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Texture Mapping

Texture Mapping. Recap: Texture Map Rendering. Rendering uses the mapping: Find the visible surface at a pixel Find the point on that surface corresponding to that pixel Find the point in the texture corresponding to that point on the surface

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Texture Mapping

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  1. Texture Mapping David Luebke 110/13/2014

  2. Recap: Texture Map Rendering • Rendering uses the mapping: • Find the visible surface at a pixel • Find the point on that surface corresponding to that pixel • Find the point in the texture corresponding to that point on the surface • Use the parameters associated with that point on the texture to shade the pixel • Using triangulated meshes reduces the problem to mapping a portion of the image to each triangle: David Luebke 210/13/2014

  3. Recap: Texture Map Rendering

  4. Recap: User-Generated Mappings • For complex 3-D objects, mapping textures is still something of an art…so we often let the user do it David Luebke 410/13/2014

  5. Recap: Naive Texture Mapping • A first cut at a texture-mapping rasterizer: • For each pixel: • Interpolate u & v using standard edge equations techniques • Look up nearest texel in texture map • Color pixel according to texel color (possibly modulated by lighting calculations) • A serious artifact is warping at the edges of triangles making up the mesh • An obvious example:http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide06.html David Luebke 510/13/2014

  6. Recap:Interpolating Parameters • The problem turns out to be fundamental to interpolating parameters in screen-space • Uniform steps in screen space  uniform steps in world coords David Luebke 610/13/2014

  7. Recap:Perspective-Correct Interpolation • The solution: • Rather than interpolating u and v directly, interpolate u/z and v/z • These do interpolate correctly in screen space • Also need to interpolate z and multiply per-pixel • Problem: we don’t know z anymore • Solution: we do know w  1/z • So…interpolate uw and vw and w, and compute u = uw/w and v = vw/w for each pixel • This unfortunately involves a divide per pixel David Luebke 710/13/2014

  8. Recap:Perspective-Correct Texturing • Known as perspective-correct texture mapping • Early PC cards and game consoles didn’t support it • Compensated by using more, smaller polygons • As mentioned, other interpolation schemes really ought to use perspective correction • E.g., Gouraud shading • Generally get away without it because it is more important to be smooth than correct • Java code fragment from McMillan’s edge-equation triangle rasterizer: David Luebke 810/13/2014

  9. Perspective-Correct Texturing: Code Fragment ... PlaneEqn(uPlane, (u0*w0), (u1*w1), (u2*w2)); PlaneEqn(vPlane, (v0*w0), (v1*w1), (v2*w2)); PlaneEqn(wPlane, w0, w1, w2); ... for (y = yMin; y <= yMax; y += raster.width) { e0 = t0; e1 = t1; e2 = t2; u = tu; v = tv; w = tw; z = tz; boolean beenInside = false; for (x = xMin; x <= xMax; x++) { if ((e0 >= 0) && (e1 >= 0) && (e2 >= 0))) { int iz = (int) z; if (iz <= raster.zbuff[y+x]) { float denom = 1.0f / w; int uval = (int) (u * denom + 0.5f); uval = tile(uval, texture.width); int vval = (int) (v * denom + 0.5f); vval = tile(vval, texture.height); int pix = texture.getPixel(uval, vval); if ((pix & 0xff000000) != 0) { raster.pixel[y+x] = pix; raster.zbuff[y+x] = iz; } } beenInside = true; } else if (beenInside) break; e0 += A0; e1 += A1; e2 += A2; z += Az; u += Au; v += Av; w += Aw; } t0 += B0; t1 += B1; t2 += B2; tz += Bz; tu += Bu; tv += Bv; tw += Bw; } David Luebke 910/13/2014

  10. Texture Tiling • It is often handy to tile a repeating texture pattern onto a surface • The previous code does this via tile(): int uval = (int) (u * denom + 0.5f); uval = tile(uval, texture.width); int vval = (int) (v * denom + 0.5f); vval = tile(vval, texture.height); int pix = texture.getPixel(uval, vval); int tile(int val, int size) { while (val >= size) val -= size; while (val < 0) val += size; } See http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide18.html David Luebke 1010/13/2014

