Texture mapping. Computer Graphics CSE 167 Lecture 9
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1 Texture mapping Computer Graphics CSE 167 Lecture 9
2 CSE 167: Computer Graphics Texture Mapping Overview Interpolation Wrapping Texture coordinates Anti aliasing Mipmaps Other mappings Including bump mapping CSE 167, Winter
3 Large triangles Advantages Often sufficient for simple geometry Fast to render Disadvantages Per vertex colors look boring and computergenerated Based on slides courtesy of Jurgen Schulze CSE 167, Winter
4 Texture mapping Map textures (images) onto surface polygons Same triangle count, much more realistic appearance CSE 167, Winter
5 Texture mapping Objective: map locations in texture to locations on 3D geometry Texture coordinate space Texture pixels (texels) have texture coordinates (s,t) Convention Bottom left corner of texture is at (s,t) = (0,0) Top right corner is at (s,t) = (1,1) (1,1) t (0,0) s Texture coordinates CSE 167, Winter
6 Texture mapping Store 2D texture coordinates s,t with each triangle vertex v 1 (s,t) = (0.65,0.75) (0.65,0.75) (1,1) v 0 (s,t) = (0.6,0.4) t (0.4,0.45) (0.6,0.4) v 2 (s,t) = (0.4,0.45) Triangle in any space before projection (0,0) Texture coordinates s CSE 167, Winter
7 Texture mapping Each point on triangle gets color from its corresponding point in texture (1,1) v 1 (s,t) = (0.65,0.75) v 0 (s,t) = (0.6,0.4) t (0.4,0.45) (0.65,0.75) (0.6,0.4) v 2 (s,t) = (0.4,0.45) Triangle in any space before projection (0,0) Texture coordinates s CSE 167, Winter
8 Primitives Modeling and viewing transformation Shading Projection Rasterization Texture mapping Fragment processing Includes texture mapping Frame-buffer access (z-buffering) Image CSE 167, Winter
9 Texture look up Given texture coordinates (s,t) at current pixel Closest four texels in texture space are at (s 0,t 0 ), (s 1,t 0 ), (s 0,t 1 ), (s 1,t 1 ) How to compute pixel color? Interpolate t 1 t t 0 s 0 s s 1 CSE 167, Winter
10 Nearest neighbor interpolation Use color of closest texel t 1 t t 0 s 0 s s 1 Simple, but low quality and aliasing CSE 167, Winter
11 Bilinear interpolation 1. Linear interpolation horizontally Ratio in s direction is c top = tex(s 0,t 1 ) (1 r s ) + tex(s 1,t 1 ) r s c bot = tex(s 0,t 0 ) (1 r s ) + tex(s 1,t 0 ) r s 2. Linear interpolation vertically Ratio in t direction is c = c bot (1 r t ) + c top r t r s r t s s t t 1 1 s s t t t 1 c top t c bot t 0 s 0 s s 1 t 1 c top c t c bot t 0 s 0 s s 1 CSE 167, Winter
12 Interpolation OpenGL Nearest neighbor Bilinear GL_NEAREST: Nearest neighbor interpolation GL_LINEAR: Bilinear interpolation CSE 167, Winter
13 Wrapping Texture image extends from [0,0] to [1,1] in texture space What if (s,t) texture coordinates are beyond that range? Wrap Repeat (and optionally mirror) texture Clamp texture CSE 167, Winter
14 Wrapping: repeat Repeat the texture Creates discontinuities at edges, unless texture is designed to line up (1,1) t (0,0) s Seamless brick wall texture (by Christopher Revoir) Texture Space CSE 167, Winter
15 Wrapping: clamp Use edge or specified color everywhere outside data range [0..1] (1,1) t (0,0) s Texture Space CSE 167, Winter
16 Wrapping Repeat Repeat and mirror Clamp to edge color Clamp to specified color OpenGL GL_REPEAT GL_MIRRORED_REPEAT GL_CLAMP_TO_EDGE: repeats last pixel in the texture GL_CLAMP_TO_BORDER: requires setting border color CSE 167, Winter
17 Texture coordinates What if texture extends across multiple polygons? Parameterize surface Mapping between 3D positions on surface and 2D texture coordinates Defined by texture coordinates of triangle vertices Example mappings Cylindrical Spherical Orthographic Cube Parametric Skin CSE 167, Winter
18 Texture atlas charts atlas surface [Sander2001] CSE 167, Winter
19 Skin mapping CSE 167, Winter
20 Skin mapping CSE 167, Winter
21 Skin mapping [Piponi2000] CSE 167, Winter
22 Skin mapping CSE 167, Winter
23 Orthographic mapping Use linear transformation of object s XYZ coordinates CSE 167, Winter w z y x t s xyz in object space xyz in camera space
24 Planar mapping CSE 167, Winter
25 Planar mapping CSE 167, Winter
26 Spherical mapping Use spherical coordinates Shrink wrap sphere to object Texture map Mapping result CSE 167, Winter
27 Spherical mapping CSE 167, Winter
28 Spherical mapping CSE 167, Winter
29 Cylindrical mapping Similar to spherical mapping, but with cylindrical coordinates CSE 167, Winter
