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CG-IDC 1
Computer Graphics
• Instructor: Oren Kapah
• Office Hours: T.B.A.
The slides for this course were created by Toky & Hagit Hel-Or
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CG-IDC 2
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CG-IDC 3
Exercise and Homework
• The exercise will cover practical
aspects of the material taught in class.
• OpenGL will be covered in the
exercise.
• Homework will be written in OpenGL
and Java
• Homework may be submitted in pairs
(No triplets).
• In general - two weeks due date.
• No exercise this week.
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CG-IDC 4
Grading Policy:
• 50% homework assignments+50% exam.
• Homework assignments are weighted.
• Exam will include class and exercise
material.
• Homework appeals can be submitted no
later than one week after they’re returned!
IMPORTANT!
You must pass the exam in order to pass
the course.
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CG-IDC 5
Course Web site:
• Lessons (PDF format).
• Homework.
• Handouts and program examples.
• Grades.
• News.
• Mailing Group
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CG-IDC 6
Books
Computer Graphics
Hearn and Baker
Second Edition, Prentice Hall, 1994.
Computer Graphics Principles and Practice,
Foley, Van Dam, Feiner, and Hughes
Second Edition, Addison Wesley, 1996.
Mathematical Elements for Computer
Graphics
Rogers and Adams
Second edition, McGraw-Hill, 1990.
• OpenGL SuperBible
S. Richard, JR Wright, M. Sweet
Waite Group Press
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CG-IDC 7
Goals:
• Implementing Practical Math.
• Getting acquainted with
graphical models, basic
techniques, and algorithms.
• Getting acquainted with a
Graphical Language (OpenGL).
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CG-IDC 8
The Visual Sciences
Computer
Vision
Rendering
ImageImage
Processing
Model
3D Object
Geometric
Modeling
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CG-IDC 9
Context
• Image Processing: images => images
• Computer Vision: images => models
• Computer Graphics:
– Geometric Modeling: object => models
– 3D-rendering: 2D/3D models =>images
– Animation: 4D models => images.
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CG-IDC 10
Applications
• CAD - Computer Aided Design (mechanical,
architectural)
• Simulators (flight, driving)
• Architectural visualization
• Advertising
• Virtual Reality
• Art
• Games
• Special effects
• Education
• Scientific visualization
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CG-IDC 11
Tin Toy – Pixar 1988
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CG-IDC 12
Rendered image
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CG-IDC 13
Rendered image
Lighting
Geometry
Viewing
Material properties
&Texture
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CG-IDC 14
Reality – Non realistic rendering
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CG-IDC 15
Photo-realistic rendering
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CG-IDC 16
Non-realistic rendering
Pensive - 2000
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CG-IDC 17
Illumination & Color Models. object’s surfaces physical properties
Solid modelingObject’s Geometrical properties
Objects:
Camera:
Projections
Light Source:
Color
theory
Spatial set-up:
3D transformations,
Coordinate Systems.
Y
XZ
Y
Viewing Factors
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CG-IDC 18
Scope and Course Flow:
• 2D Drawing.
• Vector analysis.
• 2D transformations.
• 2D viewing.
• 3D transformations.
• 3D Modeling.
• 3D viewing
• Color Models.
• Shading Models.
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CG-IDC 19
Drawing in 2D
Goal: Getting acquainted with images.
• Displays types (raster vs. vector).
• Basic image definitions:
– Pixel, Resolution, dynamic range…
• Scan conversion:
– Techniques for Line drawing
– Techniques for drawing circles.
– Fill polygons.
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CG-IDC 20
Vector Analysis
Goal: Refreshing Linear Algebra basics.
• Mathematical entities:
– Scalar, Points, Vectors.
• Fundamental operations:
– point+vector, vector+vector,
vector*scalar, dot product, cross product,
etc.
• Vector representation - the basis.
• Point representation - the frame.
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CG-IDC 21
Transformations in 2D
Goal: Introduction to 3D.
