Post on 04-Jul-2020
CS 148: Summer 2016Introduction of Graphics and ImagingZahid Hossain
Textures
http://www.pling.org.uk/cs/cgv.html
TextureMapping§ Atechniqueforspecifyingvariationsinsurfacereflectancepropertiesofan
object§ Storethereflectanceasanimageand“map”itontotheobject§ Thestoredimageiscalledatexturemap
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§ Atexturemapisdefiedinitsown2Dcoordinatesystem,parameterizedby(u,v)
§ Establishacorrespondencebyassigning(u,v)coordinatestotrianglevertices
TextureCorrespondence
(0,0) (1,0)
(0,1) (1,1)
CS 148: Introduction to Computer Graphics and Imaging (Summer 2016) – Zahid Hossain 3
OpenGLTexturingSnippet
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§ Then,foreachpixelinsideatriangle,calculatethepixel’s(u,v)texturecoordinatesusingbarycentric interpolationofthetrianglevertices’texturecoordinates
TextureCoordinates
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PixelColor§ Giventhepixel’s(u,v)texturecoordinates,useinterpolationinthetexture
maptofindthepixel’scolor
??
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PixelColor:NearestNeighbor
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PixelColor:BilinearInterpolation
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LinearlyInterpolate
PixelColor:BilinearInterpolation
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AnotherLinearlyIn
terpolate
NearestNeighborVsBilinear
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NearestNeighborVsBilinear
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More on this when we discuss “Sampling”
ScreenSpacevs.WorldSpace§ Triangleschangeshapenonlinearlyviaperspectivetransformation,
leadingtodifferentbarycentricweightsbeforeandaftertheperspectivetransformation
§ Interpolatinginscreenspaceresultsintexturedistortion§ Interpolatinginworldspacerequiresprojectingallpixellocations
backwardsfromscreenspacetoworldspace,whichisexpensive
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TextureDistortion
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p’0
p’1
p0
p1𝑠 ≠ 0.5
𝑡 = 0.5
𝑡: Screen-spaceparameter𝑠:World-spaceparameter
TextureDistortion
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p’0
p’1
p0
p1𝑡 ≠ 0.5
𝑠 = 0.5
𝑠: Screen-spaceparameter𝑡:World-spaceparameter
Screen-space and World-space parameters don’t match !
TextureDistortion§ Uniformincrementsalongtheedgeinworldspacedonotcorrespondtouniformincrements
alongtheedgeinscreenspace§ Barycentric interpolation (whichislinear)doesnotaccountforthisnonlinearity
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MeshRefinement§ Refinementofthetrianglemeshimprovestheresult§ Anonlinearfunctioncanbeapproximatedasa
piecewiselinearfunctioniftheintervalsaresmallenough
§ Howeversomeerrorsarestillobvious,especiallyatT-junctionswherelevels-of-refinementchange
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Subdivide
Tjunction
MeshRefinement
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Does not work !
PerspectiveCorrectInterpolation
§ Findtherelationshipbetweenthebarycentricweightsinscreenspaceandthoseinworldspace
§ Usethisrelationshiptocomputetheworldspacebarycentric weightsfromthescreenspacebarycentric weights
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PerspectiveCorrectInterpolation
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Twopoints inworldspace
PerspectiveCorrectInterpolation
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Twopoints inworldspace
Interpolation inworldspace
PerspectiveCorrectInterpolation
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Twopoints inworldspace
Interpolation inworldspace
Projecttheinterpolatedpointonthescreen
PerspectiveCorrectInterpolation
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Twopoints inworldspace
Interpolation inworldspace
Projecttheinterpolatedpointonthescreen
PerspectiveCorrectInterpolation
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Interpolationofthesametwopoints inscreenspace(afterprojection)
PerspectiveCorrectInterpolation
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Interpolationofthesametwopoints inscreenspace(afterprojection)
Screenspacepointandworld-spacepointafterprojectionmustmatch
PerspectiveCorrectInterpolation
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Interpolationofthesametwopoints inscreenspace(afterprojection)
Screenspacepointandworld-spacepointafterprojectionmustmatch
Afteralgebra
PerspectiveCorrectInterpolation
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ScreenSpaceTriangle WorldSpaceTriangle
PerspectiveCorrectInterpolation
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Finally!
PerspectiveCorrectInterpolation
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Finally!
