistance.

Normalizedto1(volumeunderentireconeis1)

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Filter Functions

Optimalfiltersarecomputationallymore

expensive. Conefiltersareaveryreasonablecompromisebetweencostandquality.

PedherJohanssonDepartmentofComputingScience,UmeUniversityComputer Graphics & Visualization

Anti-Aliasing

Pixel Phasing:

Pixelpositionscanbeshiftedbyafractionofapixeldiameter(1/4,1/2,or3/4)toplotpointsclosertothemathematicalline.

Line Intensity Differences:

Thediagonallineappearslessbrightthanthehorizontal.(Thediagonallineislongerthanthehorizontallinebyafactorofsqrt(2)).

- Totalintensityisproportionaltotheirlength.