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) GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLE GLUT_DOUBLE GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLE GLUT_DOUBLE 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 ); glColor* (values);

Width: Line-Style : ex) Line-Style On/Off: Line Attributes in OpenGL glLineWidth ( width ); 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 capRound capProjecting square cap Miter joinRound joinBevel 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) GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLE GLUT_DOUBLE GLUT_RGBA GLUT_RGB GLUT_INDEX GLUT_SINGLE GLUT_DOUBLE 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-connected8-connected Need a stack. Why? Seed Fill Algorithm (Cont’)

start position Seed Fill Algorithm (Cont’)

interior-defined boundary-defined flood fill algorithmboundary fill algorithm

Seed Fill Algorithm (Cont’) hole boundary pixelinterior pixelseed 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), scan line conversion seed filling + 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 ); GL_SMOOTH GL_FLAT GL_SMOOTH GL_FLAT glPolygonMode ( face, displayMode ); GL_FRONT GL_BACK GL_FRONT_AND_BACK GL_FRONT GL_BACK GL_FRONT_AND_BACK GL_LINE GL_POINT GL_FILL GL_LINE GL_POINT GL_FILL

Aliasing in CG Which is the better?

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.

32 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

34 Prefiltering

35 Prefiltering

Basis for Prefiltering Algorithms

Catmull’s Algorithm ABAB A1A1 A2A2 A3A3 Find fragment areas Multiply by fragment colors Sum for final pixel color

Prefiltering Example

39 Prefiltering So what’s the problem? Problem: most rendering algorithms generate sampled function directly –e.g., Z-buffer, ray tracing

40 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”.

41 Supersampling The process: 1.Create virtual image at higher resolution than the final image 2.Apply a low-pass filter 3.Resample filtered image

42 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

43 Supersampling: Worst Case Q: Give a simple scene containing infinite frequencies A: A checkered ground plane receding into infinity See next slide…

44

45 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."

47 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!

48 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

49 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

50 Stochastic Sampling Problem: given a pixel, how to distribute points (samples) within it? Grid Random Poisson Disc Jitter

51 Stochastic Sampling Poisson distribution: –Completely random –Add points at random until area is full. –Uniform distribution: some neighboring samples close together, some distant

52 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

53 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

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