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Anti-Aliasing Techniques Alliased vs. Antialiased 1 Polygon Edges - - PDF document
Anti-Aliasing Techniques Alliased vs. Antialiased 1 Polygon Edges - - PDF document
Anti-Aliasing Techniques Alliased vs. Antialiased 1 Polygon Edges Area Sampling 2 Catmull, 1978 Carpenter, 1984 A-Buffer 3 The A-Buffer Idea: approximate continuous filtering by subpixel sampling Summing areas now becomes
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Catmull, 1978 Carpenter, 1984 – A-Buffer
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The A-Buffer
- Idea: approximate continuous filtering
by subpixel sampling
- Summing areas now becomes simple
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Abram & Westover, 1983
- Abram & Westover, 1983
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Abram & Westover, 1983 SuperSampling
Sample at 4x4 subpixels and color the pixel according to the portion of the coverage.
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Andreas Schilling
- Andreas Schilling
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Andreas Schilling
12 13 14 15 8 9 10 11 4 5 6 7 1 2 3
- Catmull
- s i j
I i x j y dxdy
A i j
( , ) ( , )
( , )
- s(i,j)
(i,j) A(i,j)
- Carpenter
s i j I i a n j b n F a n b n
b n a n
( , ) ( , ) ( , )
- 1
1
n Abram & Westover s i j c i j F
p p p P
( , ) ( , )
-
- Fp
- P
pcp(i,j)=0 (i,j)pcp(i,j)p cp(i,j)=0 cp2(i,j)=-1 cp1(i,j)=1
- 0- p cp(i,j)=1
- pp1,p2
- Schilling
s i j O i j F a n b n
a b b n a n
( , ) ( , ) ( , )
,
- 1
1
(i,j)(a,b)Oa,b(i,j)
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- Catmull
Carpenter Abram & Westover Schilling
- (x,y)F(x,y) = 1
- Texture Aliasing
- A single screen space pixel might correspond to
many texels (texture elements):
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- Two special cases:
- Magnification: No real need in prefiltering.
The main decision is what kind of reconstruction (interpolation) to use.
- Minification: No real need in
- reconstruction. The main problem is proper
prefiltering.
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Nearest neighbor sampling Filtered Texture:
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Texture Pre-Filtering
- Problem: filtering the texture during
rendering is too slow for interactive performance.
- Solution: pre-filter the texture in advance
– Summed area tables - gives the average value
- f each axis-aligned rectangle in texture space
– Mip-maps (tri-linear interpolation) - supported by most of today’s texture mapping hardware
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MIP-Maps
- Precompute a set of prefiltered textures
(essentially an image pyramid).
- Based on the area of the pre-image of the
pixel:
– Select two “best” resolution levels – Use bilinear interpolation inside each level – Linearly interpolate the results
- Referred to as trilinear interpolation
Summed Area Tables
- A 2D table the size of the texture. At each
entry (i,j), store the sum of all texels in the rectangle defined by (0,0) and (i,j).
- Given any axis aligned rectangle, the sum
- f all texels is easily obtained from the
summed area table:
C C B B A A D D
D C B A area
- D
C B A area
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Linear interpolation of texture coordinates Perspective-correct texture coordinate interpolation
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Resampling a signal
- Given a sampled (discrete) signal:
– Reconstruct a continuous signal – Warp (apply mapping) – Prefilter warped signal – Sample
- In practice, some of the above stages are