Aliasing
Whatweget Whatwewant
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Aliasing
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LargetextureSmallimage
Source pixels covers many destination pixels
Aliasing
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LargetextureSmallimage
Source pixels covers many destination pixels
MIPMaps§ Multum inParvo:Muchinlittle,manyinsmallplaces
§ Precomputes thetexturemapsatmultiple resolutions, usingaveraging asalowpassfilter
§ Whentexturemapping, choosetheimagesizethatapproximatelygivesa1to1pixeltotexel correspondence
§ Theaveraging“bakes-in”allthenearbypixelsthatotherwisewouldnotbesampledcorrectly
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MIPMaps§ 4neighboringpixelsofthehigherlevelareaveragedtoformasingle
pixelinthelowerlevel
§ Startingatabaseresolution,youcanstoreEVERYcoarserresolutioninpowersof2
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MIPMaps§ 4neighboringpixelsofthehigherlevelareaveragedtoformasingle
pixelinthelowerlevel
§ Startingatabaseresolution,youcanstoreEVERYcoarserresolutioninpowersof2
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MIPMaps
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MIPMaps
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gluBuild2DMipmaps
Φ
y
AssigningTextureCoordinates§ Forcertainsurfaces,the(u,v)texturecoordinatescanbegenerated
procedurally§ Example:Cylinder
§ maptheucoordinatefrom[0,1]to[0,2 π]forΦ§ mapthevcoordinatefrom[0,1]to[0,h]fory§ Thiswrapstheimagearoundthecylinder
§ Formorecomplexsurfaces,(u,v)mustbedefinedpervertexmanuallyorbyusingproxyobjects
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ProxyObjects– Step1• Assigntexturecoordinatestointermediate/proxyobjects:§ Example:Cylinder§ wraptexturearoundtheoutsideofthecylinder§ notthetoporbottom,inordertoavoiddistortingthetexture
§ Example:Cube§ unwrapthecubeandmaptextureovertheunwrappedcube§ thetextureisseamless acrosssomeoftheedges,butnotnecessarily
others
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ProxyObjects– Step2§ Maptexturecoordinatesfromtheintermediate/proxyobjecttothe
finalobject§ Threewaysofmappingaretypicallyused
§ Usetheintermediate/proxyobject’ssurfacenormal§ Usethetargetobject’ssurfacenormal§ Useraysemanatingfromcenteroftargetobject
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CubeMapping
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http://learnopengl.com/#!Advanced-OpenGL/Cubemaps
ProjectiveTexturing
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• TreatlightSourceasa• Renderthescenenormallyfromtheactualcamera
http://www.nvidia.com/object/Projective_Texture_Mapping.htmlSegal et.al.SIGGRAPH’92
ProjectiveTexturing• AssignTextureCoordinates(s,t,r)toposition(x,y,z)
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ProjectiveTexturing• AssignTextureCoordinates(s,t,r)toposition(x,y,z)
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ProjectiveTexturing• AssignTextureCoordinates(s,t,r)toposition(x,y,z)
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ProjectiveTexturing• AssignTextureCoordinates(s,t,r)toposition(x,y,z)
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So much work just to say (s,t,r) = (x,y,z)Much easily done in newer OpenGL
ProjectiveTexturing
• UseasimilarView(fromthelight’spointofview)andProjectionmatrixtotransformtexturecoordinatestoNDC(-1,1)
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ProjectiveTexturing
• MapNDC(-1,1)toTextureCoordinatespace(0-1)• ScaleandaddBias
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ProjectiveTexturing
• MapNDC(-1,1)toTextureCoordinatespace(0-1)• ScaleandaddBias
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Finaltexturecoordinatesafterperspective-correctinterpolation of
ProjectiveTexturing
• MapNDC(-1,1)toTextureCoordinatespace(0-1)• ScaleandaddBias
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Finaltexturecoordinatesafterperspective-correctinterpolation of
Hardware does it for you :)
HowToSetTextureMatrices?
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HowToSetTextureMatrices?
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Much simpler in newer OpenGL(will discuss later)
ProjectiveTexturing:Issues
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ProjectiveTexturing:Issues
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SevereAliasing
CS 148: Summer 2016Introduction of Graphics and ImagingZahid Hossain
Textures
http://www.pling.org.uk/cs/cgv.html