Geometric locus associated with thriedra axonometric projections. Intrinsic curve associated with the ellipse generated

Abstract

In previous work on the axonometric perspective, the authors presented some graphic constructions that allowed a single and joint invariant description of the relations between an orthogonal axonometric system, its related orthogonal views, and oblique axonometric systems associated with it. Continuing this work and using only the items drawn on the frame plane, in this communication we start from the three segments, representing trirectangular unitary thriedra, joined in the origin and defining an axonometric perspective. Each is projected onto any direction and the square root of the summa of the squares of these projections is determined. We call this magnitude, orthoedro diagonal whose sides would be formed by the three projections axonometric unit segments. If the diagonal size is built from the origin of coordinates and onto the direction used, this describes a locus here called intrinsic curve associated with the ellipse. When the starting three segments represent an orthogonal axonometric perspective, the intrinsic curve associated with the ellipse is a circle.