Fundamentals of Computer Graphics
Part 1
prof.ing.Václav Skala, CSc.
University of West Bohemia
Plzeň, Czech Republic
©2002
Prepared with Angel,E.: Interactive Computer
Graphics – A Top Down Approach with OpenGL,
Addison Wesley, 2001
Graphics Systems
Five major elements - processor, memory,
frame buffer, output devices, input devices
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Pixels and Frame Buffer
Most graphics systems are pixel based – need of rasterization or
scan conversion; pixel = picture element
8 bits deep frame – 256 colors; 24 or 32 bits for RGB colors
picture detail
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Output Devices
The cathode-ray tube CRT
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Output Devices
RGB – shadow mask
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Output Devices
Refresh rate: 50 – 85 Hz, for stereovision 120Hz (2 x60 Hz)
Mode: interlaced versus non-interlaced
Masks: DELTA versus INLINE
LCD Displays – raster based
Raster devices
– sequential access - plotters etc.
– direct access – displays etc.
– mixed – inkjet printers – printed sequentially, accessed directly
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Fundamentals of Computer Graphics
Images – Physical versus Synthetic
Computer graphics generates pictures with the aim of:
– to create realistic images
– to create images very close to “traditional” imaging methods
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Objects and Viewers
Two basic entities (one object seen from two different positions) :
– object(s) – exists in space independent of any image-formation process
or viewer
– viewer(s)
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Objects, Viewers & Camera
Camera system
– object and viewer exist in E3
– image is formed
• in the Human Visual system
(HSV) – on the retina
• In the film plane if a camera
is used
– Object(s) & Viewer(s) in E3
– Pictures in E2
Transformation from E3 to E2
projection
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Lights & Images
Others attributes:
– light sources
• position
• monochromatic / color
– if not used scene would be
very dark and flat
– shadows and reflections - very
important for realistic
perception
– geometric optics used for light
modeling
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Colours
• Light is a form of
electromagnetic radiation
• Visible spectrum 350 – 780 nm
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Ray Tracing
Ray tracing
– building an imaging model by
following light from a source
– a ray is a semi-infinite line
that emanates from a point
and “travels” to infinity in a
particular direction
– portion of these infinite rays
contributes to the image on
the film plane of the camera
surfaces:
– diffusing
– reflecting
– refracting
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Ray Tracing
A different approach must be used:
• for each pixel intensity must be
computed
• all contributions must be taken
into account
• a ray is “followed” in the
opposite direction, when
intersect a surface it is split into
two rays
• contribution from light sources
and reflection from other
resources are counted
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Human Visual System
- HVS
• rods and cones (tyčinky a čípky) excited by electromagnetic
energy in the range 350-780 nm
• sizes of rods and cones determines the resolution of HVS – our
visual acuity
• the sensors in the human eye do not react uniformly to the light
energy at different wavelengths
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Human Visual System - HVS
Courtesy of http://www.webvision.med.utah.edu/into.html
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Human Visual System
• different HVS response for single
frequency light – red/green/blue
• relative brightness response at
different frequencies
• this curve is known as
Commision Internationale de
L’Eclairage (CIE) standard
observer curve
• the curve matches the sensitivity
of the monochromatic sensors used in
black&white films and video camera
• most sensitive to GREEN colors
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Human Visual System
• three different cones in HVS
• blue, green & yellow – often
reported as red for compatibility
with camera & film
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Pinhole Camera
Box with a small hole
• film plane z = - d
y
yp  
z
d
x
xp  
z
d
!!!yp,-d
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Pinhole Camera
point (xp,yp,-d) –
projection of the
point (x,y,z)
angle of view or field
of the camera –
angle 
ideal camera –
infinite depth of
field
h
  2 arctan
2d
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Synthetic Camera Model
computer-generated image based
on an optical system –
Synthetic Camera Model
viewer behind the camera can
move the back of the camera –
change of the distance d
i.e. additional flexibility
objects and viewer specifications
are independent – different
functions within a graphics
library
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Imaging system
20
Synthetic Camera Model
a – situation with a camera
b – mathematical model – image plane moved in front of the camera
center of projection – center of the lens
projection plane – film plane (průmětna)
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Synthetic Camera Model
Imaging with the Synthetic Camera
Model
• film plane position in a camera
• projected scene to the projection
plane
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Synthetic Camera Model
Not all objects can be seen
limit due to viewing angle
Solution:
Clipping rectangle or clipping
window placed inn front of
the camera
ad b shows the case when the
clipping rectangle is shifted
aside – only part of the the
scene is projected
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Programmer’s Interface
• Numerous ways for user
interaction with a graphics
system using input devices
- pads, mouse, keyboards
etc.
• different orientation of
coordinate systems
canvas versus OpenGL etc.
