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EXPERIENCES OF VIRTUAL REALITY 
G.Fangi - G. Gagliardini - Ancona University - e.mail:fangi@poscsi.unian.it 
ISPRS COMMISSION VI WG 3 
KEY WORDS: Virtual reality, representation, computer vision, photogrammetry 
ABSTRACT: The virtual reality is a quick and intuitive method to reproduce and understand the reality, by moving it or moving 
around it. In the geodetic sciences virtual reality can help in representing the surveys or the objects of the surveys. The first step of 
the virtual reality is the multiple transformations. They can be obtained as concatenation of simple transformation called basic 
transformation. We examine the basic transformations that are the translation, the rotation, the reflection, the perspective and the 
projection. To include in a matrix any basic transformation, and to represent a point at infinity, homogeneous co-ordinates are used. 
After the scene transformations, the clipping takes place, say removing hidden lines. Finally to make realistic the object, the 
rendering is the final step. We present some examples of architectural surveys and their animation. 
1. The scene transformations 
A quick and intuitive method to reproduce the reality, by 
moving around it. 
The virtual reality reproduces these movements. 
As scene we intend the set of objects used to represent the 
reality. 
The scene transformations are the transformations applied to 
the scene to obtain these movements. 
To depict and represent three-dimensional objects on planes 
supports, has always created many problems to the craftsman 
and designers, because of the need to translate their ideas in 
understandable ‘formats’ by those who will be involved in 
the realisation of the project. The introduction of the 
computer is modifying the things. Actually it is possible to 
reproduce virtual models of the real objects and use them to 
represent the realty. A man placed in front of an unknown 
object, examines it by moving it. The scene transformation 
reproduces, virtually, this phenomenon. Actually a three- 
dimensional virtual reality doesn't exist, so that the three- 
dimensional model must be projected on a plane support, that 
generally is that of the screen. In this manner the information 
relative to the depth of the object, are lost. The scene 
transformations, permitting the motion of the virtual object, 
cope with this problem. 
In this paper we will examine these transformations, that in 
combination reproduce the motion of the object or the motion 
of the operator around the object. 
The representation of a point in the 3D space is got with a 
four dimensions vector, the homogeneous co-ordinates. The 
use of the homogeneous co-ordinates, is needed to represent 
points to infinity and to include a translation in a 
transformation matrix. It is sufficient that the fourth 
component of the vector is equal to zero to represent a point 
to infinity. The representation in homogeneous co-ordinates 
of a point of the 3D space is not unique. 
Note how the representation changes with the parameter h. 
For sake of representation, since the fourth component has 
been added to solve the inconvenient of the infinity, we pose 
h equal to the unity when the point is to the finite. Anyhow, 
independently from that, a 4x4 matrix must represent any 
transformation applied to a point in homogeneous co 
ordinates. In this manner: 
[hx, hy, hz, h] = [x,y,z, 1 ] [ T] (1) 
Rotations 
r 
Scale 
~a b c 
P 
d e f 
<1 
Translations 
g 1 J 
r 
~1 m n~ 
s 
Projections 
Factor of scale 
c. omog. 
where [T\ is the matrix of the transformation. Such a matrix 
in general will have the form: 
(2) 
In a general forma eqns. (1) represent the 3D transformations. 
Let’s analyse the transformations one by one. 
2. The basic transformations 
All the transformations can be arranged by matrix 
concatenation of small amount of them: the basic 
transformations: 
• translation 
• scale variation 
• shear deformations 
• rotation through one co-ordinate axis 
• reflection about one co-ordinate plane 
• Transformations of translation 
It is the simplest transformation. It moves the object, without 
modifying the form or the orientation respect to the reference 
system axes. We get a matrix having the general form (3): 
10 0 0 
0 10 0 
0 0 10 
l m n 1 
(3) 
The translated homogeneous co-ordinates are obtained by 
writing (3): 
By expansion of the products we have: 
[x' ,y',z',h]= [(* + /), (y + m), (z + H),l] (4) 
The transformed co-ordinates are (5): 
The present research has been financed by Cofm97