Isometric and Oblique Projections

TL;DR

Isometric and oblique projections are both types of axonometric projections used in technical drawing to represent 3D objects on a 2D surface. Isometric projection shows objects with all three axes equally foreshortened, while oblique projection displays one face true size, with depth projected at an angle. Choosing between them depends on what aspects of the object you want to emphasize.

1. The Mental Model

Imagine you're trying to draw a box on a flat piece of paper so it looks 3D. Isometric and oblique projections are just two different rule sets for how to draw that box's edges and corners to give the illusion of depth.

2. The Core Material

When we draw an object in 3D on a 2D surface, we're using a projection. There are many types, but for technical drawing, axonometric projections are key because they show all three dimensions (length, width, height) in a single view. Isometric and oblique are two popular types within this category.

Isometric Projection

Photo by cottonbro studio on Pexels

In isometric projection, the object is rotated so that all three principal axes (X, Y, Z) appear equally foreshortened and are equally spaced at 120 degrees from each other. This means:

• Axis Angles: The vertical axis (usually height) is drawn vertically. The other two axes (length and width) are drawn at 30 degrees to the horizontal baseline.
• Scaling: All lines parallel to the main axes are drawn to their true length, but because of the projection, they appear foreshortened in the final view. We often draw them at full scale for simplicity in technical drawing, effectively using an "isometric scale" of approximately 0.816, but for practical purposes, full scale is common.
• Appearance: This projection gives a realistic, balanced view of the object, showing its overall form well without distorting any single face excessively.

Oblique Projection

In oblique projection, one face of the object is drawn parallel to the projection plane, meaning it's shown in its true shape and size. The depth is then projected at an angle, usually 30, 45, or 60 degrees. This means:

• Front Face: The front face (or another chosen face) is drawn as if you're looking straight at it, so all its angles and lengths are true.
• Receding Axis: The lines representing depth (the receding axis) are drawn at a specific angle (e.g., 45 degrees) to the horizontal.
• Depth Scaling: The length of these receding lines can be full scale (cavalier oblique), half scale (cabinet oblique), or some other ratio.
  • Cavalier Oblique: Depth lines are drawn to their true length. This can make the object look longer than it is.
  • Cabinet Oblique: Depth lines are drawn at half their true length. This provides a more realistic appearance by reducing the perceived distortion.
• Appearance: Oblique projection is excellent when you need to show one particular face of an object without any distortion, especially if that face has complex details.

Here's a quick comparison of when you'd pick one over the other:

graph TD
    A["Need 3D View?"] --> B{Emphasize balanced view or specific face?};
    B -- "Balanced view, equal emphasis on all sides" --> C["Use Isometric Projection"];
    B -- "Emphasize specific face's true shape and details" --> D{"True size for depth lines (Cavalier) or foreshortened (Cabinet)?"};
    D -- "True size depth" --> E["Use Cavalier Oblique"];
    D -- "Foreshortened depth (e.g., half)" --> F["Use Cabinet Oblique"];

Key Differences at a Glance:

3. Worked Example

Let's draw a simple cube with 50mm sides using both isometric and cabinet oblique projections.

Object: A cube, 50mm x 50mm x 50mm.

Isometric Projection:

1. Draw the vertical axis: Draw a 50mm vertical line. This is one edge of the cube.
2. Draw the two 30° axes: From the top and bottom ends of the vertical line, draw lines extending out at 30 degrees to the horizontal (one set to the left, one to the right).
3. Measure lengths: Along these 30-degree lines, measure 50mm from the vertical line's ends.
4. Complete the faces: Connect the ends of these 50mm lines with lines parallel to the initial 30-degree lines. You'll essentially be drawing three faces that meet at one corner, with all parallel lines measuring 50mm.
5. Add hidden lines (optional): If you were showing the full cube, you'd add the lines that would be hidden from view.

You'll end up with a cube where all visible edges are 50mm long, and the angles between the axes are 120 degrees.

Cabinet Oblique Projection (45° receding angle, half depth):

1. Draw the front face: Draw a 50mm x 50mm square. This is the true-size front face of the cube. Label its corners A, B, C, D.
2. Draw the receding lines: From each corner of the square (A, B, C, D), draw a line extending at 45 degrees (or another chosen angle) to the horizontal.
3. Apply depth scaling: Since it's cabinet oblique, the depth is half the true length. The true depth is 50mm, so draw these receding lines 25mm long.
4. Connect the ends: Connect the ends of these 25mm receding lines to form the back face of the cube. Make sure the lines are parallel to the lines of the front face where appropriate.
5. Erase hidden lines (optional): If you're drawing a solid object, you'd erase or use dashed lines for the edges that would be hidden from view.

You'll see a true 50mm x 50mm square front face, with depth lines appearing at 45 degrees and only 25mm long, giving a clearer view of the front face while still showing depth.

4. Key Takeaways

• Isometric projection gives a balanced, uniform view where all three axes are equally foreshortened, typically drawn with axes at 30° to the horizontal.
• Oblique projection prioritizes showing one face in its true shape and size, with depth lines drawn at an angle.
• Cavalier oblique uses full true depth, while cabinet oblique uses half true depth, making the object look less elongated.
• Choose isometric when you need a clear, overall representation of the object's form.
• Choose oblique when the details on one specific face are crucial and must not be distorted.
• Both projections are types of axonometric projections, meaning they show all three dimensions in a single view.

Common Mistakes to Avoid:
- Mixing angles: Don't use 30° for depth in an oblique drawing or 45° for isometric. Stick to the correct angles for each projection.
- Incorrect scaling: Forgetting to apply the correct depth scaling (e.g., half-scale for cabinet oblique) can make your drawing look disproportionate.
- Inconsistent parallel lines: In both projections, lines that are parallel on the actual object must be drawn parallel in your projection.
- Forgetting the "true length" rule: Remember that in isometric, lines parallel to the axes are drawn to true length (or full scale), while in oblique, only the front face is true size.

5. Now Try It

Grab a piece of paper, a pencil, and a protractor or a 30-60-90 set square. Imagine a simple L-shaped block, with the base being 60mm long, the vertical part 40mm high, and the "L" section being 20mm thick.

1. Draw the L-block in isometric projection. Use the 30-degree angles for your base and depth lines. Ensure all lines parallel to the main axes are drawn to their actual length.
2. Draw the same L-block in cabinet oblique projection. Choose the most detailed face as your true-size front face. Use a 45-degree receding angle and half true depth for the depth lines.

Success looks like: You'll have two distinct drawings of the same L-block. The isometric drawing will look balanced from three sides, while the oblique drawing will clearly show one face in its actual proportions, with the depth receding at an angle. All parallel lines in the object should appear parallel in your drawings, and your scaling (especially for cabinet oblique depth) should be correct.