Vol.3, No 2, 2005
pp. 235 - 242
UDC 514.752.2:681.3.06(045)=20
THE PLANE SECTION OF THE SURFACE OF
REVOLUTION
Ratko Obradović
University of Novi Sad, Faculty of Technical
Sciences, 21121 Novi Sad,
Serbia and Montenegro
Abstract. In this paper a procedure for
determining
a plane section of the surface of revolution was described. The surface
of revolution is given by an axis of the revolution and a meridian
which
is coplanar with the axis. The axis of revolution is parallel to the z
axis of the coordinate system. The intersecting plane is given by its
three
points; these are the points where the plane intersects axes x, y and
z.
For the determination of a plane section of the surface of revolution
we
can use horizontal planes which intersect the surface of revolution on
parallel circles and each auxiliary plane intersects the intersecting
plane
on the horizontal line. Two points of the intersecting space curve are
given as intersecting points between the horizontal line and the circle
and new points of the intersecting curve have been determined by using
several auxiliary planes.
Key words: the Surface of Revolution,
the Plane Section, Computer Geometry
RAVAN PRESEK ROTACIONE POVRŠI
U ovom radu je opisana procedura za određivanje
ravnog
preseka rotacione površi pomoću računara. Površ je zadata sa
meridijanom
i osom površi koji se nalaze u frontalnici, a osa površi je paralelna
sa
z osom koordinatnog sistema. Ravan ? koja seče površ je zadata sa svoja
tri osna traga. Za određivanje ravnog preseka rotacione površi
korišćene
su horizontalne pomoćne ravni koje rotacionu površ seku po paralelama,
a svaka pomoćna ravan seče ravan ? po horizontali. U preseku ove
horizontale
sa paralelom povši za istu pomoćnu ravan dobijaju se dve tačke
prostorne
presečne krive, dok se cela kriva dobija kao skup parova tačaka za sve
pomoćne ravni.
