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Travis Grant grant_travis@emc

CS 563 Advanced Topics in Computer Graphics Texture Sampling & antialiasing - Basic Texturing (Ch. 8) Physically Based Rendering. Travis Grant grant_travis@emc.com. Outline. Texture Space Sampling Rate Aliasing associated with Texture Refracted and Reflected Rays

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Travis Grant grant_travis@emc

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  1. CS 563 Advanced Topics in Computer GraphicsTexture Sampling & antialiasing - Basic Texturing(Ch. 8)Physically Based Rendering Travis Grant grant_travis@emc.com

  2. Outline • Texture Space Sampling Rate • Aliasing associated with Texture • Refracted and Reflected Rays • Texture Coordinate Generation • Texture Interface and basic textures grant_travis@emc.com :: Slide2

  3. p. 496 Fig. 11.5 (a) ./images/11F05A.png Grid texture on sphere w/ 1 sample per pixel grant_travis@emc.com :: Slide3

  4. Two Core Challenges for removing Texture Aliasing • Sampling Rate • Must be computed in Texture space as opposed to screen space • Must determine rate which the texture function is being sampled • Sampling Theory • Given the sampling rate we need to remove excess frequencies beyond the Nyquist limit from the texture function grant_travis@emc.com :: Slide4

  5. (s,t) (s,t) (u0,v0) (x0,y0) (u,v) (x,y) (u1,v1) (x1,y1) Texture Sampling Rate texture space object space image space PBRT Texture coordinates are (S,T): - Commonly used industry Apps often use (u,v) - PBRT uses (u,v) as a shapes “parametric description” coordinates p=f(u,v) = p(x,y) - Where p(x,y) is the Worldspace intersection point p. 488 Fig. 11.2 :: Slide5

  6. Simple Example:Finding Texture Sampling Rate s=Pxt=Py Image Space, Object Space & Texture Space perfectly aligned thus given a sample spacing of 1 pixel in the image plane the sample spacing in (s,t) texture space is (1/xr, 1/yr) grant_travis@emc.com :: Slide6

  7. Simple Example:Finding Texture Sampling Rate Image Space, Object Space & Texture Space perfectly aligned grant_travis@emc.com :: Slide7

  8. Texture Aliasing Daylon Leveller Tutorial - The previous example was purposely kept overly simple: - The following realities all lend to more complex but common scenarios: Object Visibility Object Shape Perspective Shadowing Texture Frequency Variance Daylon Leveller Tutorial :: Slide8

  9. (s,t) (u,v) from image space to world space -> p(x,y) (x,y) to parametric coordinates -> u(x,y),v(x,y) Texture Sampling Rate p. 488 Fig. 11.2 :: Slide9

  10. rx ry p px py Estimating Partial Derivatives n p. 491 Fig. 11.3 :: Slide10

  11. Estimating Partial Derivatives rx equation 1 ry n equation 2 p px dpdx = py dpdy = p. 491 Fig. 11.3 :: Slide11

  12. ∂p ∂p ∂u ∂v p (u,v) parameterization dv p’ du p. 492 Fig. 11.4 :: Slide12

  13. (u,v) parameterization or grant_travis@emc.com :: Slide13

  14. Filtering Texture Functions first evaluate band-limit: by convolving with the sinc filter convolved with the pixel filter g(x,y) centered at the point (x,y) grant_travis@emc.com :: Slide14

  15. What did we get for our efforts?

  16. Texture Aliasing p. 486 Fig. 11.1 (b) ./images/11F01B.png p. 486 Fig. 11.1 (a) ./images/11F01A.png Zoom-In of sphere from left Notice High-Frequency detail is present Severe aliasing artifacts grant_travis@emc.com :: Slide16

  17. Texture Aliasing p. 486 Fig. 11.1 (c) ./images/11F01C.png p. 486 Fig. 11.1 (a) ./images/11F01A.png Texture function applied Severe aliasing artifacts grant_travis@emc.com :: Slide17

  18. p. 496 Fig. 11.5 (c) ./images/11F05C.png antialiased image, even with a single sample per pixel grant_travis@emc.com :: Slide18