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Application Programmer’s Interface
• API functionality should
match the conceptual
model
• Synthetic Camera Model
used for APIs like
OpenGL, PHIGS, Direct
3D, Java3D, VRML etc.
Functionality needed in the
API to specify:
• Objects
• Viewers
• Light sources
• Material properties
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Application Programmer’s Interface
• Objects are defined by
points or vertices, line
segments, polygons etc. to
represent complex objects
• API primitives are
displayed rapidly on the
hardware
• usual API primitives:
–
–
–
–
points
line segments
polygons
text
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Application Programmer’s Interface
OpenGL defines primitives through list of vertices – triangular
polygon is drawn by:
glBegin(GL_POLYGON);
glVertex3f(0.0, 0.0, 0.0);
glVertex3f(0.0, 1.0, 0.0);
glVertex3f(0.0, 0.0, 1.0);
glEnd( );
attribute GL_POLYGON actually defines the primitive to be
drawn – others
GL_LINE_STRIP - draws a strip –
n+1 points define n triangles
GL_POINTS – draws only points
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Application Programmer’s Interface
Some APIs :
• work with frame buffer – read/write pixel level
• provides curves & surfaces / approximated by a
series of simpler primitives
• OpenGL provides frame buffer, curves and surfaces
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Application Programmer’s Interface
Camera specification in APIs:
• position – usually center of lens
• orientation – camera coordinate
system in center of lens
camera can rotate around those
three axis
• focal length of lens determines
the size of the image on the film
actually viewing angle
• film plane - camera has a height
and a width
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Application Programmer’s Interface
Two coordinate systems are used:
• world coordinates, where the object is defined
• camera coordinates, where the image is to be produced
Transformation for conversion between coordinate systems or
gluLookAt(cam_x, cam_y,cam_z, look_at_x, look_at_y, look_at_z,…)
glPerspective( field_of_view)
Lights – location, strength, color, directionality
Material – properties are attributes of objects
Observed visual properties of objects are given by material and light properties
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Modeling - Rendering Paradigm
In many applications the modeling is separated from production
of an image – rendering (CAD systems, animations etc.)
In this case the modeling SW/HW might be different from the
renderer
the connection between both parts can be simple or highly
complex using distributed environments
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Graphics Architectures
Early graphics systems – CRT had just basic capability to
generate line segments connecting two points
• vector based with refreshing – length of line segments limited
light pen often used for manipulation
• systems with memory CRT – the whole picture redrawn if
changed
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Graphics Architectures
Display processors
• standard architecture with capabilities to display primitives
• composition made at the host
• memory – display list – contains primitives to be displayed.
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Pipeline Architectures
VLSI circuits enabled major advances in graphics architectures
- simple arithmetic pipeline a + b * c
- when addition of (b * c) and a is performing new b * c is
computed in parallel – pipelining enabled significant speed up
- similar approach can be used for processing of geometric
primitives as well
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Pipeline Architectures
There are 4 major steps in the geometric pipeline:
• transformations – like scaling, rotations, translation, mirroring,
sheering etc.
• clipping – removal of those parts that are out of the viewing
field
• projection
• rasterization
homogeneous coordinates and matrix operations geometric
transformations are used
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Clipping, Projection & Rasterization
• Clipping is used to remove those parts of the world that cannot
be seen.
• Objects representation is “kept” in 3D as long as possible.
After transformation and clipping must be projected to 2D
somehow
• projected objects or their parts must be displayed – and
therefore rasterized.
All those steps are performed on your graphics cards in haerware
nowadays.
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Conclusion
• Consider a standard camera with 36x24 mm film and having a
zoom 26 – 140mm. How the viewing angle or viewing field is
defined.
• what is the difference in viewing between cases a) and b)?
• answer question from Chapter 1
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Exercise No.1
The aim of the first experiment is:
• to read data of a complex geometric model defined by the
TRI format (routine for reading will be given)
• to store it in the data structure
• to display the model as a set of triangles as wire-model
(without shading, visibility)
• to explore other possibilities of drawing
– visible parts only by
– with constant shading
by setting some attributes
• to explore a possibility to create your own data model
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Exercise No.1 – TRI format
# (data originally from powerflip, not avalon)
# Object name : --- The canonical cow --# Number of triangles : 5804
# Number of vertices : 2905
[Vertices]
0.0 0.0 0.0
0.151632 -0.043319 -0.08824
0.163424 -0.033934 -0.08411
0.163118 -0.053632 -0.080509
x,y,z coordinates of the j-th vertex
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Exercise No.1 – TRI format
[Triangles]
123
245
546
………..
vertex indices forming the i-th triangle
[Triangles' Normals]
0.442 -0.167 -0.881 i-th normal vector for the i-th triangle
0.595 -0.088 -0.798
0.735 -0.093 -0.671
…………………………………………..
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