Isometric and Oblique Projections
This domain tests pictorial projection: isometric axes and scale, isometric drawing of lines and curves, and oblique cavalier and cabinet projections. You need to distinguish an isometric drawing from an isometric projection.
Isometric
Three axes are 120° apart: one vertical and two at 30° to the horizontal. True lengths are used in an isometric drawing; an isometric projection uses the isometric scale of 0.816 (cos 35°16′). Circles appear as ellipses; on each face the major axis is perpendicular to the axis normal to that face. Non-isometric lines are located by their endpoints.
Oblique
The front face is drawn true shape and size. Receding edges are drawn at 30°, 45° or 60°. Cavalier uses full depth; cabinet uses half depth to reduce distortion.
Worked example
Draw a 30 mm cube isometrically. Draw a vertical edge 30 mm. From its top and bottom, draw two axes at 30° to the horizontal. Measure 30 mm along all three isometric axes and complete the parallelogram faces. If an isometric projection is asked, multiply every true length by 0.816: 30 × 0.816 = 24.5 mm. The reasoning is that isometric drawing preserves true lengths along axes, while projection foreshortens them equally.
Traps
Do not measure non-isometric edges at true length. Do not draw a circle as a circle on an isometric face. In oblique, the front face is true shape, but the depth is foreshortened in cabinet; mixing full and half depth is a common error. Keep all receding lines parallel to the chosen axis.