  19. Reflected & Refracted Rays p. 496 Fig. 11.5 (a) ./images/11F05A.png Tracking ray differentials Left is glass (reflection & refraction) Right is Mirror (reflection) grant_travis@emc.com :: Slide19

  20. Tracking Ray Differentials p. 496 Fig. 11.5 (b) ./images/11F05B.png p. 496 Fig. 11.5 (c) ./images/11F05C.png aliasing artifacts antialiasing w/ ray differentials grant_travis@emc.com :: Slide20

  21. Specular Reflection r r’ θ θ θ’ θ’ p. 497 Fig. 11.6 :: Slide21

  22. Specular Reflection where: is the reflected direction with respect to a shift of a pixel in the x and y directions p. 497 Fig. 11.6 :: Slide22

  23. (s,t) Texture Coordinate Generation p. 499 Fig. 11.7 ./images/11F05A.png (u,v) Spherical Planer Cylindrical Different texture coordinate generation techniques Checkerboard texture applied to a hyperboloid grant_travis@emc.com :: Slide23

  24. TextureInterfaces and Basic Texture • Constant • Scale • Mix • Bilinear

  25. References “Physically Based Rendering” by Gregg Humphreys & Matt Pharr • All Images Obtained from “Physically Based Rendering” CD-ROM • Figures recreated by tgrant from figures cited in “Physically Based Rendering” textbook Daylon Graphics – Leveller Documentation • Raytracer Texturing www.cambridgeincolour.com (Sean T. Mchugh) • Digital Image Interpolation “Computer Graphics: Principles & Practice” by Foley, van Dam, Feiner, Hughes “What We Need Around Here is More Aliasing” by Blinn, J.F. “Return of the Jaggy” by Blinn, J.F. “The Aliasing Problem in Computer-Generated Shaded Images” by Crow, F. “A Comparison of Antialiasing Techniques” by Crow, F. Harvey Mudd College HMC Tutorial on Partial Differentiation grant_travis@emc.com :: Slide25

  26. Questions?

  27. Backup Slides grant_travis@emc.com :: Slide27

  28. Geometric Meaning of Partial Derivatives Suppose the graph of z = f(x,y) is the surface shown. Consider the partial derivative of f with respect to x at a point (x0,y0). Holding y constant and varying x, we trace out a curve that is the intersection of the surface with the vertical plane y = y0. The partial derivative fx(x0,y0) measures the change in z per unit increase in x along this curve. That is, fx(x0,y0) is just the slope of the curve at (x0,y0). The geometrical interpretation of fy(x0,y0) is analogous. Harvey Mudd College (see References) :: Slide28

  29. Blinn “What we need around here is more Aliasing” :: Slide29

  30. Blinn “What we need around here is more Aliasing” :: Slide30

  31. Blinn “What we need around here is more Aliasing” :: Slide31

  32. Blinn “What we need around here is more Aliasing” :: Slide32

  33. resampled Aliasing Review jaggies = staircasing = aliasing Ideal Line on Low Resolution Grid Aliased reproduced from cambridgeincolour.com :: Slide33

  34. resampled Aliasing Review IF (Line_Is_Inside_Pixel) = black Ideal Line on Low Resolution Grid Aliased reproduced from cambridgeincolour.com :: Slide34

  35. resampled Aliasing Review High Frequency Variation Ideal Line on Low Resolution Grid Aliased reproduced from cambridgeincolour.com :: Slide35

  36. resampled Aliasing Review Ideal Line on Low Resolution Grid Anti-Aliased reproduced from cambridgeincolour.com :: Slide36

  37. resampled Unweighted Area Sampling Three Properties of Unweighted area sampling: 1) Intensity of the pixel intersected by a line edge decreases as the distance between the pixel center and the edge increases 2) Non-intersected pixels are not influenced 3) Only the total amount of overlapped area matters (not weighted based on orientation towards the center of the pixel) Ideal Line on Low Resolution Grid Anti-Aliased reproduced from cambridgeincolour.com :: Slide37

  38. resampled Unweighted Area Sampling Accounting for contributions of original -> result is % of BLACK (light Gray) Ideal Line on Low Resolution Grid Anti-Aliased reproduced from cambridgeincolour.com :: Slide38

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