CS 563 Advanced Topics in Computer Graphics Texture Sampling

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CS 563 Advanced Topics in Computer
GraphicsTexture Sampling antialiasing - Basic
Texturing (Ch. 8)Physically Based Rendering

• Travis Grant
• grant_travis_at_emc.com

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Outline

• Texture Space Sampling Rate
• Aliasing associated with Texture
• Refracted and Reflected Rays
• Texture Coordinate Generation
• Texture Interface and basic textures

grant_travis_at_emc.com Slide 2
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p. 496 Fig. 11.5 (a) ./images/11F05A.png
Grid texture on sphere w/ 1 sample per pixel
grant_travis_at_emc.com Slide 3
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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_at_emc.com Slide 4
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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 pf(u,v) p(x,y) - Where p(x,y) is
the Worldspace intersection point
p. 488 Fig. 11.2 Slide 5
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Simple ExampleFinding Texture Sampling Rate
Image Space, Object Space Texture Space
perfectly aligned

• sPx tPy

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_at_emc.com Slide 6
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Simple ExampleFinding Texture Sampling Rate
Image Space, Object Space Texture Space
perfectly aligned
grant_travis_at_emc.com Slide 7
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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 Slide 8
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Texture Sampling Rate
p. 488 Fig. 11.2 Slide 9
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Estimating Partial Derivatives
n
p. 491 Fig. 11.3 Slide 10
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Estimating Partial Derivatives
p. 491 Fig. 11.3 Slide 11
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(u,v) parameterization
dv
p
du
p. 492 Fig. 11.4 Slide 12
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(u,v) parameterization
or
grant_travis_at_emc.com Slide 13
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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_at_emc.com Slide 14
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• What did we get for our efforts?

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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_at_emc.com Slide 16
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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_at_emc.com Slide 17
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p. 496 Fig. 11.5 (c) ./images/11F05C.png
antialiased image, even with a single sample per
pixel
grant_travis_at_emc.com Slide 18
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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_at_emc.com Slide 19
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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_at_emc.com Slide 20
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Specular Reflection
r
r
?
?
?
?
p. 497 Fig. 11.6 Slide 21
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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 Slide 22
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Texture Coordinate Generation
(s,t)
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_at_emc.com Slide 23
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TextureInterfaces and Basic Texture

• Constant
• Scale
• Mix
• Bilinear

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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_at_emc.com Slide 25
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Questions?
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Backup Slides
grant_travis_at_emc.com Slide 27
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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) Slide 28
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Blinn What we need around here is more Aliasing
Slide 29
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Blinn What we need around here is more Aliasing
Slide 30
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Blinn What we need around here is more Aliasing
Slide 31
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Blinn What we need around here is more Aliasing
Slide 32
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Aliasing Review
jaggies staircasing aliasing
Ideal Line on Low Resolution Grid
Aliased
reproduced from cambridgeincolour.com Slide 33
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Aliasing Review
IF (Line_Is_Inside_Pixel) black
Ideal Line on Low Resolution Grid
Aliased
reproduced from cambridgeincolour.com Slide 34
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Aliasing Review
High Frequency Variation
Ideal Line on Low Resolution Grid
Aliased
reproduced from cambridgeincolour.com Slide 35
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Aliasing Review
Ideal Line on Low Resolution Grid
Anti-Aliased
reproduced from cambridgeincolour.com Slide 36
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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 Slide 37
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Unweighted Area Sampling
Accounting for contributions of original -gt
result is of BLACK (light Gray)
Ideal Line on Low Resolution Grid
Anti-Aliased
reproduced from cambridgeincolour.com Slide 38