Isometric and Oblique Projections
Isometric
Isometric axes are 120° apart and drawn at 30° to the horizontal. Isometric projection foreshortens every axis to √(2/3) = 0.816 of true length, so an isometric scale marks 0.816 of each true length; isometric drawing uses full lengths along the axes and is the usual exam answer - same shape, larger size. Lines parallel to the axes follow the axes; non-isometric lines are located through their end points. Circles become ellipses: in an isometric drawing the major axis is 1.22d and the minor 0.71d, drawn by the four-centre method, with the major axis perpendicular to the axis of the face containing the circle.
Oblique
Oblique projection keeps the front face true shape and recedes along a single axis, usually 45° (30° and 60° are also used). Cavalier takes full scale on the receding axis, cabinet half scale. Circles on the front face stay circles; circles on receding faces become ellipses.
Worked example
A cube of 50 mm edge: its isometric drawing has edges of 50 mm at 30° to the horizontal; its isometric projection has edges of 50 × 0.816 = 40.8 mm. Whichever is asked, every dimension is set out along the three isometric axes, never along a slanted edge.
Traps
Scaling along non-isometric lines; drawing axes at 45° instead of 30°; showing hidden edges in an isometric view (normally omitted); turning the ellipse the wrong way for the top face; drawing cabinet receding edges at full length instead of half.