An isometric drawing keeps parallel edges parallel and equal edges equal. A perspective view lets parallel edges meet at a vanishing point, so farther edges look smaller.
This lesson is part of pictorial representations. Next, interpreting an oblique drawing adds a third pictorial style.
What three questions identify the style?
Ask these in order.
- Are parallel edges drawn parallel, or do they converge?
- Are equal edges drawn equal, or do the far ones shrink?
- Are the receding edges at 30° to the horizontal, with a vertical axis?
Three yeses point to isometric. Converging lines and shrinking edges point to perspective.
Worked example: one 40 mm cube, two pictures
Draw an original cube with 40 mm edges in isometric style. The vertical edges are 40 mm long. The edges going to the lower left and lower right are each drawn 40 mm long at 30° to the horizontal. All twelve edges are drawn at 40 mm, and four edges in each direction are parallel.
Now draw the same cube in perspective. The front face is a square of 40 mm. The back face is a smaller square, about 28 mm across, placed up and towards a vanishing point on the horizon. The edges joining front to back are not parallel: they converge.
Apply the test. In the first picture, the answers to questions 1, 2 and 3 are yes, so it is isometric. In the second, the answer to question 1 is no, since the receding edges converge, and to question 2 is no, since the back face is smaller. It is perspective.
How to measure in an isometric drawing
Measure only along the three axes. A cube of 40 mm edge gives three axis lengths of 40 mm each.
Now take a box 60 mm wide, 30 mm deep and 20 mm high. On the width axis, draw 60. On the depth axis, draw 30. Vertically, draw 20.
The box is fully described by these three lengths from one corner, so you can build the whole drawing by stepping along the axes.
The mistake: using isometric rules on a perspective picture
A student sees a perspective picture of a box and measures the far edge as 28 mm, then writes that the box is 28 mm deep. The picture was not drawn to isometric rules, so its lengths cannot be taken from it.
| Step | Wrong | Right |
|---|---|---|
| Identify the style | Assumed isometric | Converging edges, so perspective |
| Reading a length | Measure the far edge | Use the stated dimension |
| Result | Depth of 28 mm | Depth as stated, for example 40 mm |
In a perspective view, sizes are not reliable. Read them from figures, not from the picture.
Check yourself
Picture P shows a box whose four vertical edges are all drawn 35 mm and whose horizontal edges at the left and right are drawn at 30° and are parallel in pairs. Picture Q shows a box whose top edges slope inwards towards a point in the distance. Name each style and give a reason.
Answer
P is isometric: equal vertical edges, parallel edges stay parallel, and the receding axes are at 30°. Q is perspective: its top edges converge towards a vanishing point, so parallel edges are not drawn parallel.
What to study next
Continue with interpreting an oblique drawing without confusing true lengths. Then try the pictorial representations practice set.
If you want a teacher to show you pairs of pictures and listen to your reasons, see online one-to-one Engineering Drawing tuition.