Determination of intersecting curve between two surfaces of revolution with parallel axes by use of auxiliary planes and auxiliary spheres

Abstract

In this paper the space intersecting curve between two surfaces of revolution with parallel axes of surfaces have been determined. Two mathematical models for determination of intersecting curve between two surfaces of revolution have been formed: auxiliary planes have been used in the first mathematical model and auxiliary spheres have been used in the second model (Obradovic 2000). In the first case each auxiliary plane intersected with each surface of revolution on circle and two points of intersecting curve are obtained as intersecting points between these two circles. In the second case centres of two locks of auxiliary spheres are put on axes of surfaces of revolution (centre of first lock is on axis of the first surface of revolution and centre of second lock is on axis of the second surface of revolution) on saine z coordinate (when axes of surfaces of revolution are parallel with z axis of coordinate system). First lock sphere intersects the first surface of revolution on w1 parallels and second lock corresponding sphere intersects the second surface of revolution on w2 circles. It is possible to find a relationship that for selected radius of the first lock sphere can determine the radius of second lock sphere and real points of intersecting curve have been determined by use of these two spheres. The points of intersecting curve between two surfaces of revolution are obtained by intersection between w1 circles from the first surface with w2 circles from the second surface (Obradovic 2000).