Axonometric Drawing - SSR (Scale, Shear/Skew, Rotate) technique

 The SSR (Scale, Shear, Rotate) technique is a highly efficient mathematical workflow used in vector graphic programs like Adobe Illustrator and Inkscape to precisely transform flat 2D orthographic drawings into a 3D isometric axonometric projection. Instead of tracing flat blueprints onto an isometric grid by hand, the SSR method automates the deformation using exact numerical inputs.

The technique relies on mathematically shifting the 2D plane so that a standard square conforms perfectly to the true 30-degree / 120-degree orientation of an isometric drawing.

The Three Pillars of SSR

To project a flat 2D face onto one of the three visible planes of a 3D cube (Top, Left, or Right), you apply three sequential operations to your vector object:

1.  Scale: This accounts for the foreshortening effect of looking at an object from an isometric angle. You scale the vertical height of the object down to 86.602% while leaving the width at 100%.
2.  Shear (or Skew): This slants the vertical edges of the object to mimic a parallel projection angle, tilting them by 30° or -30°.
3.  Rotate: This turns the entire asset into the final orientation required for that specific plane, shifting it by 30° or -30°.

The Standard Transformation Values

Depending on which side of the axonometric drawing you are generating, apply these specific transformations in order:

Isometric Plane	1. Scale (Vertical)	2. Shear (Skew)	3. Rotate
Top Plane 🪵	86.602%	30°	-30°
Left Plane 🧱	86.602%	-30°	-30°
Right Plane 🧱	86.602%	30°	30°

(Note: Some software packages require a 30° Shear and a 30° Rotation for the Left Plane, or flipped symbols depending on how the software measures clockwise vs. counter-clockwise angles).

The 86.602% vertical scale factor in the SSR technique is not an arbitrary number—it is the exact trigonometric value of 

It acts as a mathematical pre-compensation filter. When you skew (shear) an object in a vector program by 30°, the software stretches the geometry. Scaling the vertical axis down to 86.602% beforehand ensures that after it stretches, the final lines return to exactly 100% of their original true length, maintaining a perfect 1:1:1 aspect ratio across all 3D axes.

Here is the exact geometric breakdown of why this happens.

1. The Trigonometry of the Shear Step

When you apply a 30° Shear to a flat square, the horizontal lines of your drawing tilt upward by 30°.

In vector graphics, a shear shifts points along one axis proportional to their distance from the other axis. This distorts the right angles of your flat square into an isometric diamond (rhombus). During this distortion:

• The width (horizontal boundary) of the bounding box remains fixed.
• The horizontal lines tilt up at a 30° angle, turning into the hypotenuse of a right-angled triangle.

According to right-triangle trigonometry:

Rearranging this formula to find the new length:

This means that shearing a flat object by 30° automatically stretches its line segments by roughly 115.47%.

2. Eliminating the Distortion (Why we Scale First)

If you don't scale the graphic before shearing it, your final 3D object will look elongated and structurally warped because the lines on the isometric plane are longer than they should be.

To counteract this 115.47% expansion, you must shrink the asset by the exact reciprocal amount before the shear takes place:

By scaling the vertical size to 86.602%, you intentionally compress the object. When the 30° shear step elongates the lines by 115.47%, the two operations cancel each other out perfectly:

3. Isometric Drawing vs. Isometric Projection

There is a subtle but important distinction in technical drawing that explains why this scale factor is so highly regarded:

• True Isometric Projection: When an actual 3D cube is rotated in physical space (45° horizontally, then 35.264° downward toward the camera), all axes shrink uniformly to 81.65% of their real-world size due to perspective foreshortening.
• Isometric Drawing (The SSR Approach): Graphic designers prefer a 1:1 scale so that a 100px line on a flat blueprint remains exactly 100px long on the 3D isometric axis. The SSR technique achieves this "true measurement" standard. By scaling vertically to 86.602% before shearing, the final 3D drawing retains an un-foreshortened, easily measurable 100% scale on all visible faces.

To calculate alternative scale values for other axonometric projections, you must determine how much the shear (skew) angle stretches the artwork and use trigonometry to cancel out that distortion.

The universal formula to find the required vertical scale factor for any parallel projection using the Shear-Rotate method is:

(Where ϴ is the shear angle you intend to use).

Thank you for reading.