travis grant grant_travis@emc
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CS 563 Advanced Topics in Computer Graphics Texture Sampling & antialiasing - Basic Texturing (Ch. 8) Physically Based Rendering. Travis Grant [email protected]. Outline. Texture Space Sampling Rate Aliasing associated with Texture Refracted and Reflected Rays - PowerPoint PPT PresentationTRANSCRIPT
CS 563 Advanced Topics in Computer Graphics
Texture Sampling & antialiasing - Basic Texturing (Ch. 8)Physically Based Rendering
Travis [email protected]
Outline
[email protected] :: Slide 2
Texture Space Sampling Rate
Aliasing associated with Texture
Refracted and Reflected Rays
Texture Coordinate Generation
Texture Interface and basic textures
[email protected] :: Slide 3
Grid texture on sphere w/ 1 sample per pixel
p. 496 Fig. 11.5 (a) ./images/11F05A.png
Two Core Challenges for removing Texture Aliasing
[email protected] :: Slide 4
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
Texture Sampling Rate
p. 488 Fig. 11.2 :: Slide 5
(x0,y0)
(u0,v0)
(u1,v1)
(x1,y1)
(s,t)
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
image space
object space
texture space
(x,y)
(u,v)
(s,t)
Simple Example:Finding Texture Sampling Rate
rx
xs
s=Px t=Py
[email protected] :: Slide 6
Image Space, Object Space &Texture Space perfectly aligned
ry
yt
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)
Simple Example:Finding Texture Sampling
Rate
0
1
y
s
xx
s
r
[email protected] :: Slide 7
Image Space, Object Space &Texture Space perfectly aligned y
fyy
x
fxxyxfyxf
)'()'(),()','(
ryy
tx
t
1
0
Texture Aliasing
Daylon Leveller Tutorial :: Slide 8
- The previous example was purposely kept overly simple:- The following realities all lend to more complex but
common scenarios:Object VisibilityObject ShapePerspectiveShadowingTexture Frequency Variance
Daylon Leveller Tutorial
Texture Sampling Rate
p. 488 Fig. 11.2 :: Slide 9
(x,y)
(u,v)
(s,t)
from image space to world space -> p(x,y)x
p
y
p
x
u
y
u
x
v
y
v
to parametric coordinates -> u(x,y),v(x,y)
Estimating Partial Derivatives
p. 491 Fig. 11.3 :: Slide 10
ppy
px
nry
rx
Estimating Partial Derivatives
p. 491 Fig. 11.3 :: Slide 11
ppy
px
nry
rx
ppx
px
dpdx = ppy
py
dpdy =
0 dczbyaxxna yna
zna )( pnd equation 1
dcba
dcbat
),,(
)0),,((
equation 2
(u,v) parameterization
p. 492 Fig. 11.4 :: Slide 12
p
dv
du
∂u∂p
∂v∂p
p’
(u,v) parameterization
v
p
u
ppp vu
'
[email protected] :: Slide 13
or
v
u
v
pv
pv
p
u
pu
pu
p
pp
pp
pp
z
y
x
z
y
x
z
y
x
'
'
'
Filtering Texture Functions
)),(( yxfTfirst evaluate
band-limit: by convolving with the sinc filter
''))','((')'(sinc)'(sinc),(' dydxyyxxfTyxyxTb
convolved with the pixel filter g(x,y) centered at the point (x,y)
2/
2/
2/
2/
b '')','(')Ty',g(x'),('xWidth
xWidth
yWidth
yWidth
f dydxyyxxyxT
[email protected] :: Slide 14
What did we get for our efforts?
Texture Aliasing
[email protected] :: Slide 16
Severe aliasing artifacts Zoom-In of sphere from leftNotice High-Frequency detail is present
p. 486 Fig. 11.1 (a) ./images/11F01A.png p. 486 Fig. 11.1 (b) ./images/11F01B.png
Texture Aliasing
[email protected] :: Slide 17
Severe aliasing artifacts Texture function applied
p. 486 Fig. 11.1 (a) ./images/11F01A.png p. 486 Fig. 11.1 (c) ./images/11F01C.png
[email protected] :: Slide 18antialiased image, even with a single sample per pixel
p. 496 Fig. 11.5 (c) ./images/11F05C.png
Reflected & Refracted Rays
[email protected] :: Slide 19
Tracking ray differentialsLeft is glass (reflection & refraction)Right is Mirror (reflection)
p. 496 Fig. 11.5 (a) ./images/11F05A.png
Tracking Ray Differentials
[email protected] :: Slide 20
aliasing artifacts antialiasing w/ ray differentials
p. 496 Fig. 11.5 (b) ./images/11F05B.png p. 496 Fig. 11.5 (c) ./images/11F05C.png
Specular Reflection
p. 497 Fig. 11.6 :: Slide 21
r’r
θ θ
θ’ θ’
Specular Reflection
x
ii
www
p. 497 Fig. 11.6 :: Slide 22
iwwhere: is the reflected direction with respect to a shift of a pixel in the x and y directions
nnwww ooi )(2
nx
nw
x
nnw
x
wnnww
xx
w oo
ooo
i 2)(2
x
nwn
x
w
x
nwo
oo
Texture Coordinate Generation
[email protected] :: Slide 23
Different texture coordinate generation techniquesCheckerboard texture applied to a hyperboloid
p. 499 Fig. 11.7 ./images/11F05A.png
(u,v) Spherical Cylindrical Planer
(s,t)
TextureInterfaces and Basic
Texture
Constant Scale Mix Bilinear
References
[email protected] :: Slide 25
“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
Questions?
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
Blinn “What we need around here is more Aliasing” :: Slide 29
Blinn “What we need around here is more Aliasing” :: Slide 30
Blinn “What we need around here is more Aliasing” :: Slide 31
Blinn “What we need around here is more Aliasing” :: Slide 32
Aliasing Review
reproduced from cambridgeincolour.com :: Slide 33
Ideal Line on Low Resolution Grid Aliased
resampled
jaggies = staircasing = aliasing
Aliasing Review
reproduced from cambridgeincolour.com :: Slide 34
Ideal Line on Low Resolution Grid Aliased
resampled
IF (Line_Is_Inside_Pixel) = black
Aliasing Review
reproduced from cambridgeincolour.com :: Slide 35
Ideal Line on Low Resolution Grid Aliased
resampled
High Frequency Variation
Aliasing Review
reproduced from cambridgeincolour.com :: Slide 36
Ideal Line on Low Resolution Grid Anti-Aliased
resampled
Unweighted Area Sampling
reproduced from cambridgeincolour.com :: Slide 37
Ideal Line on Low Resolution Grid Anti-Aliased
resampled
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 increases2) Non-intersected pixels are not influenced3) Only the total amount of overlapped area matters (not weighted based on orientation towards the center of the pixel)
Unweighted Area Sampling
reproduced from cambridgeincolour.com :: Slide 38
Ideal Line on Low Resolution Grid Anti-Aliased
resampled
Accounting for contributions of original
-> result is % of BLACK (light Gray)