Vol. 5, No 1, 2007
pp. 49 - 59
UDC 514.757(045)=111
DETERMINATION OF THE CHARACTERISTIC PARAMETERS
IN THE SPECIAL COLLINEAR SPACE IN THE GENERAL
CASE
Sonja Krasić, Miroslav Marković
University of Nis, The Faculty of Civil Engineering
and Architecture, Serbia
Abstract. The projective space consists of
the finitely and infinitely distant elements. The special collinear spaces
in the general case, are set with five pairs of biunivocally associated
points, so the quadrangle in the first space obtained by the three principal
and one penetration point of the remaining two through the plane of the
first three identical or similar to the associated quadrangle obtained
in the same way in the second space. In order to associate two special
collinear spaces, it is necessary to determine the following characteristic
parameters: vanishing planes, space axes (principal normal lines), foci
(apexes of the associated identical bundles of straight lines) and directrix
plane (associated identical fields of points). The paper is based on constructive
processing of the special collinear spaces in the general case. The structural
methods which are used are Descriptive Geometry (a pair of Monge’s projections)
and Projective geometry.
Key words: special collinear
spaces, vanishing planes, axes, foci and directrix planes of space
ODREDJIVANJE KARAKTERISTIČNIH
PARAMETARA U
SPECIJALNIM KOLINEARNIM PROSTORIMA U OPŠTEM
SLUČAJU
Specijalni kolinearni prostori u opštem položaju
zadati su sa pet parova jednoznačno (biunivoko) pridruženih tačaka,
čiji je položaj specijalno podešen. I u ovim prostorima potrebno je
da se odrede karakteristični parametri: nedogledne ravni, ose prostora,
žiže prostora, (temena pridruženih identičnih svežnjeva pravih) i
direktrisne ravni, (pridružena identična polja tačaka). žiže i direktrisne
ravni u specijalnim kolinearnim prostorima u opštem položaju postoje,
{to je na konstruktivan način dokazano u ovom radu, u paru Monžovih projekcija.
