Axonometric and cavalier perspectives
The isometric block asks you to read a dihedral drawing and rebuild it in three dimensions, or the reverse. Marks go to correct axis angles, consistent coefficients and properly oriented ellipses for circles.
Axonometric systems
Orthogonal axonometries project the object with the axes foreshortened: isometric (three equal axes, 120° apart), dimetric (two equal) and trimetric (three different). In true isometric projection every axis is reduced by 0.816, which is why a circle of diameter d becomes an ellipse with major axis d and minor axis 0.577d. In isometric drawing, the standard used in the exam, the full scale is used along the three axes; the resulting ellipse has major axis 1.22d and minor axis 0.71d, with the major axis perpendicular to the axis normal to the face containing the circle.
Cavalier (oblique) perspective
The front face is drawn true size with the X and Z axes at 90°; the Y axis is drawn obliquely, typically at 45° (also 30° or 60°) with a reduction coefficient of 0.5, sometimes 2/3 or 1 for a quick sketch. Circles parallel to the front plane stay true circles; circles in the receding planes become ellipses. The apparent depth is therefore a decision that must be stated, not improvised.
Construction routine
- Draw the axes with the correct angles.
- Mark the dimensions along the axes, never along the oblique edges of the figure.
- Close the parallelograms face by face and add the hidden edges of the solid.
- For circles, inscribe them in the isometric square (or parallelogram) and pass the ellipse through the midpoints of the sides, using the diagonal method for the eight points.
Worked example
Cube of 40 mm edge in isometric drawing. Draw the vertical axis and the two axes at 30° above the horizontal, measure 40 mm along each of the three and build the three visible faces as rhombi of 40 mm side; the hidden vertex is found by parallels. A circle of diameter 40 on the top face becomes an ellipse with major axis 48.8 mm, horizontal on the paper, and minor axis 28.4 mm, on the vertical direction.
Traps
Applying the 0.816 factor when the exam asks for isometric drawing at full scale; measuring along the oblique edges instead of parallel to the axes; drawing the isometric ellipses as compass ovals with wrong axes; forgetting the reduction coefficient in the cavalier Y axis, which makes the solid look stretched.