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Published byKatrina McDonald Modified over 2 years ago

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Texture Mapping CMSC435 UMBC *With lots of borrowing from the usual victims…

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Motivation Flat and Boring“Textured”

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Texture Mapping “Texture”Boring Geometry Texture An image that’s mapped onto something Texel Texture pixel (Also, an island in Denmark…)

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Texture Mapping Interesting Geometry

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Kinds of Functions Stuff we might want to map –Color –Opacity –Normals –Displacement –Specularity –Precomputed Lighting

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Texture Mapping 3D Coordinate Mapping Function 2D Texture Coordinate Texture Image

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Texture Coordinates Normalized 2D space –0-1 on each axis Letters vary: –U,V are most common –GL/RMan specs like s,t Typically periodic u v s t D3D OGL Texture Coordinates as RGB

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Texture Tiling 1,0 0,1 0,0 4,0 0,4 0,0 8,0 0,8 0,0 2,0 0,2 0,0 Scale UV Coordinates Alter texture frequency

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Planar Mapping For xy aligned plane Reverse projection 9

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Planar Mapping 10

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Cylindrical Mapping For cylinder with point –(r cos Θ, r sin Θ, h z) Texture coordinates –(u,v) =(Θ/2π, z) 11

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Cylindrical Mapping 12

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Spherical Mapping For sphere with point –(r cos Θ sin Φ, r sin Θ sin Φ, r cos Φ) Texture coordinates 13

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Spherical Mapping 14

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Mapping onto Parametric Patches Use scaled surface u,v parameters for texture u,v 15

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Mapping onto Parametric Patches 16

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Mapping onto Polygons Wikipedia Explicit per-vertex coordinates…

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Perspective Correction Wikipedia One does not simply interpolate values over a projected triangle…

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Perspective Correction Worldspace midpoint Screenspace midpoint The lines sweep out the same points, but at different ‘t’ values

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Perspective Correction A B P Not with ten thousand interpolators could you do this! It is madness! Project interpolated points != Interpolate projected points

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Perspective Correction 1/w will interpolate u/w will interpolate

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Perspective Correction Given vertices (x,y,z,w) and UV coords (u,v) –Compute 1/w at each vertex –Compute u/w, v/w at each vertex Use multiplication! –Interpolate 1/w, u/w, v/w in screenspace –Divide u/w,v/w by 1/w at each pixel “Perspective Divide”

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Texture Atlas Properties of good UV layout: –Minimizes stretch –Maximize packing efficiency –Easy for artist to paint into Unlike that one… –Automatic is possible, but manual often preferred Zhou et al.

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Texture Atlas Not always a 1:1 mapping

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Texture Seams Discontinuity at UV chart boundaries Solutions: –Fix them: Copy/Blend texels across boundary –Hide them Armpits, ankles, backs of heads, under clothing Peter Kojesta (Gamasutra)

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26 Environment Mapping Surround scene with maps simulating surrounding detail

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27 Distant Reflection Look up reflection direction in reflection or environment map

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Cubic Environment Maps Pick a face based on largest normal component Project onto the face –Divide through Use resulting coordinates for 2D lookup DirectX Documentation

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Spherical Environment Maps Photograph of shiny sphere –Lookup based on x/y coordinates of normal DirectX Documentation

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Texture Sampling Point Sampling –Map UV coordinate onto texel grid, grab corresponding texel i = floor(u*width) j = floor(v*height) –Just like in 1995

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Point Sampling Point sampling under magnification

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Filtered Sampling Bilinear Filtering –Interpolate texels in 2x2 neighborhood Top-left texel: –floor(u*(width-1)), floor(v*(height-1)) Weight by fractional coordinates

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Point Sampling Point sampling under magnification

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Linear Sampling Linear sampling under magnification

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3D Textures Array of 2D slices 3D Coordinates (u,v,w) Bilinear tap in each slice using u,v Blend using w

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Minification Aliasing! Pixels:Texels > 1: Magnification Pixels:Texels < 1: Minification Pixels:Texels ~= 1

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Minification Filtering Anti-aliasing problem Projected pixel footprint Texel grid Large jumps between pixels. Texture is undersampled…

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Minification Filtering One solution: –Just super-sample it Problems: - Expensive - Guessing the right sampling rate - Performance death spiral for heavy minification

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Mip-Mapping Prefiltering: –Precalculate chain of filtered images Each level is ½ previous resolution From Latin: "multum in parvo" (much in little)

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Mip-Mapping Memory overhead is 33% –Level i+1 is ½ resolution of i: W/2*H/2=WH/4 –So… Geometric series

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Mip-Mapping Derive footprint using UV derivatives in screenspace du/dy, dv/dy du/dx, dv/dx

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Mip-Mapping Approximate footprint with a square –W = Width of square in texels Find mip level matching footprint size w

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Mip-Mapping Level of detail0… Width of square in texels Base texels per ith level texel Finest level that won’t alias Aliasing Magnification “Just Right”

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Mip-Mapping Level i Level i+1 Increasing footprint size Blend bilinear taps at two nearest levels (8 texels accessed) Sometimes incorrectly called “Trilinear”

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Without

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With

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Getting Derivatives Rasterizer: 2x2 Quads + Differencing Each 2x2 quad is self-contained Missing pixels are extrapolated… This is a collosal pain in the collective necks of hardware architects

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Getting Derivatives Raytracer –Intersect “differential” rays with tangent plane –Track derivatives during secondary bounces

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Mip-Mapping Advantages: –Cheap approximation to super-sampling –Ensures 1:1 pixel/texel ratio May actually be FASTER than bilinear –Avoids cache thrashing

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Mip-Mapping Disadvantages: –Needs derivatives Complicates renderer –33% Memory overhead –Needs some preprocessing

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Anisotropic Filtering Mipmapping is isotropic –Same in all directions At oblique angles, footprint is NOT isotropic –Result: Too much blur

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Anisotropic Filtering Ideal solution: –Elliptical Weighted Average (EWA) –Anisotropic gaussian kernel –“Gold Standard”

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Anisotropic Filtering Actual Solution: –Approximate ellipse with rectangle Box kernel –Minor axis picks level –Multiple filter taps along major axis 4x Anisotropic

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No mipmapping

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Trilinear

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4x Anisotropic

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