University of Palestine
Computer Graphics
ITGD3107
Presentation name :
Three Dimensional Viewing
Prepare:
Mohammed J. el-masre
Nidal M. El-Borbar
Supervision:
Dr. Sana'a
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Contents
3D Viewing
Camera Analogy
Viewing Pipeline
Camera Modeling w/ OpenGL
Projections
Types of Projections
Perspective Projection
Parallel Projection
Projection Matrix
Projection of Lines
3D Viewing with OpenGL
Matrix Modes
Three Dimensional Viewing
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3D Viewing
The steps for computer generation of a view of a three
dimensional scene are somewhat analogous to the
processes involved in taking a photograph.
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Camera Analogy
1.
2.
3.
Viewing position
Camera orientation
Size of clipping
window
Orientation
Window (aperture)
of the camera
Position
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Viewing Pipeline
The general processing steps for modeling and
converting a world coordinate description of a
scene to device coordinates:
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Viewing Pipeline
1.
Construct the shape of individual objects in a scene within modeling
coordinate, and place the objects into appropriate positions within the scene
(world coordinate).
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Viewing Pipeline
World coordinate positions are converted to viewing
coordinates.
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Viewing Pipeline
Convert the viewing coordinate description of the
scene to coordinate positions on the projection
plane.
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Viewing Pipeline
Positions on the projection plane, will then mapped
to the Normalized coordinate and output device.
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Camera Modeling w/ OpenGL
camera coordinate
system
viewport coordinate
system
glMatrixMode(GL_MODELVIEW)
...
device/screen
coordinate system
glViewport(0,0,xres,yres)
glMatrixMode(GL_PROJECTION)
...
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Projections
Once the view volume is
determined, a
projection
transformation will
convert the object in
the 3D view volume to
a 2D image on the
projection plane.
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Types of Projections
Perspective Projection
Parallel Projection
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Perspective Projection (1/2)




Give a realistic view of 3D objects, but does
not preserve shape of object or scale
Perspective images of parallel lines not
parallel with projection plane converge to a
point called vanishing point
Size of object is diminished with distance
Used in architectural, engineering, industrial
design, and advertising drawings
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Perspective Projection (2/2)
1-point perspective
Most popular
2-point perspective
3-point perspective
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Parallel Projection



Accurate and same-scale
measurements
Not realistic, and may require
multiple projections to get a
complete feeling of the object
Used in drawings of machine
parts and in working
architectural drawings
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Parallel Projection (3/3)
Isometric
Multi-view orthographic
cavalier
cabinet
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Oblique
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Projection Matrix (1/3)
y
Pp(xp,yp,d) = ???
P(x,y,z)
x
COP
= Mper/ort
Mort =
1
0
0
0
.
x
y
z
1
z
d
Mper =
xp
yp
d
1
1
0
0
0
0 0
1 0
0 1
0 1/d
0
0
0
0
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0 0
1 0
0 0
0 0
0
0
d
1
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Projection Matrix (2/3)
y
Pp(xp,yp,0) = ???
P(x,y,z)
x
COP
= Mper/ort
Mort =
1
0
0
0
.
x
y
z
1
z
d
Mper =
xp
yp
0
1
1
0
0
0
0 0
1 0
0 0
0 1/d
0
0
0
1
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0 0
1 0
0 0
0 0
0
0
0
1
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Projection Matrix (3/3)
Pp(xp,yp,0) = ???
Mgeneral =
x or y
COP
Q
1
0
0
0
0
1
0
0
–a/c
–b/c
–d/Q/c
–1/Q/c
da/c
db/c
d2/Q/c+d
d/Q/c+1
P(x,y,z)
z
d
(a, b, c)
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Projection of Lines
y
Parametric representation of a line that goes
through P(px, py, pz) and has direction c = (cx,
cy, cz)
x
l(t) = P+ct where t  (-, + )
The projected line is
x(t) = d(px+cxt)/(pz+czt)
COP
d
z
y(t) = d(py+cyt)/(pz+czt)
If the original line is parallel to the projection plane (cz = 0)
x(t) = d(px+cxt)/pz, y(t) = d(py+cyt)/pz, the slope of the projected line is cy/cx,
independent of the position of the original line. The projected lines of parallel lines
must be parallel
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3D Viewing with OpenGL




Viewing transformation: set the position and
orientation of the viewpoint
Modeling transformation: set the orientation of the
model (translate, rotate, scale)
Projection transformation: set the view volume and
do the projection
Viewport transformation: Set the viewport on the
computer screen where the scene will be drawn
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Matrix Modes



Modelview matrix
 Set the viewpoint and object location by modifying
this matrix
 glMatrixMode(GL_MODELVIEW)
If projection matrix is modified
 Specify the view volume by modifying this matrix
 glMatrixMode(GL_PROJECTION)
If texture matrix is modified
 glMatrixMode(GL_TEXTURE)
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References & External links
•http://en.wikipedia.org/wiki/3dviewing
•http://anonymouse.org/cgi-bin/anonwww.cgi/http://www.eazyupload.net/download/jtg3c0c6/0135309247.zip.htm
•http://eazy1.eazyupload.net/download/0ea47c0c7d5c5b872be23f3a8933086
3/0135309247.zip
•http://dl1.s24.ifile.it/9gtkix4c/prentice_hall__computer_graphics_c_version_2ed_-_hearn__baker.pdf
Our Book computer_graphics_c_version_2ed
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