OpenGL Selection and Picking

Antialiasing

What is alias?


Alias

-

A false signal in telecommunication links from
beats between signal frequency and sampling frequency

(from dictionary.com)


Not just telecommunication, alias is everywhere in
computer graphics because rendering is essentially a
sampling process


Examples:



Jagged edges


False texture patterns


Rendering is a sampling process?



Yes indeed.

Image display example

Rendering is a sampling process?


Another example

Render a smooth surface

Ssignal sampling and filtering


Two important steps when information are
represented digitally:
sampling

and
reconstruction









Alias can be caused by any of the steps


Alias caused by under
-
sampling


Have

you ever look
ed

at an electric fan and
found it is rotated in a reverse direction?

Sample at only ¼ of the frequency

Incorrect result is seen !!
-

under
-
sampling

problem

Alias caused by under
-
sampling


1D signal sampling example

Actual signal

Sampled signal

How often is enough?


What is the right sampling frequency?


Sampling theorem (or Nyquist limit)
-


the
sampling frequency has to be at least twice
the
maximum

frequency of the signal to be
sampled

Need two samples in this cycle


www.
microsoft
.ca

Can alias be totally avoided


Given the sampling theorem by Nyquist ?


Not really
–

this is because the
maximum

frequency might be infinite, i.e., not
bandlimited


Most of

graphics scenes are not bandlimited:
sharp edges can never be completely sampled

in a
discrete manner (point sampling)


We will talk about what we can do to correct
alias for real time graphics


Strobe light on dripping water:
Temporal aliasing


Spokes on a rotating wheel:
Temporal aliasing


Moir
é

patterns:
Spatial aliasing


Examples of Aliasing

Antialiasing Lines


Idea:


Make line “fatter”


Fade line out (removes high frequencies)


Now sample the line

Antialiasing Lines


Solution 1
–

Unweighted Area Sampling:


Treat line as a single
-
pixel wide rectangle


Color pixels according to the percentage of each
pixel that is “covered” by the rectangle

Solution 1: Unweighted Area Sampling


Pixel area is unit square


Constant weighting function


Pixel color is determined by computing the
amount of the pixel covered by the line, then
shading accordingly


Easy to compute, gives reasonable results

Line

One Pixel

Solution 2: Weighted Area Sampling


Treat pixel area as a circle with a radius of one pixel


Use a radially symmetric weighting function
(e.g.,
cone)
:


Areas closer to the pixel center are weighted more heavily


Better results than unweighted, slightly higher cost

Line

One Pixel

Solution 3: Super
-
sampling


Divide pixel up into “sub
-
pixels”:
2

2, 3

3, 4

4, etc.


Sub
-
pixel is colored if inside line


Pixel color is the average of its sub
-
pixel colors


Easy to implement
(in software and hardware)


Expensive

No antialiasing

Antialiasing
(2

2 super
-
sampling)

Different Supersampling Schemes


The common
formula:


c(i,x,y): color of the ith sample
for pixel(x,y)
;
Wi: weight


Different super
-
sampling schemes

Reconstruction


After the (ideal) sampling is done, we still
need to reconstruct back the original
continuous signal


The reconstruction is done by reconstruction
filter

Reconstruction Filters



Common reconstruction filters:

Box filter

Tent filter

Sinc filter = sin(
p
x)/
p
x

Box filter


Very simple, but not very good

Tent Filter


Based on linear interpolation. Better, but still
not smooth

Sinc Filter


Ideal low
-
pass filter

Anti
-
aliased texture mapping


The above anti
-
aliasing methods work better
for removing jagged edges but not texture
aliasing


Two problems to address
–



Magnification


Minification

Re
-
sampling


Minification and Magnification
–

resample the
signal to a different resolution

Magnification

Minification

(note the minification is done badly here)

Magnification


Simpler to handle, just resample the
reconstructed signal

Reconstructed signal Resample the reconstructed signal

Magnification


Common methods: nearest neighbor (box
filter) or linear interpolation (tent filter)

Nearest neighbor bilinear interpolation

Minification


Harder to handle


The signal’s frequency is too high to avoid
aliasing


A possible solution:


Increase the low pass filter width of the ideal sinc
filter
–

this effectively blur the image


Blur the image first (using any method), and then
sample it

Minification


Several texels cover one pixel (under
sampling happens)

Under sample artifact

one pixel

Solution:


Either increase
sampling rate or
reduce the
texture
Frequency


We will discuss:


1.
Mip
-
mapping

2.
Rip
-
mapping

3.
Sum Area Table

Mip
-
mapping


By Lance Williams
(SIGGRAPH ’83)


Mip
–

many things in a
small place


The original texture is
augmented with a set of low
resolution textures


Which resolution to use
depends on the screen
projection size
–

try to
maintain pixel to texel
ration close to 1

average 2x2

texels

Mipmapping problem


Overblurring!
–

When a pixel covers many u
texels but few v texels, we always choose the
largest pixel coverage to decide the level





Non mipmapping




mipmapping

Ripmapping


Correct the over
-
blurring problem of
mipmapping
–

separating x and y filtering

•
Scale by half by x
across a row.

•
Scale by half in y
going down a column.

•
The diagonal has the
equivalent mip
-
map.

•
Four times the amount
of storage is required.

•
Four different texel
values to average

?

Summed Area Table


Another way to perform anisotropic filtering
-

can be used to compute the average color for
any arbitrary rectangular region in the texture
space
at a constant speed



A two dimensional array that has the same
size as the texture

Every pixel stores the sum of all the texel colors in the

lower left corner

Summed Area Table (SAT)


How to calculate the sum of texels in the area
between A and B?

R

A

B

C

D

R = SAT[B]
–

SAT[C]
–

SAT[D] + SAT[A]

The average value can be computed by



R / num of texels in R

Summed Area Table (SAT)


is used to filter the texture


Compute the rectangular bounding box of the pixel
area in the texture and then


use summed area table to compute the average
color (i.e., filter the texels when


magnification takes place)


pixel

polygon

Texture space

x

y

Summed Area Table


Less blurry than Mipmapping


Still blurry when the texture is viewed along
its diagonal
–



the bounding box of the pixel area is larger than
the actual pixel area

pixel

polygon

Texture space

x

y

not quit fit

Comparison

Non filtering





Mipmapping






Summed area table

Note that only mipmap is implemented by hardware and supported by OpenGL

Motion Blur
–

Temporal Antialias


Tricky


Simplest Solution:


supersampling in time


brute force approach


motion blur increases temporal
resolution


Just as pixel antialiasing increases
spatial resolution


If an object moves 16 pixels in one
frame, then 16 supersample images
(or even less) should be adequate