1. 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

2. Fundamentals of Computer Graphics
Graphics Systems
Five major elements - processor, memory, frame buffer, output devices, input devices
Fundamentals of Computer Graphics

3. 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
Fundamentals of Computer Graphics

4. Fundamentals of Computer Graphics
Output Devices
The cathode-ray tube CRT
Fundamentals of Computer Graphics

5. Fundamentals of Computer Graphics
Output Devices
RGB – shadow mask
Fundamentals of Computer Graphics

6. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

7. 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
Fundamentals of Computer Graphics

8. Fundamentals of Computer Graphics
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)
Fundamentals of Computer Graphics

9. 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
Fundamentals of Computer Graphics

10. Fundamentals of Computer Graphics
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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11. Fundamentals of Computer Graphics
Colours
Light is a form of electromagnetic radiation
Visible spectrum 350 – 780 nm
Fundamentals of Computer Graphics

12. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

13. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

14. Human Visual System - HVS
rods and cones (tyčinky a čípky) excited by electromagnetic energy in the range 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
Fundamentals of Computer Graphics

15. Human Visual System - HVS
Courtesy of
Fundamentals of Computer Graphics

16. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

17. Fundamentals of Computer Graphics
Human Visual System
three different cones in HVS
blue, green & yellow – often reported as red for compatibility with camera & film
Fundamentals of Computer Graphics

18. Fundamentals of Computer Graphics
Pinhole Camera
Box with a small hole
film plane z = - d
!!!yp,-d
Fundamentals of Computer Graphics

19. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

20. 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
Imaging system
Fundamentals of Computer Graphics

21. 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)
Fundamentals of Computer Graphics

22. Synthetic Camera Model
Imaging with the Synthetic Camera Model
film plane position in a camera
projected scene to the projection plane
Fundamentals of Computer Graphics

23. 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
Fundamentals of Computer Graphics

24. 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.
Fundamentals of Computer Graphics

25. 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
Fundamentals of Computer Graphics

26. 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
Fundamentals of Computer Graphics

27. 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
Fundamentals of Computer Graphics

28. 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
Fundamentals of Computer Graphics

29. 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
Fundamentals of Computer Graphics

30. 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
Fundamentals of Computer Graphics

31. 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
Fundamentals of Computer Graphics

32. 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
Fundamentals of Computer Graphics

33. Graphics Architectures
Display processors
standard architecture with capabilities to display primitives
composition made at the host
memory – display list – contains primitives to be displayed.
Fundamentals of Computer Graphics

34. 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
Fundamentals of Computer Graphics

35. 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
Fundamentals of Computer Graphics

36. 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.
Fundamentals of Computer Graphics

37. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

38. Fundamentals of Computer Graphics
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
Fundamentals of Computer Graphics

39. 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]
x,y,z coordinates of the j-th vertex
Fundamentals of Computer Graphics

40. Exercise No.1 – TRI format
[Triangles]
vertex indices forming the i-th triangle
2 4 5
5 4 6
………..
[Triangles' Normals]
i-th normal vector for the i-th triangle
…………………………………………..
Fundamentals of Computer Graphics