Descriptive Geometry - Protocols

Protocols

• Project two images of an object into mutually perpendicular, arbitrary directions. Each image view accommodates three dimensions of space, two dimensions displayed as full-scale, mutually-perpendicular axes and one as an invisible (point view) axis receding into the image space (depth). Each of the two adjacent image views shares a full-scale view of one of the three dimensions of space.

• Either of these images may serve as the beginning point for a third projected view. The third view may begin a fourth projection, and on ad infinitum. These sequential projections each represent a circuitous, 90° turn in space in order to view the object from a different direction.

• Each new projection utilizes a dimension in full scale that appears as point-view dimension in the previous view. To achieve the full-scale view of this dimension and accommodate it within the new view requires one to ignore the previous view and proceed to the second previous view where this dimension appears in full-scale.

• Each new view may be created by projecting into any of an infinite number of directions, perpendicular to the previous direction of projection. (Envision the many directions of the spokes of a wagon wheel each perpendicular to the direction of the axle.) The result is one of stepping circuitously about an object in 90° turns and viewing the object from each step. Each new view is added as an additional view to an orthographic projection layout display and appears in an "unfolding of the glass box model".

Aside from the Orthographic, six standard principal views (Front; Right Side; Left Side; Top; Bottom; Rear), descriptive geometry strives to yield four basic solution views: the true length of a line (i.e., full size, not foreshortened), the point view (end view) of a line, the true shape of a plane (i.e., full size to scale, or not foreshortened), and the edge view of a plane (i.e., view of a plane with the line of sight perpendicular to the line of sight associated with the line of sight for producing the true shape of a plane). These often serve to determine the direction of projection for the subsequent view. By the 90° circuitous stepping process, projecting in any direction from the point view of a line yields its true length view; projecting in a direction parallel to a true length line view yields its point view, projecting the point view of any line on a plane yields the plane's edge view; projecting in a direction perpendicular to the edge view of a plane will yield the true shape (to scale) view. These various views may be called upon to help solve engineering problems posed by solid-geometry principles