Exercise 3.1: Cube & Cylinder: Planometric Projections by Hand

Cube: planometric projection at 45° angles:

I started with drawing a horizontal line and first, smaller square at 45° angles to the horizontal line. After that I drew diagonal lines through the middle of my square, in order to measure the bigger square measuring 4mm away from outside corners of the smaller square (fig. 1).

Fig. 1

Then I measured 4mm outside of two corners and marked them on the diagonal line. After that I connected the points (Fig . 2).

Then I connected remaining points while measuring and ensuring I retain 90° angles using my set square (quite handy these guides on see through set squares). Fig 3 below shows it didn’t go quite to plan, but I realised and amended by marking 4mm outside bottom corner of square and redrawing the line while ensuring the right angle (Fig. 4)

Then I drew vertical lines to ‘explode’ my cube up and using compass to measure the distance from each corner I marked its height (Fig. 5).

Fig. 5

After that I connected the remaining lines, erased what should not be visible and my finished drawing can be seen in Fig. 6. It reminds me of art deco pattern when looked at straight on.

Fig. 6

Cube: planometric projection at 30°/60° angles:

I started by drawing a horizontal line and then left line at 30° and right one at 60° (Fig.7).

Fig. 7

Then I used my compass to measure and mark the lengths of the squares lower sides. After that I marked the top corner of the square measuring with compass from the marked criss-cross points (Fig. 8)

Fig. 8

I drew my lines longer on purpose for easy marking with compass (Fig. 9)

Fig. 9

Then I connected the edges of larger square while measuring the right angles (fig. 10).

Fig. 10

After that I erased ‘internal’ lines between the squares and drew vertical lines at 90° to the horizontal line (Fig. 11). I must admit it all looked a bit skew to me at this point, but I carried on anyway.


I measured and marked ‘top’ squares using compass again (Fig. 12 and Fig. 13). I find using compass much more accurate than measuring same distances with a ruler each time.

I connected corners of lower and upper larger squares. It looked even more off at this point. (Fig. 14)

Fig. 14

I erased non-visible lines and Fig.15 shows the result of the process. Looks better and less skew than with all the lines in place.

Fig. 15

Cylinder: planometric projection:

I drew my cylinder in a slightly different way than the course book instructed but I measured my radius at 1500mm (in scale 1:50) so my smaller circle would fit inside square 3000 x 3000mm.

I started with drawing horizontal line, then a line at 90° angle to it. I measured the radius of my circle on that last line, marked it and drew my circle from there (Fig 16).

Fig. 16

After that I marked the middle of upper circle and drew it using same measurements as for lower circle. Then I changed my radius (extra 200mm so 4mm in my scale) and drew two larger circles. At this point I decided to draw horizontal lines (parallel to the first line) to see the ‘meeting’ points of circles and vertical lines that connect them. Then I drew these vertical lines. (Fig. 17 and Fig. 18)

After that I erased the non-visible lines and Fig. 19 shows my finished drawing. I found cylinder much easier and faster to draw than the cube.

Fig. 19

Reflection on the task:

I enjoyed this exercise, but I think it will be easier to be accurate in CAD where a point is really a point, on paper despite being small it still has dimensions…

Also it was interesting after the contextual study about lines. Guidelines helped to create plotlines, but sometimes I was extending the plotlines so they were half plotlines, half guidelines…

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