MAE : Lecture #5-2D Graphics

Transcription

1 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

2 Teaching Assistants: 1. Nidal A Al-Masoud Naa2@eng.buffalo.edu Office: 311 Jarvis Hall Office hours: Tuesday, Thursday: 11-1 Lab hours: none Newsgroup: sunyab.mae Kok-Lam Lai Klai2@eng.buffalo.edu Office: 1017 Furnas Hall Office hours: Tuesday, Thursday: 1-3 Lab hours: 8-10 Monday (139 Hochstetter), 3-5 Friday (1018 Furnas) 3. Pradeep Pinto Pjpinto@eng.buffalo.edu Office hours: none Lab hours: 8-10 Tuesday (1018 Furnas), 12-3 Thursday (139 Hochstetter) 4. Parijat Bhide Pbhide@eng.buffalo.edu Office: 1014 Furnas Hall Office hours: Monday, Wednesday: Lab hours: none

3 Instructor Office Hours: Dr. Chugh: Monday (10-11) Thursday (2-3) Dr. Hulme Tuesday (9-10) Thursday (9-10)

4 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)

5 Overview of computer graphics: End result: A 2D picture on a computer screen Often a projection of a 3D image Colors, 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)

6 Building Blocks: Representation - points (used to create polygons and lines, ) ex: unit square - represent by points/lines/polygons ex: VRML - indexed face set data

7 Preparing pictures for presentation Storage of picture (points) - data base To specify point position - use relative or absolute coordinates Related concern - integer coordinate word length (2 n-1-1) For 16 bit machine: wl = Can instead use homogeneous coordinates: Represent n-dimensional space with n+1 dimensions (x,y,z) - (x,y,z,h); h - homogeneous coordinate ex: for x = use: (30000, y/2, z/2, 1/2) (Less of a concern with 32-bit machines )

8 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

9 windowing (2D)

10 view frustum (3D)

11 Presenting previously prepared images (cont.) Multiple viewports in a single window (translation/scaling): Interaction Conventional: mouse, keyboard, tablet (CAD) Novelty: Joystick, track ball High-tech (VR): Haptic glove, wand

12 Coordinate systems: World/Global, Model/Local, Screen, Camera...

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

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

15 Bandwidth requirements Importance of communication speed: CPU and graphics device Example: Refresh a curved line with 250 segments: Refresh rate[(no. points)(no. coord./pt.)(no. sig figs./pt.)(no. bits/char.)] 30 frames/second 250 points 3 coords. (x,y,z) 1 8-bit byte per character = 1,080,000 bits/second bandwidth

16 Rasterization Conversion of primitive objects to a 2D screen image Determine which squares of an integer grid are occupied Assign color, and other values to the square Anti-aliasing - correction for inclined lines, which cause jagged lines Commonly called staircasing, in graphics

17 Rasterization - numerical methods for determining lit pixels A. 1st order: Pick coordinate with largest variation (assume x). Start at min value, and increment by 1. Use 1st order T.S.E. to approximate corresponding y. Then, round off for final value: x o = x a x 1 = x a y n yn 1 where : y x y x b b y x a a y x (1)

18 B. Parametric Approach: can yield a more uniform density for lines in arbitrary orientations Define an integer parameter n (a pixel density) Then: dx dn x b n x a ; dy dn y b n y a x n x n 1 dx dn ; y n y n 1 dy dn Round off to get pixel positions: x = [x n ], y = [y n ] Example (overhead)

19 Hardware: Frame buffering DEF: A large contiguous piece of computer memory which stores the image to be displayed Common example: 8 bit planes per color (RGB) - 24 total 256 (2 8 ) intensities of each color (2 8 ) 3 = 16,777,216 possible colors

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21 Hardware: Frame buffering (cont.) Pixel access time (nanoseconds): 1/(Frame buffer size x Desired screen resolution) (Typically, 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

22 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.