1Texture MappingAdam FinkelsteinPrinceton UniversityCOS 426, Spring 2003SurfaceImageTextureTextures• Describe color variation in interior of 3D polygono When scan converting a polygon, vary pixel colors according to values fetched from a textureAngel Figure 9.33D Rendering Pipeline (for direct illumination)3D PrimitivesModelingTransformationModelingTransformationProjectionTransformationProjectionTransformationClippingClippingLightingLightingImageViewportTransformationViewportTransformationScanConversionScanConversion2D Image Coordinates3D Modeling Coordinates3D World Coordinates3D Camera Coordinates2D Screen Coordinates2D Screen CoordinatesViewingTransformationViewingTransformation3D World Coordinates2D Image CoordinatesTexture mappingSurface Textures• Add visual detail to surfaces of 3D objectsPolygonal modelWith surface textureSurface Textures• Add visual detail to surfaces of 3D objects[Daren Horley]Overview• Texture mapping methodso Parameterizationo Mappingo Filtering• Texture mapping applicationso Modulation textureso Illumination mappingo Bump mappingo Environment mappingo Image-based renderingo Non-photorealistic rendering2Parameterizationgeometrygeometry++==imageimagetexture maptexture map• Q: How do we decide where on the geometryeach color from the image should go?Option: Varieties of projections[Paul Bourke][Paul Bourke]Option: unfold the surface[Piponi2000]Option: make an atlas[Sander2001]charts atlas surfaceOverview• Texture mapping methodso Parameterizationo Mappingo Filtering• Texture mapping applicationso Modulation textureso Illumination mappingo Bump mappingo Environment mappingo Image-based renderingo Volume textureso Non-photorealistic renderingTexture Mapping• Steps:o Define textureo Specify mapping from texture to surfaceo Lookup texture values during scan conversion(0,0)(1,0)(0,1)uvxyModelingCoordinateSystemImageCoordinateSystemstTextureCoordinateSystem3Texture Mapping• When scan convert, map from …o image coordinate system (x,y) too modeling coordinate system (u,v) too texture image (t,s)(0,0)(1,0)(1,1)(0,1)uvxyModelingCoordinateSystemImageCoordinateSystemstTextureCoordinateSystemTexture MappingAllison Klein, Princeton• Texture mapping is a 2D projective transformationo texture coordinate system: (t,s) too image coordinate system (x,y)Texture Mapping• Scan conversiono Interpolate texture coordinates down/across scan lineso Distortion due to bilinear interpolation approximation» Cut polygons into smaller ones, or» Perspective divide at each pixelTexture MappingLinear interpolationof texture coordinatesCorrect interpolationwith perspective divideHill Figure 8.42Overview• Texture mapping methodso Parameterizationo Mappingo Filtering• Texture mapping applicationso Modulation textureso Illumination mappingo Bump mappingo Environment mappingo Image-based renderingo Non-photorealistic renderingTexture FilteringAngel Figure 9.4• Must sample texture to determine color at each pixel in image4Texture FilteringAngel Figure 9.5• Aliasing is a problemPoint samplingArea filteringTexture Filtering• Ideally, use elliptically shaped convolution filtersIn practice, use rectanglesTexture FilteringAngel Figure 9.14• Size of filter depends on projective warpo Can prefiltering images » Mip maps» Summed area tablesMagnification MinificationMip Maps• Keep textures prefiltered at multiple resolutionso For each pixel, linearly interpolate between two closest levels (e.g., trilinear filtering) o Fast, easy for hardwareSummed-area tables• At each texel keep sum of all values down & righto To compute sum of all values within a rectangle,simply subtract two entrieso Better ability to capture very oblique projectionso But, cannot store values in a single byteS1S2Overview• Texture mapping methodso Parameterizationo Mappingo Filtering• Texture mapping applicationso Modulation textureso Illumination mappingo Bump mappingo Environment mappingo Image-based renderingo Non-photorealistic rendering5Modulation textures)))()(((),(SSTTLLLnSDAAEIKIKISRVKLNKIKItsTI ++•+•++=∑Map texture values to scale factorWood textureTexturevalueIllumination MappingSSTTLLLnSDAAEIKIKISRVKLNKIKII ++•+•++=∑))()((Map texture values to surface material parametero KAo KDo KSo KTo nKT= T(s,t)Bump MappingTexture values perturb surface normals Bump MappingH&B Figure 14.100Environment MappingTexture values are reflected off surface patch H&B Figure 14.93Image-Based RenderingMap photographic textures to provide details for coarsely detailed polygonal model6Solid texturesTexture values indexed by 3D location (x,y,z)• Expensive storage, or• Compute on the fly,e.g. Perlin noise ÆNonphotorealistic RenderingArt-Maps Summary• Texture mapping methodso Parameterizationo Mappingo Filtering• Texture mapping applicationso Modulation textureso Illumination mappingo Bump mappingo Environment mappingo Image-based renderingo Volume textureso Non-photorealistic
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