Introduction to descriptive geometry

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Descriptive geometry builds on the practice, evolved over centuries, of displaying two images of a single object simultaneously; one image is seen from one direction while a second image is seen from a direction 90° rotated (e.g., a "front" and a "side" view). Gaspard Monge, the father of descriptive geometry, developed a graphical protocol which creates three-dimensional virtual space on a two-dimensional plane.

Understanding The Concepts of Descriptive Geometry

Assuming you know the basics of Geometry (Geometry wikibook), the concept of the point, the line, the plane, we'll start off by introducing the first projection system.

A projection system is a conventional system used for representing a 3D image on a 2D plane. The plane we're using refers to the sheet of paper or the computer screen, if you're using a CAD program.

An orthographic projection is a projection which uses multiple views of the 3D object, each obtained by rotating the viewer angle by 90°.

As you can see, by projecting the views onto the projection plans, you obtain three distinguished images which represent the horizontal projection (floor), the vertical projection (left vertical plane), and the lateral projection (right vertical plane).

The Isometric Projection

The axonometric projection, more exactly the isometric projection is a 3D perspective view of the object, in which the perpendicular plans are seen at an angle of 120°. In this view, the real dimensions are kept only on the direction of the 3 axes: X, Y and Z. See the image on the right for details.

As in any orthographic projection, the lines that in the real 3D object are parallel remain parallel in the projection as well, but in the isometric projection the angles are not the same as in reality, they are distorted so the angle of 90° isn't 90° anymore, it's 120°. You can see that in the planes that are perpendicular, the angle between them is 120°.

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