Related is the same author's axonometric calculator.
This page is based on a suggestion from technical illustrator David Akawie.
Introduced in this report are protractors for use in the axonometric projections of technical drawing, where the projection of a circle becomes an ellipse.
These protractors differ from those of the same author's elliptical protractor page, where the ellipse might be independent of any axonometric context.
Throughout this report, all angles are in degrees, even if not marked. By contrast, radians are rarely useful for this kind of illustrative work.
Figure one shows an axonometric projection of a unit cube in standard orientation, with names given to several of its measures.
figure one |
legend |
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Figure two, below, explains the rationale for the design of the axonometric protractor segments. Each of the segments (drawn in brown) represents an angle of 90 degrees in three-dimensional space, but appears to subtend a larger or smaller angle in this two-dimensional axonometric projection. Each protractor is drawn as lying on the face of a unit cube, in standard orientation, whose edges are reduced in the scale ratio indicated.
The protractors are intended for use in any plane parallel to a face of the standard cube. Any other plane, in other words an oblique plane, would require a different protractor.
figure two | |
apparent angle: 90 − RI = 49° | apparent angle: 90 + RI = 131° |
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apparent angle: 90 − LI = 75° | apparent angle: 90 + LI = 105° |
apparent angle: 90 − CI = 56° | apparent angle: 90 + CI = 124° |
one side up | other side up | |||||
LI | CI | RI | LI | CI | RI | |
---|---|---|---|---|---|---|
15° | 34° | 41° | 15° | 41° | 34° | |
34° | 41° | 15° | 34° | 15° | 41° | |
41° | 15° | 34° | 41° | 34° | 15° |