Blender 3D: Noob to Pro/Orthographic Projections

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Orthographic projections are the staple of 3D visualization. In short, they describe the shape of an object from at least two (usually three) different angles. From this information alone, one can come up with the full shape of a 3D object. The normal views used are front, side, and top, though back, and bottom may also be used. In orthographic projections, everything is to scale and proportional.

Notice in the above drawing there are three views (outlined in red). These represent the object from the front, top, and left. You may notice some dashed lines on the left view. These are there to indicate that these lines are behind something, namely the left wall of the staircase. Ordinarily, this projection would be made with the right view so that no lines would be hidden.

Earlier, I mentioned that at least two views are necessary. This is because of some of the properties of orthographic projections, namely:

1. The front view is constrained by the left (side) and top views. Any horizontal line in the side view will match a corresponding line in the front view. That is, if you draw lines from the top of each stair in the side projection, it'll be the top of that particular stair in the front view as well. Likewise, were you to extend a vertical line from the wall beside the staircase in the top view into the front view, it would also be the same wall. Using this property, it is fairly simple to "box" in every feature of the object in the front view.
2. The top view is constrained by the left and front views. This one is harder to see, as one cannot draw a vertical line from the "left" view and have it intersect anything. For this, we imagine that each vertical line in the left view extends to the bottom edge of the red box. We will then draw 45° diagonal lines from each of these points of intersection down and left towards the top view. Where these intersect the bounds of the red box are horizontal lines in the top view, the length of which is constrained by vertical lines from the front view.
3. The left view follows the same logic as above. Simply draw the diagonal lines up and to the right to determine where each vertical line is. The height of each line is constrained by the front view.

However, it should be noted that different projections, e.g. top-right-front have slightly different properties. For example, were I to have used the right projection, the layout would need to be almost a mirror-image with the right view on the upper left, the front view to the right of it, and the top view on the lower right, in order to keep these properties.

Some cases are ambiguous, such as when only the top and front view of the staircase are drawn. In this case, it would be impossible to know whether the riser of each step slopes in or out. Therefore, the side view is necessary. However, if instead only the side and front views were drawn, there would be no such ambiguity. So in most cases, two projections are all that are required.