• Basic 2D transformations:
– Translation, Scaling, Rotation, Shear.
• Composition of transformations and
transformation groups:
Rigid
Affine
Similarity
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CG-IDC 22
• Transformations in Matrix notation:
• Composition of transformations in
matrix notation.
• The homogeneous coordinates in 2D:
• Change of coordinates:
y
x
dc
ba
y
x
'
'
x
y
x’y’
),,(),,(),( ttytxWYXyx
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CG-IDC 23
Viewing in 2D
Goal: Preperation to 3D and some
rendering concepts.
• Viewing transformation pipe-line:
• Line and Polygon Clipping techniques:
x world
y world
Clipping
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CG-IDC 24
Transformations in 3D
Goal: Geometrical transformations to be
used in viewing pipe-line.
• Similar to 2D but in 3D.
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CG-IDC 25
Viewing in 3D
Goal: Geometrical transformations in
viewing pipe-line.
• From Model coordinates to Viewer
coordinates.
yw
zw
xw
world
P0
xv
yv
zvViewer
System
Body
System
Front-
Wheel
System
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CG-IDC 26
• Projections:
– Orthographic.
– Oblique.
– Perspective.
• The Viewing Volume:
zv
far
near
yv
xv
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CG-IDC 27
Solid Modeling
Goal: Learn how to define solid objects.
• 1D Curves in 3D
– Primitive based: line segments.
– Free form:
• Implicit, Explicit, Parametric (polynomials,
splines)
• 2D Surfaces in 3D
– Primitive Based: Polygon mesh.
– Free Form: As above
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CG-IDC 28
• 3D volumes in 3D
– Volume Rep.
• Sweep volumes
• Spatial Occupancy(voxels, Octree, BSP)
• Constructive Solid Geometry
– Boundary Rep.
• Polyhedra
• Free form: as above
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CG-IDC 29
Approximated/Interpolated
Parametric Surfaces
• Bilinear interpolation.
• Splines:
– Cardinal spline.
– Hermite spline.
– Bezier Spline.
– B spline.
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CG-IDC 30
y
x
650
610
590
550
570
600
580
560
540
505
500
510
520530
490
495
485
480
470450
1.00.50.0
0.5
0.9
green
yellow-green
yellow
orange
red
magenta
purple
blue
cyan white
pink
Goal: Understanding what a color is.
• The Trichromatic Color Theory.
• Linear color space and color
representations: RGB, CMY,HSB.
• Perceptual color spaces: LAB,YIQ.
• The CIE Chromaticity Diagram.
Color Theory
R
G
B
Brightness
Hue
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CG-IDC 31
Illumination Models &
ShadingGoal: Understanding the physical properties of
an object.
• Light source parameters (shape,
position, color, intensity).
• Surface parameters: Ambient, diffuse,
specular.
• Polygon Rendering methods.
• Transparency.
• Shadow.
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CG-IDC 32
Ambient, Diffuse, and
Specular components
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Composition of Light
Sources
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CG-IDC 35
Image based lighting - 2000
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CG-IDC 36
Example: A Sequence of creating
an images from a given model.
(from Foley Van Dam)
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CG-IDC 37
Polygonal model generated from spline patches.
Orthographic projection
Polygonal model generated from spline patches.
Perspective projection
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CG-IDC 38
Depth cueing.
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CG-IDC 39
Colored vectors.
Depth Clipping
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CG-IDC 40
Hidden line removal
Visible surface determination with ambient illumination
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CG-IDC 41
Individually shaded polygon with diffuse reflection
Gouraud shaded polygon with diffuse reflection
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CG-IDC 42
Gouraud shaded polygon with specular reflection
Phong shaded polygon with specular reflection
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CG-IDC 43
Curved surfaces with specular reflection
multiple lights
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CG-IDC 44
Texture mapping
shadows
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CG-IDC 45
Final image
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CG-IDC 46
Pixar 1986 – best of Siggraph 1986
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CG-IDC 47
Real time – off line rendering
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CG-IDC 48