P_16_10 @hotmail.com it4ever2008 @hotmail.com1 University of Palestine Computer Graphics ITGD3107...

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University of Palestine

Computer GraphicsITGD3107

Prepare:

Mohammed J. el-masre

Nidal M. El-Borbar

Supervision:

Dr. Sana'a

Presentation name :

Three Dimensional Viewing


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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 ModesThree 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

Position

Orientation

Window (aperture)

of the camera

1. Viewing position2. Camera

orientation3. Size of clipping

window


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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

glMatrixMode(GL_MODELVIEW)...

glMatrixMode(GL_PROJECTION)...

glViewport(0,0,xres,yres)

camera coordinatesystem

viewport coordinatesystem

device/screencoordinate system


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ProjectionsOnce 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)

3-point perspective

1-point perspective

2-point perspective

Most popular


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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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Oblique

Parallel Projection (3/3)

Isometric

cavalier cabinet

Multi-view orthographic


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Projection Matrix (1/3)

xp

yp

d1

xyz1

= Mper/ort .

1 0 0 00 1 0 00 0 1 00 0 1/d 0

Mper =

1 0 0 00 1 0 00 0 0 d0 0 0 1

Mort =

Pp(xp,yp,d) = ???

P(x,y,z)

dCOP

z

x

y


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xp

yp

01

xyz1

= Mper/ort .

1 0 0 00 1 0 00 0 0 00 0 1/d 1

Mper =

1 0 0 00 1 0 00 0 0 00 0 0 1

Mort =

P(x,y,z)

d

Pp(xp,yp,0) = ???

COP z

x

y


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P(x,y,z)

d

Pp(xp,yp,0) = ???

COP

z

x or y

Q

(a, b, c)

1 0 –a/c da/c0 1 –b/c db/c0 0 –d/Q/c d2/Q/c+d0 0 –1/Q/c d/Q/c+1

Mgeneral =


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Projection of Lines

dCOP

z

xy Parametric representation of a line that goes through P(px, py, pz) and has direction c = (cx, cy, cz)

l(t) = P+ct where t (-, + )

The projected line is

x(t) = d(px+cxt)/(pz+czt)

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/anon-www.cgi/http://www.eazyupload.net/download/jtg3c0c6/0135309247.zip.htm•http://eazy1.eazyupload.net/download/0ea47c0c7d5c5b872be23f3a89330863/0135309247.zip•http://dl1.s24.ifile.it/9gtkix4c/prentice_hall_-_computer_graphics_c_version_2ed_-_hearn__baker.pdf

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