When they are collinear, projective spaces set with five pairs of biuni-vocally associated points are general. In order to map quadrics (II degree surfaces), in these spaces, the absolute conic was used. Geometrical position of all the absolute points in the infinitely distant plane of one space, i.e. an absolute conic of space cannot be graphically represented. To the infinitely distant planes are associated by the vanishing planes, and the absolute conics are associated by the conic in the vanishing planes, that is, figures of the absolute conics. Prior to mapping the quadrics, it is necessary to constructively determine the characteristics parameters such as the vanishing planes, axes and centers of space, and then the figures of the absolute conics, in the vanishing planes of both spaces. In order to constructively determine the figure of the absolute conic in the second space, a sphere in the first space was used, which maps into a rotating ellipsoid in the second space. The center of the sphere is on the axis of the first space, and the infinitely distant plane intersects it along the absolute conic. The associated rotational ellipsoid, whose center is on the axis of the seconds space is intersected by the vanishing plane of the first space along the imaginary circumference aI, whose real representative is circumference az. The circumference aI is the figure of the absolute conic of the first space. General collinear spaces are presented in a pair of Monge's projections.
Constructive procedure for determination of absolute conic figure in general collinear spaces
