How does descriptive geometry use orthogonal projections to show three-dimensional objects?
The sight lines drawn from the image in the reality plane (RP) to the artist's eye intersect the picture plane (PP) to form a projective, or perspective, drawing. The horizontal line drawn parallel to PP corresponds to the horizon. Early perspective experimenters sometimes used translucent paper or glass for the picture plane, which they drew on while looking through a small hole to keep their focus steady.
In descriptive geometry, three-dimensional objects are represented by projecting them onto two planes positioned at right angles to each other. This method, formalized by Gaspard Monge, utilizes orthogonal projection to create two distinct views of an object: the plan and the elevation.12
In this process, the lines of sightâreferred to as projectorsâare parallel and strike the picture plane at a perpendicular angle. By mapping the object onto these perpendicular horizontal and vertical planes, descriptive geometry allows for the deduction of both the projective and metrical properties of the object. This technique serves as the mathematical foundation for drafting, enabling the clear and accurate communication of complex engineering and architectural designs without the need for physical models.3415