Orthographic projection corresponds to a perspective projection with a hypothetical viewpoint—e.g., one where the camera lies an infinite distance away from the object and has an infinite focal length, or "zoom".
With multiview orthographic projections, up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object.
The views are positioned relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a 6-sided box around the object.
These quadrant labels are the same as used in 2D planar geometry, as seen from infinitely far to the "left", taking H and V to be the X-axis and Y-axis, respectively.
The 3D object of interest is then placed into either quadrant I or III (equivalently, the position of the intersection line between the two planes is shifted), obtaining first- and third-angle projections, respectively. Quadrants II and IV are also mathematically valid, but their use would result in one view "true" and the other view "flipped" by 180° through its vertical centerline, which is too confusing for technical drawings.
Monge's original formulation uses two planes only, and obtains the top and front views only. The addition of a third plane to show a side view (either left or right) is a modern extension. The terminology of quadrant is a mild anachronism, as a modern orthographic projection with three views corresponds more precisely to an octant of 3D space.
Here is the construction of third angle projections of the same object as above. Note that the individual views are the same, just arranged differently.
Third-angle is as if the object were a box to be unfolded. If we unfold the box so that the front view is in the center of the two arms, then the top view is above it, the bottom view is below it, the left view is to the left, and the right view is to the right. It is standard in the United Kingdom (BS 8888:2006 specifies it as the default projection system), USA, Canada and Australia.
Both first-angle and third-angle projections result in the same 6 views; the difference between them is the arrangement of these views around the box.
A great deal of confusion has ensued in drafting rooms and engineering departments when drawings are transferred from one convention to another. On engineering drawings, the projection angle is denoted by an international symbol consisting of a truncated cone, respectively for first-angle (FR) and third-angle (US):
The 3D interpretation of the symbol can be deduced by envisioning a solid truncated cone (Mnemonic: a "gift-wrapped megaphone"), standing upright with its large end on the floor and the small end upward. The top view is therefore two concentric circles ("donut"). In particular, the fact that the inner circle is drawn with a solid line instead of dashed disambiguates this view as the top view, not the bottom view.
Descriptive geometry customarily relies on obtaining various views by imagining an object to be stationary, and changing the direction of projection (viewing) in order to obtain the desired view.
See Figure 1. Using the rotation technique above, note that no orthographic view is available looking perpendicularly at any of the inclined surfaces. Suppose a technician desired such a view to, say, look through a hole to be drilled perpendicularly to the surface. Such a view might be desired for calculating clearances or for dimensioning purposes. To obtain this view without multiple rotations requires the principles of Descriptive Geometry. The steps below describe the use of these principles in third angle projection.
Within orthographic projection there is an ancillary category known as Pictorials. Pictorials show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in one picture. Orthographic pictorial instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because pictorial projections innately have this distortion, in the instrument drawing of pictorials, great liberties may then be taken for economy of effort and best effect. Orthographic pictorials rely on the technique of axonometric projection ("to measure along axes").
"Techniques to Present Hierarchical Information Using Orthographic Projections" in Patent Application Approval Process
Oct 02, 2012; By a News Reporter-Staff News Editor at Information Technology Newsweekly -- A patent application by the inventors Sullivan, Lee...
US Patent Issued to Pasco, the University of Tokyo on July 10 for "Spatial Information Database Generating Device and Spatial Information Database Generating Program" (Japanese Inventors)
Jul 15, 2012; ALEXANDRIA, Va., July 15 -- United States Patent no. 8,218,824, issued on July 10, was assigned to Pasco Corp. (Tokyo) and The...