Computer GraphicsComputer Graphics

Chapter 6Chapter 6

Andreas SavvaAndreas Savva

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Interactive GraphicsInteractive Graphics

Graphics provides one of the most natural means of communicating with a computer.

Interactive computer graphics permits user-computer interaction.

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Graphics SoftwareGraphics Software

Programming packages (OpenGL)Designed for programmers

General-Purpose Applications packages (Paint)

Designed for non-programmers

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Graphics FunctionsGraphics FunctionsA general-purpose graphics package provides users with a variety of functions for creating and manipulating pictures. These routines can be categorized according to whether they deal with:

Output

Input

Attributes

Transformations

Viewing

General control

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Output PrimitivesOutput Primitivesbasic tools for constructing picturesbasic tools for constructing pictures

Character strings

Geometric entitiesPoints

Straight lines

Curved lines

Filed areas (Polygons, Circles, etc)

Shapes defined with arrays or color points

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AttributesAttributesproperties of the output primitivesproperties of the output primitives

Intensity Color specifications Line styles Text styles Area-filling patterns

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Geometric TransformationsGeometric Transformationssize, position and orientation of an object within the scenesize, position and orientation of an object within the scene

Translate Scale Rotate

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Control OperationsControl Operations

Clearing a display screen Initialize a parameter

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Software StandardsSoftware Standards

Primary goal – portability Software can be moved easily from one

hardware system to another Software can be used in different

implementations and applications Without standards, software need to be

rewritten for different systems

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A simple Paint ProgramA simple Paint ProgramIt should have the ability to work with geometric objects such as line segments and polygons. Given that geometric objects are defined through vertices, the program should allow us to enter vertices interactively.It should have the ability to manipulated pixels, and thus to draw directly into the frame buffer.It should provide control of attributes such as color, line type, and fill patterns.It should include menus for controlling the application.It should behave correctly when the window is moved or resized.

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Coordinate RepresentationsCoordinate RepresentationsModeling coordinates: (xm , ym)

World coordinates: (xw , yw)

Normalized coordinates (Range: 0 - 1): (xn , yn)

Device coordinates: (xd , yd)

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World to DeviceWorld to Device

hDeviceWidt

MinXMaxXxScale ww

htDeviceHeig

MinYMaxYyScale ww

xScale

MinXxx ww

d

(xw ,yw) (xd ,yd)

Display area

yScale

MinYyy ww

d

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World to NormalizedWorld to Normalized

ww

wwn MinXMaxX

MinXxx

ww

wwn MinYMaxY

MinYyy

Normalized to DeviceNormalized to DevicehDeviceWidtxx nd

htDeviceHeigyy nd

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Device CoordinatesDevice Coordinates

(xw ,yw)

(xd ,yd)

Display area(xd ,DeviceHeight-yd)

(0,0)

(0,0)

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ExercisesExercises

Assume that the screen monitor has 1200800 pixels. Find and display:

(0,0)

(1200,800)

1. the device coordinates for the point (-18,12) if the display area is -25 ≤ x ≤ 8 and -8 ≤ y ≤ 16, as shown below:

2. the device coordinates for the point (-18,12) if the display area is -216 ≤ x ≤ -2 and -30 ≤ y ≤ 30.

(-18,12)

Display area

8-25

-8

16

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3. the device coordinates for the triangle shown in the figure below, by using the normalized coordinates which you should calculate first.

4. the device coordinates for the triangle shown above if the display area is 25 ≤ x ≤ 100 and -5 ≤ y ≤ 40. You should also find the device coordinates for the two points where the triangle sides intersect the line x = 25.

5. the world coordinate of the pixel (400,167) for the display area in question 1.

(35,30)

Display area

5010-5

40

(43,15)(18,10)

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Pipeline Vs ParallelismPipeline Vs Parallelism

Multiprocessing has two basic forms:A pipeline processor contains a number of processing elements (PEs) arranged such that the output of one becomes the input of the next, in pipeline fashion.

The PEs of a parallel processor are arranged side-by-side and operate simultaneously on different portions of the data.

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Drawing PipelineDrawing Pipeline

Standard drawing process uses a pipeline of computations

Starts with: Collection of polygons Ends with: Image stored in frame buffer

(Desired result)

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PipelinePipelineInput device

Model traversalnew view of the model

Model transform

Viewing transform

Clipping

Project & Map to Viewport

Lighting

Shading

Rasterization

Display

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Model TraversalModel Traversal

Data structure of Polygons Each polygon in own coordinate system List:

01

2

3

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Modeling TransformationsModeling Transformations

Move each polygon to its desired location

Operations: Translate, Scale, Rotate

01

2

3 x

y

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ClippingClipping

Viewport is the area of the Frame Buffer where the new image is to appear

Clipping eliminates geometry outside the viewport

Viewport

Clipping

ResultingPolygon

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Project & Map to ViewportProject & Map to Viewport

Projection takes 3D data and flattens it to 2D

Eye

Projection Plane(Screen)

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LightingLighting

Simulate effects of light on surface of objects

Each polygon gets some light independent of other objects

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ShadingShading

Lighting could be calculated for each pixel, but that’s expensive

Shading is an approximation:Gouraud shading: Light each vertex

Interpolate color across pixels

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RasterizationRasterization

Find which pixels are covered by polygon:

Plane Sweep: For each polygongo line-by-line from min to max

go from left boundary to right boundary pixel by pixelFill each pixel (color & density)

2D Process