What Is Isometric Projection?- A Basic Guide

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 handy technique used to show three-dimensional objects on a flat surface, especially in engineering and technical drawings. What sets isometric projection apart is that all three axes the height, width, and depth are equally foreshortened, and each one is separated by a neat 120-degree angle.

When you come across an isometric drawing (sometimes called isometric projection), you’re looking at a method often favored by engineers, technical illustrators, and, from time to time, architects. The goal here is to give a realistic sense of depth almost like a perspective drawing while still keeping the real measurements of the object clear and undistorted, especially along the three main axes.

Technically speaking, isometric projection falls under the broader family of orthographic projections. In this process, every point on the actual object gets mapped onto the drawing by imagining a straight line dropping perpendicularly from that point to the drawing’s surface.

What makes an isometric drawing unique is the orientation of that drawing plane: it’s tilted so that it forms equal angles with the object’s three principal planes hence the name “isometric,” which literally means “equal measure.”

To visualize this, think about drawing a cube. In an isometric view, you’d see three faces, each appearing as an equilateral parallelogram.

All the parallel edges of the cube stay parallel in the drawing, but there’s a twist the horizontal edges are drawn at an angle, usually 30 degrees from the standard horizontal axis, while the vertical edges keep their true proportions because they line up with the main axes.

This approach allows you to represent objects in a way that feels both accurate and three-dimensional, without the distortion you get in regular perspective drawings.

Principle of Isometric Projections

Imagine you have an object placed inside a transparent cube. In this particular type of orthographic projection, the entire cube along with the object is tilted in such a way that one of its solid diagonals stands upright, perfectly perpendicular to the vertical plane.

What’s interesting here is that, as a result of this tilt, all three axes of the object end up being equally inclined to that same vertical plane. This setup gives us a unique pictorial view, allowing us to see the object’s dimensions more clearly and in proportion.

Lines in Isometric Projection

When working with isometric projection, it’s important to understand how the lines from the original object translate onto the isometric drawing:

• Lines that are parallel on the object will stay parallel in the isometric projection.
• Any vertical line you see on the object will also show up as vertical in the isometric view.
• The horizontal lines from the object, on the other hand, are shown at a 30° angle from the horizontal when drawn isometrically.
• A line that runs parallel to one of the isometric axes is called an isometric line, and you’ll notice that it appears slightly shorter—about 82% of its true length, thanks to foreshortening.
• If a line isn’t parallel to any isometric axis, it’s referred to as a non-isometric line. The degree to which these lines are foreshortened will vary, depending on how they’re angled in relation to the vertical planes.

Isometric & Non-Isometric Lines

In the illustration, the cube’s three perpendicular edges—OX, OY, and OZ—are each shortened by the same amount and positioned so they make equal angles of 120º with one another. These edges are referred to as isometric axes. Any line you draw parallel to one of these axes is known as an isometric line.

Now, not every line in the figure will neatly align with one of these axes. If a line doesn’t run parallel to any of the isometric axes, it’s called a non-isometric line. For instance, lines such as XY, YZ, and ZX fall into this category.

What’s interesting about these non-isometric lines is that, because they aren’t parallel to the isometric axes, they don’t get foreshortened in the same way. Their proportions differ from those of isometric lines, so you have to treat them a bit differently when you’re drawing.

For example, if you’re dealing with horizontal edges of the object that happen to be non-isometric, don’t automatically draw them at a 30º angle. Instead, it’s best to first pinpoint the ends of these lines and then connect them, making sure you accurately capture their orientation.

One more thing worth noting: the surface labeled XYZ in isometric projection is actually an oblique surface—meaning it doesn’t align squarely with the principal axes, giving the object a bit of visual complexity.

Isometric Scale

When creating an isometric projection, we use what’s known as the isometric scale. This scale isn’t just for show it actually takes the true dimensions of an object and slightly reduces them to what we call isometric lengths.

This process is referred to as “foreshortening.” In simple terms, it means that the edges of the object don’t appear at their full, real length. Instead, they look a bit shorter, almost as if you’re seeing them from an angle rather than head-on.

METHOD I

• To begin, draw a horizontal reference line labeled AB. From point A, construct two lines: one (AC) at a 45° angle to AB, which will represent the actual or true length, and another (AD) at a 30° angle to AB, which will be used to measure the isometric length.
• Next, on line AC, mark points 0, 1, 2, and so on, according to the actual dimensions you’re working with. From each of these points, draw vertical lines downward (or upward, depending on your orientation) until they intersect with line AD. Mark these intersections as 0′, 1′, 2′, and so on. The segment from A to 1′ on line AD now represents the isometric length that corresponds to the actual length from A to 1 on line AC, and this applies similarly to the other divisions.
• In isometric projection, the actual lengths of an object are visually reduced, or foreshortened. Specifically, all the edges aligned with the three isometric axes appear approximately 0.82 times shorter than their true measurements. three isometric axes are foreshortened to 0.82 times their actual/true lengths.

METHOD II

• Start by drawing a horizontal line AC to represent the true length. Divide this line into equal segments, marking them as 0, 1, 2, and 3 according to the desired divisions.
• At point A, draw another line at a 15° angle to AC. Similarly, from point C, draw a line at a 45° angle back towards CA, so that the two new lines intersect at point D.
• Now, through each division point on AC (0, 1, 2, and 3), draw lines parallel to CD. These lines will meet the 15°-inclined line (AD) at new points labeled 0′, 1′, 2′, and 3′. The segment AD, thus constructed, provides the corresponding isometric lengths for each division of the true length.

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