Survey of the common conic beast of 2 pairs of conjunct virtual points - Part 1

Abstract

Plane conic beams have 3 types: beams with 4 real points, beams with 2 real points and 2 imaginary points, conic beams with 2 pairs of conjugated virtual points.Thearticle “Two flat conic beams share at least 2 real points in common, by the same author, has published in the journal of architectural science, number 47, 2023.As for the common cluster of 4 virtual points, surveyed in this article, the investigation also uses the synthesis method, algebraic and analytic implementations, done on the computer, and in my argument, it is done in the following way: cutting projections, projective transformations, but do not use analytical algebra. The drawings are also drawn using autolisp programming, written by themselves. The content of surveying plane conic beams with 2 pairs of virtual points is divided into parts. Part 1: apply the previous results of projective projection, and use part of the results ofthe oblique antipodal intersection transformation to establish the conics of the beam. Part 2 investigates the nominal transformation of the perpendicular antipodal intersection.special cases of plane conic beams with 2 pairs of conjugated virtual points.