  11. Texture Transparency • McMillan’s code also includes a “quick fix” for handling transparent texture: if ((pix & 0xff000000) != 0) { raster.pixel[y+x] = pix; raster.zbuff[y+x] = iz; } • Note that this doesn’t handle partial transparency • Demo at: http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide19.html David Luebke 1110/13/2014

  12. 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 in screen-space (a la Gouraud shading) is incorrect • Perspective foreshortening should compress the texture image on distant regions of the surface • Demo at http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture21/Slide06.html David Luebke 1210/13/2014

  13. Recap: Perspective-Correct Interpolation • Skipping some math… • Rather than interpolating u and v directly, interpolate u/z and v/z • These do interpolate correctly in screen space • Also need to interpolate z and multiply per-pixel • Problem: we don’t know z anymore • Solution: we do know w  1/z • So…interpolate uw and vw and w, and compute u = uw/w and v = vw/w for each pixel • This unfortunately involves a divide per pixel David Luebke 1310/13/2014

  14. Texture Map Aliasing • Naive texture mapping looks blocky, pixelated • Problem: using a single texel to color each pixel: int uval = (int) (u * denom + 0.5f); int vval = (int) (v * denom + 0.5f); int pix = texture.getPixel(uval, vval); • Actually, each pixel maps to a region in texture • If the pixel is larger than a texel, we should average the contribution from multiple texels somehow • If the pixel is smaller than a texel, we should interpolate between texel values 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 1410/13/2014

  15. Recap: Texture Map Antialiasing • Use bilinear interpolation to average nearby texel values into a single pixel value (Draw it) • Find 4 nearest texture samples • Round u & v up and down • Interpolate texel values in u • Interpolate resulting values in v • Also addresses the problem of many pixels projecting to a single texel (Why?) David Luebke 1510/13/2014

  16. Recap: Texture Map Antialiasing • What if a single pixel covers many texels? • Problem: sampling those texels at a single point (the center of the pixel): • Produces Moire patterns in coherent texture (checkers) • Leads to flicker or texture crawling as the texture moves • Show OpenGL Texturing tutor • Approach: blur the image under the pixel, averaging the contributions of the covered texels • But calculating which texels every pixel covers is way too expensive, especially as the texture is compressed • Solution: pre-calculate lower-resolution versions of the texture that incorporate this averaging David Luebke 1610/13/2014

  17. 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 1710/13/2014

  18. 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

  19. R G R G B R G B R G B B Representing MIP-maps Trivia: MIP = Multum In Parvo(many things in a small place)

  20. 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 2010/13/2014

  21. 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 2110/13/2014

  22. 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 2210/13/2014

  23. MIP-map Example • No filtering: • MIP-map texturing: David Luebke 2310/13/2014

  24. 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 2410/13/2014

  25. 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 2510/13/2014

  26. 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 2610/13/2014

  27. Texture Mapping Variations • A texture can modulate any parameter in the rendering process: Texture asdiffuse lightingcoefficients: Texture asR,G,B: David Luebke 2710/13/2014

  28. 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 2810/13/2014

  29. More Bump Mapping • How can you tell a bumped-mapped object from an object in which the geometry is explicitly modeled? + = David Luebke 2910/13/2014

  30. Last Bump Mapping Example David Luebke 3010/13/2014

  31. Displacement Map • A displacement map actually displaces the geometry • Treats the texture as a height field to be applied to the surface • Starting to appear in the interactive graphics pipeline • First supported in Matrox Parhelia card • Can sort of implement with beta drivers in ATI & NVIDIA cards • Will soon appear in all cards • Implemented by recursive subdivision of triangles/quads David Luebke 3110/13/2014

  32. Displacement Map Example • What is the biggest visual difference between displacement mapping and bump mapping? David Luebke 3210/13/2014

  33. Illumination Maps • Quake introduced illumination mapsor light maps to capture lighting effects in video games Texture map: Light map Texture map+ light map: David Luebke 3310/13/2014

  34. 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, modern level builders David Luebke 3410/13/2014

  35. Other Texture Applications • Lots of other interesting applications of the texture-map concept (we’ll return to some): • Shadow maps • 3-D textures (marble, wood, clouds) • Procedural textures • Environment maps & cube maps • For a neat explanation of the first three (with cool applets, as usual) check out: http://graphics.lcs.mit.edu/classes/6.837/F98/Lecture22/Slide21.html David Luebke 3510/13/2014

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