The term "isometric" means "equal measure".

• The Axes: The three principal axes are spaced exactly 120° apart. One axis is vertical, and the two receding axes are drawn at exactly 30° to the horizontal reference line.
• Isometric Lines vs. Non-Isometric Lines:
• Isometric Lines: Lines that are parallel to any of the three principal axes. They can be measured directly along their true length using the isometric scale.
• Non-Isometric Lines: Lines that are NOT parallel to the axes (e.g., inclined surfaces, diagonals). Their true length is distorted in the drawing. They cannot be measured directly; their endpoints must be plotted using coordinates along the isometric axes and then connected.
• Isometric Circles: A circle appearing on any isometric plane is distorted into an ellipse. This is typically drawn using the "four-center approximation method" or CAD ellipse tools.

A crucial distinction exists between a true projection and the standard drawing method used by drafters.

• Isometric Projection (True Scale): When an object is physically tilted forward (approx. $35^\circ 16'$) and rotated (45°) to create equal angles to the projection plane, all edges are foreshortened. The mathematical scale factor is approx 0.816. This means a 100mm edge appears as 81.6mm long in a true projection.
• Isometric Drawing (Full Scale): Because calculating the 0.816 foreshortening for every line is tedious in manual drafting, engineers use Isometric Drawings. We simply ignore the foreshortening and draw lines at full, 1:1 true length along the 30° axes. The resulting drawing is visually identical in proportion but is technically ~22.5% larger than the true isometric projection.

The most detailed face of the object, or the face with the most circles/curves, should be placed as the front face to avoid distorting complex geometry.

• Front Face: Always drawn true size and true shape. A circle on the front face remains a perfect circle, not an ellipse.
• Receding Axes: Depth lines are drawn receding at an arbitrary angle, most commonly 30°, 45°, or 60° to the horizontal.
• Cavalier Projection: The depth (receding axis) is drawn at full scale (1:1). This mathematically preserves depth but creates a severe visual illusion where the object appears stretched or distortedly long.
• Cabinet Projection: The depth is intentionally drawn at half scale (1:2 or 50%). This compensates for the visual distortion of Cavalier, making the object look far more realistic and proportionate, similar to how furniture cabinets are drawn.

Perspective drawings rely on a horizon line and vanishing points.

• One-Point Perspective (Parallel): The object has one face parallel to the picture plane (true shape). All receding depth lines converge at a single vanishing point on the horizon. Frequently used for interior room layouts or long hallways.
• Two-Point Perspective (Angular): The object is rotated so only its vertical edges are parallel to the picture plane. Both width and depth lines converge at two separate vanishing points located on the horizon line. This is the standard method for architectural exterior renderings of buildings.
• Three-Point Perspective (Oblique): The object is tilted so no edges are parallel to the picture plane. Width, depth, and height lines all converge at three distinct vanishing points. Used for dramatic "bird's-eye" (looking down from above) or "worm's-eye" (looking up from below) views of tall structures like skyscrapers.