Attributes of Graphics Primitives

Sang Il Park

Sejong University

OpenGL State variables:

• Color• Point attributes• Line attributes• Fill-Area attributes

• Color buffer Setting:

• Setting the color value:

Ex)

Color in OpenGL

glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB)glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB)

GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLEGLUT_DOUBLE

GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLEGLUT_DOUBLE

glColor* (values);glColor* (values);

glColor3f (0.0, 1.0, 0.5);glColor3i ( 0, 255, 128);glColor3f (0.0, 1.0, 0.5);glColor3i ( 0, 255, 128);

• Size:

• Color :

Point Attributes in OpenGL

glPointSize ( size );glPointSize ( size );

glColor* (values);glColor* (values);

• Width:

• Line-Style :

ex)

• Line-Style On/Off:

Line Attributes in OpenGL

glLineWidth ( width );glLineWidth ( width );

glLineStipple (repeatFactor, pattern); glLineStipple (repeatFactor, pattern);

glLineStipple (1, 0x00FF);glLineStipple (1, 0x0101);glLineStipple (1, 0x00FF);glLineStipple (1, 0x0101);

glEnable (GL_LINE_STIPPLE);glDisable (GL_LINE_STIPPLE);glEnable (GL_LINE_STIPPLE);glDisable (GL_LINE_STIPPLE);

• Line Caps:

• Connecting:

Other Line Attributes Not in OpenGL

Butt cap Round cap Projecting square cap

Miter join Round join Bevel join

• Pen and Brush Options:

Other Line Attributes Not in OpenGL

• Color buffer Setting:

• Setting the color value:

Ex)

Color in OpenGL

glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB)glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB)

GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLEGLUT_DOUBLE

GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLEGLUT_DOUBLE

glColor* (values);glColor* (values);

glColor3f (0.0, 1.0, 0.5);glColor3i ( 0, 255, 128);glColor3f (0.0, 1.0, 0.5);glColor3i ( 0, 255, 128);

Area Filling

• Scan line approach• Seed Fill Algorithm

Area Filling (Scan line Approach)

• For each scan line(1) Find intersections (the extrema of spans)

• Use Bresenham's line-scan algorithm(2) Sort intersections (increasing x order)(3) Fill in between pair of intersections

Area Filling (Scan line Approach)

• Take advantage of– Edge coherence: edges intersected by

scan line i are also intersected by scan line i+1

Area Filling (Scan line method)

basic idea− Start at a pixel interior to a polygon

− Fill the others using connectivity

Area Filling (Seed Fill Algorithm)

seed

4-connected 8-connected

Need a stack.

Why?

Seed Fill Algorithm (Cont’)

start position

Seed Fill Algorithm (Cont’)

Seed Fill Algorithm (Cont’)

interior-defined boundary-defined

flood fill algorithm boundary fill algorithm

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6

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0 2 4 6 8 10 0 2 4 6 8 10

8

6

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2

Seed Fill Algorithm (Cont’)

0 1 2 3 4 5 6 7 8 91

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9

1

2

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hole

boundary pixel interior pixel seed pixel

The stack may contain duplicated or unnecessary information !!!

Boundary Filling

Flood Filling

: Start a point inside the figure, replace a specified interior color only.

Shani, U., “Filling Regions in Binary Raster Images:A Graph-Theoretic Approach”, Computer Graphics,14, (1981), 321-327

scan lineconversion

seedfilling

+

Scan Line Seed Fill

Boundary Filling

• Efficiency in space! – finish the scan line

containing the starting position

– process all lines below the start line

– process all lines above the start line

Problems of Filling Algorithm

• What happens if a vertex is shared by more than one polygon, e.g. three triangles?

• What happens if the polygon intersects itself?

• What happens for a “sliver”?

Solutions? Redefine what it means to be inside of a triangle Different routines for nasty little triangles

OpenGL Fill-Area Function

• Shade model:

• Wire-frame or point:

glShadeModel ( shadeModel );glShadeModel ( shadeModel );

GL_SMOOTHGL_FLATGL_SMOOTHGL_FLAT

glPolygonMode ( face, displayMode );glPolygonMode ( face, displayMode );

GL_FRONTGL_BACK

GL_FRONT_AND_BACK

GL_FRONTGL_BACK

GL_FRONT_AND_BACK

GL_LINEGL_POINTGL_FILL

GL_LINEGL_POINTGL_FILL

Aliasing in CG

Wh

ich

is th

e

bette

r?

