Vol.1, No 10, 2003 pp. 1317 - 1326
UDC 515.173:535.317.24
STEREOMETRIC PROJECTION OF 3D AND 4D
OBJECTS IN CURVILINEAR PROJECTIVE SPACE
Risto Tashevski, Vladimir Dukovski
Faculty of Mechanical Engineering
The "Sts. Cyril and Methodius" University
P.O. Box 464, 1000 Skopje, Macedonia
E-mail: risto@mf.ukim.edu.mk
Abstract. In this paper a mathematical model and a computer program
for stereometric projection of 3D and 4D objects in curvilinear (hyperboloid
and paraboloid) projective spaces are presented. The aim of this projection
is a realistic presentation of objects in the human surrounding. This means
that the presented objects should not be different from the real ones.
In reality the objects are projected on the retina of the eye mechanism.
The retina does not have a regular geometric shape. The shape of the retina
could be approximated with a hyperboloid or paraboloid surface. The way
to the realistic visual presentation of objects is the stereometrical projection
in the curvilinear projective space. Stereometricaly projected objects
in various projective spaces presented on two-dimensional plane (paper,
monitor) are received by optical apparatus (stereoscope, glasses).
Key words: Stereometry (Stereo Geometry), Curvilinear
(Hyperboloid, Paraboloid) Projective Space, 3D And 4D Objects
STEREOMETRIJSKO PROJEKTOVANJE 3D I 4D
OBJEKATA U KRIVOLINIJSKIM PROJEKTIVNIM PROSTORIMA
Urađen je matematički model i kompjuterski program za stereometrijsko projektovanje
3D i 4D objekata u cilindričnom, sferičnom, elipsoidnom, hiperboloidnom
i paraboloidnom projektivnom prostoru. Cilj spomenutog projektovanja je
realno pretstavlanje objekata iz čovekove okoline. To podrazumeva da se
pretstavljeni objekti ne razlikuju od realnih. Objekti se projektuju na
mrežnici očnog mehanizma. Mrežnice nemaju pravilnu geometrijsku formu,
mogu se aproksimirati sa cilindričnom, sferičnom, elipsoidnom, hiperboloidnom
ili paraboloidnom površinom. Znači jedini način realnog vizuelnog prikazivanja
je stereometrijsko projektovanje u jednom od krivolinijskih projektivnih
prostora. Da bi se dobila tri dimenziona pretstava, stereometrijski projektovani
objekti u raznim projektivnim prostorima prezentovani na dvodimenzionoj
ravnini (hartija, ekran) uočavaju se pomoću optičkih aparata (stereoskop,
naočara).
Ključne reči: stereometrija, krivolinijski (elipsoidan, hiperboloidan,
paraboloidan) projektivni prostor.
