48610 Chap.3 Isometric and Parallel Oblique Pictorial Views
Isometric and Parallel Oblique Pictorial Views
Week 3 adds the view that shows the whole solid at once. Orthogonal sets are complete and unambiguous, and almost nobody can look at three of them and see the object; a pictorial answers the other question, what is this thing. The subject uses two families and the choice between them is technical rather than aesthetic.
Isometric tilts the object so that all three principal axes project at 120 degrees to one another, which puts the two horizontal axes at 30 degrees to the horizontal on the page.
Edges running along an axis are drawn true length, so they come straight off a rule, but no face is true shape: squares become parallelograms and circular holes become ellipses.
Parallel oblique keeps the principal face parallel to the picture plane, so that face and every face parallel to it show in true shape, with the depth lines run off at an angle other than 90 degrees, conventionally 30, 45 or 60. A cavalier drawing uses 45 degrees with depth lines at full length; a cabinet drawing halves the depth, which looks more natural.
The drawing assignment asks for one isometric view and one cavalier drawing at 45 degrees on 5 mm grid paper, with the depth scale stated on the sheet, and each carries 2.5 marks.
What this chapter covers
- 01
Why a drawing set carries both orthogonal and pictorial views
- 02
Axonometric projection and its three methods: isometric, dimetric, trimetric
- 03
The isometric axis rosette at 120 degrees and 30 degrees to the horizontal
- 04
True length along an axis, but no face in true shape
- 05
Circles becoming ellipses, boxed inside a parallelogram
- 06
Constructing an isometric: box it, carve it, then curve it
- 07
Never measuring a diagonal or a sloping edge
- 08
Oblique projection with the front face in true shape
- 09
Cavalier at full depth, cabinet at half depth, general otherwise
- 10
Stating which convention and which depth scale you used
Boxing and carving a stepped block with a hole
- +1Box first. From the chosen bottom front corner set 60 mm along the right hand 30 degree axis, 30 mm along the left hand 30 degree axis and 40 mm vertically, in light construction line, and close the box. Check: the three pairs of opposite edges are parallel and equal.
- +1Carve the step. Measure 20 mm back from the top right edge along the width axis and 15 mm down the vertical axis, then join with lines parallel to the depth axis to cut through the full 30 mm. Check: the new vertical face is parallel to the original right hand face.
- +1Locate the hole centre with axis aligned measurements only: 20 mm along the width axis and 25 mm up the vertical axis on the front face. Both are true length because both run along an axis. Check: the centre lies inside the tall portion rather than inside the removed step.
- +1Box the circle before drawing it. Draw the 16 mm square that would enclose it on the front face, which appears as a parallelogram with 16 mm sides, and fit an ellipse touching the midpoint of each side. Check: the major axis of the ellipse runs across the long diagonal of that parallelogram, not vertically.
Key terms
- Axonometric projection
- A parallel projection whose lines of sight meet the plane at right angles while the object is turned so that all three principal axes lean away from it. Isometric, dimetric and trimetric are its three methods.
- Isometric view
- The axonometric method in which the three projected axes make equal 120 degree angles, so the two horizontal axes sit at 30 degrees to the horizontal. Edges along an axis are true length; faces are not true shape.
- Oblique projection
- A parallel projection in which the lines of sight are inclined to the plane while the principal face stays parallel to it, so that face and those parallel to it appear in true shape.
- Cavalier drawing
- An oblique drawing with projecting lines at 45 degrees and depth lines drawn at full length. It is arithmetically honest and makes the solid look stretched.
- Cabinet drawing
- An oblique drawing whose depth lines are drawn at half scale, producing a more natural looking picture at the cost of no longer being to one scale in all directions.
- True shape
- A face drawn without distortion, so that angles and proportions on the drawing match those on the object. Only the front face of an oblique view is true shape; no face of an isometric view is.
- Construction line
- A light line used to locate geometry before the outline is darkened in. The drawing task requires construction lines to be left on the sheet as evidence that the method was used.
Isometric and Parallel Oblique Pictorial Views FAQ
When should I choose oblique over isometric?
Choose oblique when the interest is concentrated on one face, especially a face full of circles. Because the front face of an oblique is true shape, circles there are drawn with a compass at full size, whereas an isometric turns every one of them into a constructed ellipse.
A cover plate with a central bore and a ring of bolt holes is the clear case: oblique needs one compass setting per circle, isometric needs seven boxed ellipses.
Why do circles become ellipses in an isometric view?
Because no face is true shape. Tilting the object so that all three axes are equally inclined foreshortens every face, and a circle inscribed in a square face becomes an ellipse inscribed in the parallelogram that face has become. The reliable construction is to draw that parallelogram first and then fit the ellipse to the midpoints of its four sides, which automatically gives the correct orientation of the major axis.
Do I need to remember which is cavalier and which is cabinet?
The lecture does not ask you to memorise which label belongs to which, only to be able to produce either on demand, and the assignment asks specifically for a cavalier drawing at 45 degrees with the depth scale indicated on the sheet. So the practical requirement is to know that one uses full length depth lines and the other halves them, and to state on your drawing which you have used and at what scale.
Can I dimension a pictorial view?
Not meaningfully, and that is why the drawing set carries both kinds. Distances along the axes of an isometric are true length and could in principle be dimensioned, but anything else is foreshortened, and no face is true shape, so a reader has no way of knowing which numbers can be trusted. The orthogonal views carry the dimensions; the pictorial carries the shape.
Assessment move
Buy or print isometric grid paper and use it until the 30 degree directions feel automatic, then switch to plain paper with a set square to prove you can do it without the grid. Practise the boxing habit on objects around you: a stepped bracket, a phone, a mug with a handle.
For each one, draw the enclosing box first and time yourself carving it, then repeat the same object as an oblique and notice which one was faster and why. Before the assignment, do one full sheet of each type with construction lines left on, and state the convention and depth scale as if it were being marked.
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