mae 473-573: lecture #5 - 2d graphics€¦ · mae 473-573: lecture #5 - 2d graphics • overview of...

MAE 473-573: Lecture #5 - 2D Graphics

Lecture Overview:

• Lecture motivation• Overview of computer graphics• Building Blocks• Screen vs. world vs. model coordinates• Basics of Projection• 2D windowing and clipping• Viewport and view frustum• Bandwidth requirements• Rasterization• Frame buffering• Next up: Programmatic generation of 2D graphics using X

Assignment #2 - 2D Graphics exercise - delayed


Teaching Assistants:

Newsgroup: sunyab.mae.573

1. Nidal A [email protected]: 311 Jarvis HallOffice hours: Tuesday, Thursday: 11-1Lab hours: none

2. Kok-Lam [email protected]: 1017 Furnas HallOffice hours: Tuesday, Thursday: 1-3Lab hours: 8-10 Monday (139 Hochstetter), 3-5 Friday (1018 Furnas)

3. Pradeep [email protected] hours: noneLab hours: 8-10 Tuesday (1018 Furnas), 12-3 Thursday (139 Hochstetter)

4. Parijat [email protected]: 1014 Furnas HallOffice hours: Monday, Wednesday: 10-12Lab hours: none


Instructor Office Hours:

Dr. Chugh: Monday (10-11)Thursday (2-3)

Dr. Hulme Tuesday (9-10)Thursday (9-10)


Lecture Motivation:

• This class: programmatic generation of computer graphics

• Understand the basics of how graphics appear on a computer screen

• Prepare for more complex graphics operations (transformations)


• Overview of computer graphics:

End result: A 2D picture on a computer screenOften a projection of a 3D imageColors, lighting, intensity, (depth)

Must understand how:

• pictures are represented• pictures are prepared for presentation• previously prepared pictures are represented• interaction with picture is accomplished

(Picture: collection of points/lines/text displayed on a screen)


• Building Blocks:

• Representation - points (used to create polygons and lines, … )

ex: unit square - represent by points/lines/polygons

ex: VRML - indexed face set data

• Preparing pictures for presentation

Storage of picture (points) - data baseTo specify point position - use relative or absolute coordinatesRelated concern - integer coordinate word length (2n-1 -1)For 16 bit machine: wl = 32767… … …

Can instead use homogeneous coordinates:Represent n-dimensional space with n+1 dimensions(x,y,z) - (x,y,z,h); h - homogeneous coordinateex: for x = 60000 - use: (30000, y/2, z/2, 1/2)

(Less of a concern with 32-bit machines… )


• Presenting previously prepared images

Display file - some portion of the entire scene (clipping)

Displayed picture: rotated, translated, scaled, projected, … (not static)

Result: (compound) Transformation matrix

Then: hidden line removal, shading, transparency, textures, colors, ...

Windowing - the portion of the scene that is seen



windowing (2D)


view frustum (3D)

• InteractionConventional: mouse, keyboard, tablet (CAD)Novelty: Joystick, track ballHigh-tech (VR): Haptic glove, wand


• Presenting previously prepared images (cont.)

Multiple viewports in a single window (translation/scaling):


• Coordinate systems:

World/Global, Model/Local, Screen, Camera...


• Basics of Projection - defines the viewing volumePerspective - uses foreshortening (~ distance from viewpoint)Implements a view frustum:


Orthographic - uses a viewing volume, which has static sizeUsed in CAD/Architecture, where object size/angles are crucial


• Bandwidth requirements

Importance of communication speed: CPU and graphics deviceExample: Refresh a curved line with 250 segments:

Refresh rate[(no. points)(no. coord./pt.)(no. sig figs./pt.)(no. bits/char.)]

30 frames/second250 points3 coords. (x,y,z)1 8-bit byte per character

= 1,080,000 bits/second bandwidth


• RasterizationConversion of primitive objects to a 2D screen imageDetermine which squares of an integer grid are occupiedAssign color, and other values to the square

Anti-aliasing - correction for inclined lines, which cause jagged linesCommonly called “staircasing”, in graphics

• Rasterization - numerical methods for determining “lit pixels”


A. 1st order:

Pick coordinate with largest variation (assume x). Start at minvalue, and increment by 1. Use 1st order T.S.E. to approximatecorresponding y. Then, round off for final value:

ab

ab

1nn

xxyy

xy

:where

)1(xyyy

???

??

???? ?xo = xa

x1 = xa+1...

B. Parametric Approach: can yield a more uniform densityfor lines in arbitrary orientations

Define an integer parameter n (a pixel density)Then:

Round off to get pixel positions: x = [xn], y = [yn]

Example (overhead)


dndyyy;

dndxxx

nyy

dndy;

nxx

dndx

1nn1nn

abab

????

????

??


Hardware: Frame buffering

DEF: A large contiguous piece of computer memory whichstores the image to be displayed

Common example:

8 bit planes per color (RGB) - 24 total256 (28) intensities of each color(28)3 = 16,777,216 possible colors

Pixel access time (nanoseconds):

• 1/(Frame buffer size x Desired screen resolution)(Typically, 30-60 Hz is required for smooth visuals… )

• ex: 512 x 512 element square raster, 30 Hz:1/(512 x 512 x 30) = 127 nanoseconds

• Resolution degradation at 1024 x 1024:1/(1024 x 1024 x res) = 127 ns; res = 7.5 Hz.

Q: Relevance? A: “The battle of the clock” - detail vs. performance


Hardware: Frame buffering (cont.)


Next up: Programmatic generation of 2D graphics using X

You build the entire graphics scene from the ground up

Programmatic control over:• Viewing (“positioning the tripod”) • Modeling (“designing the scene”)• Projection (“adjusting the camera lens”) • Viewport (“take the photograph”)

Will incorporate translation, rotation, scaling, etc… .

mae 473-573: lecture #5 - 2d graphics€¦ · mae 473-573: lecture #5 - 2d graphics • overview of...

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