Graphical projection in the context of "Diagram"

Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.

An azimuth (/ˈæzəməθ/ ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit. 'the directions') is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.

Mathematically, the relative position vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane (the horizontal plane); the angle between the projected vector and a reference vector on the reference plane is called the azimuth.

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. The theoretical basis for descriptive geometry is provided by planar geometric projections.

The earliest known publication on the technique was "Underweysung der Messung mit dem Zirckel und Richtscheyt" (Observation of the measurement with the compass and spirit level), published in Linien, Nuremberg: 1525, by Albrecht Dürer. Italian architect Guarino Guarini was also a pioneer of projective and descriptive geometry, as is clear from his Placita Philosophica (1665), Euclides Adauctus (1671) and Architettura Civile (1686—not published until 1737). Gaspard Monge (1746–1818) is usually credited with the invention of descriptive geometry, called the "father of descriptive geometry" due to his developments in geometric problem solving. His first discoveries were in 1765 while he was working as a draftsman for military fortifications, although his findings were published later on.

In linear algebra and functional analysis, a projection is a linear transformation ${\displaystyle P}$ from a vector space to itself (an endomorphism) such that ${\displaystyle P\circ P=P}$. That is, whenever ${\displaystyle P}$ is applied twice to any vector, it gives the same result as if it were applied once (i.e. ${\displaystyle P}$ is idempotent). It leaves its image unchanged. This definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object.