30 Cylindrical mapping CSE 167, Winter
31 Spherical and cylindrical mapping spherical cylindrical CSE 167, Winter
32 Multiple mappings Complex objects CSE 167, Winter
33 Cube mapping CSE 167, Winter
34 Cube mapping CSE 167, Winter
35 Cube mapping CSE 167, Winter
36 Parametric mapping Surface given by parametric functions Very common in CAD Clamp (u,v) parameters to [0..1] and use as texture coordinates (s,t) CSE 167, Winter
37 Aliasing What could cause this aliasing effect? CSE 167, Winter
38 Aliasing Sufficiently sampled, no aliasing Insufficiently sampled, aliasing Image: Robert L. Cook High frequencies in the input data can appear as lower frequencies in the sampled signal CSE 167, Winter
39 Antialiasing: Intuition Pixel may cover large area on triangle in camera space Corresponds to many texels in texture space Need to compute average Image plane Camera space Texture space Texels Pixel area CSE 167, Winter
40 Antialiasing using MIP maps Averaging over texels is expensive Many texels as objects get smaller Large memory access and computation cost Precompute filtered (averaged) textures Texture at multiple resolutions Practical solution to aliasing problem Fast and simple Available in OpenGL, implemented in GPUs Reasonable quality CSE 167, Winter
41 MIP maps (mipmaps) MIP stands for multum in parvo (much in little) (Williams 1983) Before rendering Precompute and store down scaled versions of textures Reduce resolution by factors of two successively Use high quality filtering (averaging) scheme Increases memory cost by 1/3 1/3 = ¼+1/16+1/64+ Width and height of texture should be powers of two (non power of two supported since OpenGL 2.0) CSE 167, Winter
42 Mipmaps Example: resolutions 512x512, 256x256, 128x128, 64x64, 32x32 pixels Level 1 Level CSE 167, Winter
43 Mipmaps One texel in level 4 is the average of 44=256 texels in level 0 Level 1 Level CSE 167, Winter
44 Mipmaps Level 0 Level 1 Level 2 Level 3 Level 4 CSE 167, Winter
45 Rendering with mipmaps Mipmapping Interpolate texture coordinates of each pixel as without mipmapping Compute approximate size of pixel in texture space Look up color in nearest mipmap E.g., if pixel corresponds to 10x10 texels use mipmap level 3 Use interpolation as before CSE 167, Winter
46 Image plane Mipmapping Camera space Texture space Texels Pixel area Mip-map level 0 Mip-map level 1 Mip map level 2 Mip map level 3 CSE 167, Winter
47 Nearest mipmap, nearest neighbor interpolation Visible transition between mipmap levels CSE 167, Winter
48 Nearest mipmap, bilinear interpolation Visible transition between mipmap levels CSE 167, Winter
49 Trilinear mipmapping Use two nearest mipmap levels E.g., if pixel corresponds to 10x10 texels, use mipmap levels 3 (8x8) and 4 (16x16) 2 Step approach: 1. Perform bilinear interpolation in both mip maps 2. Linearly interpolate between the results Requires access to 8 texels for each pixel Supported by hardware without performance penalty CSE 167, Winter
50 Anisotropic filtering Method of enhancing the image quality of textures on surfaces that are at oblique viewing angles Different degrees or ratios of anisotropic filtering can be applied The degree refers to the maximum ratio of anisotropy supported by the filtering process. For example, 4:1 anisotropic filtering supports presampled textures up to four times wider than tall CSE 167, Winter
51 Mipmaps in OpenGL Mipmapping tutorial with source code /mipmapping/text.php CSE 167, Winter
52 Bump mapping Texture = change in surface normal Sphere w/ diffuse texture Swirly bump map Sphere w/ diffuse texture and swirly bump map CSE 167, Winter
53 Displacement mapping CSE 167, Winter
54 Displacement map base surface hand-painted displacement map (detail) Paweł Filip tolas.wordpress.com displaced surface CSE 167, Winter
55 Illumination maps Quake introduced illumination maps or light maps to capture lighting effects in video games Texture map: Light map Texture map + light map: CSE 167, Winter
56 Environment maps Images from Illumination and Reflection Maps: Simulated Objects in Simulated and Real Environments Gene Miller and C. Robert Hoffman SIGGRAPH 1984 Advanced Computer Graphics Animation Course Notes CSE 167, Winter
57 Environment map CSE 167, Winter
58 Solid textures Texture values indexed by 3D location (x,y,z) Expensive storage, or Compute on the fly, e.g. Perlin noise CSE 167, Winter
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