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CS 551 / 645: Introductory Computer Graphics

CS 551 / 645: Introductory Computer Graphics. David Luebke cs551@cs.virginia.edu http://www.cs.virginia.edu/~cs551. Administrivia. Next semester: Intro Graphics again Look for Brogan’s animation seminar. Recap: Texture Mapping.

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CS 551 / 645: Introductory Computer Graphics

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  1. CS 551 / 645: Introductory Computer Graphics David Luebke cs551@cs.virginia.edu http://www.cs.virginia.edu/~cs551 David Luebke 8/20/2014

  2. Administrivia • Next semester: Intro Graphics again • Look for Brogan’s animation seminar David Luebke 8/20/2014

  3. Recap: Texture Mapping • Problem: it is impractical to explicitly model fine surface detail with geometry • Solution: use images to capture the “texture” of surfaces David Luebke 8/20/2014

  4. Recap: Texturing Fundamentals

  5. Recap: Texture Coordinates • Give each vertex of the triangle a texture coordinate(u, v) • For other points on the triangle, interpolate texture coordinate from the vertices • Problem: interpolating u & v in screen-space (a la Gouraud shading) is incorrect • Instead, interpolate uw, vw, and w, and calculate uw/w and vw/w for each pixel • Known as perspective-correcttexture mapping David Luebke 8/20/2014

  6. Recap: Texture Map Aliasing • Naïve texturing looks blocky and pixelated • Problem: using only one texel to color each pixel • Actually, each pixel maps to a region in texture • Pixel is smaller than a texel, we should interpolate between texel values somehow • Pixel is larger than a texel, we should average the contribution from multiple texels somehow • Even if pixel size  texel size, a pixel will in general fall between four texels • An example of a general problem called aliasing David Luebke 8/20/2014

  7. Texture Map Antialiasing • Use bilinear interpolation to average nearby texel values into a single pixel value • Find 4 nearest texels • Round u & v up and down • Interpolate texel values in u •  = u - u • A = (1-)T4 + T1, B = (1-)T3 + T2 • Interpolate resulting values in v •  = v - v • P = (1- )A + B • Also addresses the problem of many pixels projecting to a single texel (oversampling) T1 T2 A P B T4 T3 David Luebke 8/20/2014

  8. Texture Map Antialiasing • What about undersampling, when a single pixel covers many texels? • Problem: sampling those texels at a single point • Produces Moire patterns in coherent texture (checkers) • Leads to flicker or texture crawling as the texture moves • Approach: blur the image under the pixel, averaging the contributions of the covered texels • But calculating which texels each pixel covers is expensive, especially as the texture is very compressed • Solution: pre-calculate lower-resolution versions of the texture that incorporate this averaging David Luebke 8/20/2014

  9. Original Texture Lower Resolution Versions MIP-maps • For a texture of 2n x 2n pixels, compute n-1 textures, each at ½ the resolution of previous: • This multiresolution texture is called a MIP-map David Luebke 8/20/2014

  10. Generating MIP-maps • Generating a MIP-map from a texture is easy • For each texel in level i, average the values of the four corresponding texels in level i-1 • If a texture requires n bytes of storage, how much storage will a MIP-map require? • Answer: 4n/3 David Luebke 8/20/2014

  11. R G R G B R G B R G B B Representing MIP-maps Trivia: MIP = Multim In Parvo(many things in a small place) David Luebke 8/20/2014

  12. Using MIP-maps • Each level of the MIP-map represents a pre-blurred version of multiple texels • A texel at level n represents 2n original texels • When rendering: • Figure out the texture coverage of the pixel (i.e., the size of the pixel in texels of the original map) • Find the level of the MIP map in which texels average approximately that many original texels • Interpolate the value of the four nearest texels David Luebke 8/20/2014

  13. Using MIP-maps • Even better: • Likely, the coverage of the pixel will fall somewhere between the coverage of texels in two adjacent levels of the MIP map • Find the pixel’s value in each of the two textures using two bilinear interpolations • Using a third interpolation, find a value in between these two values, based on the coverage of the pixel versus each of the MIP-map levels • This is (misleadingly?) called trilinear interpolation David Luebke 8/20/2014

  14. Using MIP-maps • How many interpolations does a texture lookup using trilinear interpolation in a MIP-mapped texture involve? • How many texel values from the MIP-map must be fetched for such a lookup? David Luebke 8/20/2014

  15. MIP-map Example • No filtering: • MIP-map texturing: David Luebke 8/20/2014

  16. Can We Do Better? • What assumption does MIP-mapping implicitly make? • A: The pixel covers a square region of the texture • More exactly, the compression or oversampling rate is the same in uandv • Is this a valid assumption? Why or why not? David Luebke 8/20/2014

  17. MIP-maps and Signal Processing • An aside: aliasing and antialiasing are properly topics in sampling theory • Nyquist theorem, convolution and reconstruction, filters and filter widths • Textures are particularly difficult because a tiled texture can easily generate infinite frequencies • E.g., a checkered plane receding to an infinite horizon • Using a MIP-map amounts to prefiltering the texture image to reduce artifacts caused by sampling at too low a rate David Luebke 8/20/2014

  18. Summed-Area Tables • A technique called summed-area tableslets us integrate texels covered by the pixel more exactly (but still quickly) • Details in the book • Example: MIP-map texturing Summed-area table texturing David Luebke 8/20/2014

  19. Texture Mapping Variations • A texture can modulate any parameter in the rendering process: Texture asdiffuse lightingcoefficients: Texture asR,G,B: David Luebke 8/20/2014

  20. Bump Mapping • The texture map can even modulate the surface normal used for shading Sphere w/ diffuse textureand swirly bump map Sphere w/ diffuse texture Swirly bump map David Luebke 8/20/2014

  21. More Bump Mapping • How can you tell a bumped-mapped object from an object in which the geometry is explicitly modeled? + =

  22. Last Bump Mapping Example David Luebke 8/20/2014

  23. Displacement Map • A displacement map actually displaces the geometry • Treats the texture as a height field to be applied to the surface • Hard to do in interactive graphics pipeline • But doable in ray tracing David Luebke 8/20/2014

  24. Displacement Map Example • What is the fundamental difference between displacement mapping and bump mapping? David Luebke 8/20/2014

  25. Illumination Maps • Quake uses illumination mapsor light maps to capture lighting effects: Texture map: Light map Texture map+ light map: David Luebke 8/20/2014

  26. Illumination Maps • Illumination maps differ from texture maps in that they: • Usually apply to only a single surface • Are usually fairly low resolution • Usually capture just intensity (1 value) rather than color (3 values) • Illumination maps can be: • Painted by hand: Disney’s Aladdin ride • Calculated by a global illumination process: Nintendo64 demo • Origin of the idea David Luebke 8/20/2014

  27. Other Texture Applications • Lots of other interesting applications of the texture-map concept: • Shadow maps • 3-D textures (marble, wood, clouds) • Chrome maps • Procedural textures • For a neat explanation of the first two (with cool applets, as usual) check out: http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture22/Slide21.html David Luebke 8/20/2014

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