The Basics of Isometric Projection

The term “isometric” is one of the most misapplied words in the design industry. We tend to call every non-perspective 3-dimensional drawing “isometric.”

What is Isometric Projection?

Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees.

Isometric drawing, also called isometric projection, method of graphic representation of three-dimensional objects, used by engineers, technical illustrators, and, occasionally, architects.

The technique is intended to combine the illusion of depth, as in a perspective rendering, with the undistorted presentation of the object’s principal dimensions—that is, those parallel to a chosen set of three mutually perpendicular coordinate axes.

The isometric is one class of orthographic projections. In making an orthographic projection, any point in the object is mapped onto the drawing by dropping a perpendicular from that point to the plane of the drawing.

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An isometric projection results if the plane is oriented so that it makes equal angles (hence “isometric,” or “equal measure”) with the three principal planes of the object.

Thus, in an isometric drawing of a cube, the three visible faces appear as equilateral parallelograms; that is, while all of the parallel edges of the cube are projected as parallel lines, the horizontal edges are drawn at an angle (usually 30°) from the normal horizontal axes, and the vertical edges, which are parallel to the principal axes, appear in their true proportions.

Isometric Projection

Principle of Isometric Projections

It’s a pictorial orthographic projection of an object where a transparent cube containing the object is tilted before one of those solid diagonals of the cube becomes perpendicular to the vertical plane along with the three axes are equally inclined to this vertical plane.

Lines in Isometric Projection

The following are the relations between the lines in isometric projection:

  • The lines which are parallel to the object are parallel at the isometric projection.
  • Vertical lines on the object appear vertical at the isometric projection.
  • Horizontal lines on the item are drawn at an angle of 3 0° with the horizontal at the isometric projection.
  • A line parallel to an isometric axis is called an isometric line, and it’s fore-shortened to 82 percent.
  • A line that’s not parallel to any isometric axis is known as the non-isometric line, and the extent of the fore-shortening of non-isometric lines is different if their inclinations with the vertical planes are different.

Isometric & Non-Isometric Lines

In the figure, the three perpendicular edges of the cube OX, OY, & OZ are foreshortened equally and are at equal inclinations of 120º to each other and are known as isometric axes. The lines drawn parallel to the isometric axes are known as Isometric Line.

Isometric & Non-Isometric Lines

Any other line which is not parallel to any of the isometric axes is known as a Non-Isometric Line. The lines XY, YZ & ZX are called non-isometric lines.

Since these lines are not parallel to the isometric axes, they are not foreshortened in the same proportion as the isometric lines. Also, those horizontal edges of the object which are non-isometric must not be drawn at 30º. To draw the non-isometric lines, their ends should be located and then joined. The surface XYZ is an oblique surface in isometric.

Isometric Scale

Isometric projection is drawn using the Isometric scale, which converts true lengths into isometric lengths which are foreshortened. (“Edges of an object are foreshortened” means that “the edges are caused to appear as if shortened”.)

METHOD I

  • Dia.1 Draw a horizontal line AB.
  • From A draw a line AC at 45º to represent actual or true length and another line AD at 30º to AB to measure isometric length.
  • On AC mark the points 0,1,2, etc., to represent actual lengths.
  • From these points draw verticals to meet AD at 0′,1′,2′, etc. the length A1′ represents the isometric scale length of A1 and so on.
  • In Isometric projection, actual (true) length of an object is foreshortened i.e., in the isometric projection, all the edges of an object along the direction of the three isometric axes are foreshortened to 0.82 times their actual/true lengths.

METHOD II

  • Dia.2 draw a horizontal line AC = true length.
  • Mark the division points of true length on AC as 0,1,2 and 3.
  • At the point A, draw a line inclined at an angle of 15º to AC.
  • Also, at the point C draw a line at an angle of 45º to CA. Both meet at D.
  • Draw lines parallel to CD through the points 0,1,2 and 3 to meet AD at the points 0′,1′,2′ and 3′. The line AD gives the isometric lengths.