Two Generalizations of the Isometric Projection in Geometric Design

Abstract

The well-known pictorial drafting technique of isometric drawing is here generalized in two ways, called “isoclinal” and “axial,” or collectively, “symmetric.” Although the isoclinal projection preserves the useful property of foreshortening adjacent edges equally, and the axial projection foreshortens adjacent normals equally, the directions for these projections usually differ from that for isometric projection. Formulas are derived for the isoclinal and axial directions and their foreshortening factors and rotation matrices. Although intended for three-dimensional computer-aided design, the symmetric projections also can be performed on a drawing board with a protractor. Graphic examples involving design of nonrectangular connectors for three skew structural members and adjacent plates in space are presented.