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Graphics-1
Gentle Introduction to Computer Graphics
• Based on:– David Brogan’s “Introduction to Computer
Graphics” Course Slides, University of Virginia
– Jack van Wijk’s “Computer Graphics” Course Slides, University of Eindhoven.
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Outline
• Graphics Applications
• What is Computer Graphics
• Representations in Graphics
• Supporting Disciplines
• Introduction to 2d Modeling Transformations
• Matrix Representations
• Linear Transformations
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Graphics Applications
• Entertainment: Cinema
Pixar: Monster’s Inc.
A Bug’s Life (Pixar)
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Graphics Applications
• Medical Visualization
MIT: Image-Guided Surgery Project
Th
e V
isib
le H
um
an
Pro
jec
t
Graphics-5
Graphics Applications
• Everyday use
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Graphics Applications
• Scientific Visualization
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Graphics Applications
• Computer Aided Design (CAD)
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Graphics Applications
• Training
Designing Effective Step-By-Step Assembly Instructions (Maneesh Agrawala et. al)
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Graphics Applications
• Games
GT Racer 3
Polyphony Digital: Gran Turismo 3, A Spec
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Graphics Applications
• Games
Circus Atari (Atari)
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What is Computer Graphics?
• Computer graphics: generating 2D images of a 3D world represented in a computer.
• Main tasks:– modeling: (shape) creating and representing
the geometry of objects in the 3D world– rendering: (light, perspective) generating 2D
images of the objects– animation: (movement) describing how
objects change in time
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What is Computer Graphics?
ImageMath. ModelImage Analysis(pattern recognition)
Image Synthesis(Rendering)
Modeling Image processing
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Representations in graphics
Vector Graphics
• Image is represented by continuous geometric objects: lines, curves, etc.
Raster Graphics
• Image is represented as a rectangular grid of colored pixels
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Vector graphics
• Graphics objects: geometry + color
• Relatively low processing time– in terms of the number of graphic objects
• Geometric transformation possible without loss of information (zoom, rotate, …)
• Examples: PowerPoint, CorelDraw, ...
Graphics-15
Raster graphics
• Generic
• Image processing techniques
• Geometric Transformation: loss of information
• Relatively high processing time– in terms of the number of pixels
• Realistic images, textures, ...
• Examples: Paint, PhotoShop, ...
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Supporting Disciplines
• Computer science (algorithms, data structures, software engineering, …)
• Mathematics (geometry, numerical, …)
• Physics (Optics, mechanics, …)
• Psychology (Colour, perception)
• Art and design
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Introduction to Modeling Transformations
• Specify transformations for objects – Allows definitions of objects in own
coordinate systems– Allows use of object definition multiple
times in a scene
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2D Modeling Transformations
ScaleRotate
Translate
ScaleTranslate
x
y
World Coordinates
ModelingCoordinates
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Scaling
• Scaling a coordinate means multiplying each of its components by a scalar
• Uniform scaling means this scalar is the same for all components:
2
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• Non-uniform scaling: different scalars per component:
• How can we represent this in matrix form?
Scaling
X 2,Y 0.5
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Scaling
• Scaling operation:
• Or, in matrix form:
by
ax
y
x
'
'
y
x
b
a
y
x
0
0
'
'
scaling matrix
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2-D Rotation
(x, y)
(x’, y’)
x’ = x cos() - y sin()y’ = x sin() + y cos()
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2-D Rotation
• This is easy to capture in matrix form:
• Even though sin() and cos() are nonlinear functions of ,– x’ is a linear combination of x and y– y’ is a linear combination of x and y
y
x
y
x
cossin
sincos
'
'
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2-D Translation
(x, y)
(x’, y’)
x’ = x + txy’ = y + ty
tx
ty