Aliasing in CG

• Digital technology can only approximate analog signals through a process known as sampling

• The distortion of information due to low-frequency sampling (undersampling)

• Choosing an appropriate sampling rate depends on data size restraints, need for accuracy, the cost per sample…

• Errors caused by aliasing are called artefacts. Common aliasing artefacts in computer graphics include jagged profiles, disappearing or improperly rendered fine detail, and disintegrating textures.

The Nyquist Theorem

the sampling rate must be at least twice the frequency of the signal or aliasing occurs

Aliasing Effects

Artifacts - Jagged profiles

• Jagged silhouettes are probably the most familiar effect caused by aliasing.

• Jaggies are especially noticeable where there is a high contrast between the interior and the exterior of the silhouette

Artefacts - Improperly rendered detail

Artefacts - Disintegrating textures

• The checkers should become smaller as the distance from the viewer increases.

Antialiasing

• Antialiasing methods were developed to combat the effects of aliasing. The two major categories of antialiasing techniques are prefiltering and postfiltering.

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Prefiltering

• Eliminate high frequencies before sampling (Foley & van Dam p. 630)– Convert I(x) to F(u)– Apply a low-pass filter

• A low-pass filter allows low frequencies through, but attenuates (or reduces) high frequencies

– Then sample. Result: no aliasing!

High Frequency

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Prefiltering

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Prefiltering

Basis for Prefiltering Algorithms

Catmull’s Algorithm

AB

A1A2

A3

• Find fragment areas

• Multiply by fragment colors

• Sum for final pixel color

Prefiltering Example

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Prefiltering

• So what’s the problem?• Problem: most rendering algorithms generate

sampled function directly– e.g., Z-buffer, ray tracing

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Supersampling

• The simplest way to reduce aliasing artifacts is supersampling – Increase the resolution of the samples– Average the results down

• Or sometimes, it is called “Postfiltering”.

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Supersampling

• The process:1. Create virtual image at higher resolution than the

final image

2. Apply a low-pass filter

3. Resample filtered image

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Supersampling: Limitations

• Q: What practical consideration hampers super-sampling?

• A: Storage goes up quadratically• Q: What theoretical problem does

supersampling suffer?• A: Doesn’t eliminate aliasing! Supersampling

simply shifts the Nyquist limit higher

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Supersampling: Worst Case

• Q: Give a simple scene containing infinite frequencies

• A: A checkered ground plane receding into infinity

• See next slide…

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Supersampling

• Despite these limitations, people still use super-sampling (why?)

• So how can we best perform it?

Sampling in the Postfiltering method

• Supersampling from a 4*3 image. • Sampling can be done randomly or

regularly. The method of perturbing the sample positions is known as "jittering."

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Stochastic Sampling

• Stochastic: involving or containing a random variable

• Sampling theory tells us that with a regular sampling grid, frequencies higher than the Nyquist limit will alias

• Q: What about irregular sampling?• A: High frequencies appear as noise, not aliases• This turns out to bother our visual system less!

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Stochastic Sampling

• An intuitive argument:– In stochastic sampling, every region of the image has

a finite probability of being sampled– Thus small features that fall between uniform sample

points tend to be detected by non-uniform samples

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Stochastic Sampling

• Idea: randomizing distribution of samples scatters aliases into noise

• Problem: what type of random distribution to adopt?

• Reason: type of randomness used affects spectral characteristics of noise into which high frequencies are converted

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Stochastic Sampling

• Problem: given a pixel, how to distribute points (samples) within it?

Grid Random Poisson Disc Jitter

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Stochastic Sampling

• Poisson distribution: – Completely random– Add points at random until area is full.– Uniform distribution: some neighboring

samples close together, some distant

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Stochastic Sampling

• Poisson disc distribution: – Poisson distribution, with minimum-

distance constraint between samples– Add points at random, removing

again if they are too close to any previous points

– Very even-looking distribution

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Stochastic Sampling

• Jittered distribution– Start with regular grid of samples– Perturb each sample slightly in a

random direction– More “clumpy” or granular in appearance

Nonuniform Supersampling

Adaptive Sampling

Adaptive Sampling

Final Samples

Problem:• Many more blue

samples than white samples

• But final pixel actually more white than purple!

• Simple filtering will not handle this correctly

Filters

Antialiasing

http://www.siggraph.org/education/materials/HyperGraph/aliasing