Editing 3D projection (section)

===Orthographic projection===
{{Main|Orthographic projection}}
{{See also|Geometric transformation}}
The orthographic projection is derived from the principles of [[descriptive geometry]] and is a two-dimensional representation of a three-dimensional object. It is a parallel projection (the lines of projection are parallel both in reality and in the projection plane). It is the projection type of choice for [[plan (drawing)|working drawings]].

If the normal of the viewing plane (the camera direction) is parallel to one of the primary axes (which is the ''x'', ''y'', or ''z'' axis), the mathematical transformation is as follows;
To project the 3D point <math>a_x</math>, <math>a_y</math>, <math>a_z</math> onto the 2D point <math>b_x</math>, <math>b_y</math> using an orthographic projection parallel to the y axis (where positive ''y'' represents forward direction - profile view), the following equations can be used:
:<math>
b_x = s_x a_x + c_x
</math>
:<math>
b_y = s_z a_z + c_z
</math>
where the vector '''s''' is an arbitrary scale factor, and '''c''' is an arbitrary offset. These constants are optional, and can be used to properly align the viewport. Using [[matrix multiplication]], the equations become:
:<math>
 \begin{bmatrix}
   b_x  \\
   b_y
\end{bmatrix} = \begin{bmatrix}
   s_x & 0 & 0 \\
   0 & 0 & s_z
\end{bmatrix}\begin{bmatrix}
   a_x  \\
   a_y  \\
   a_z
\end{bmatrix} + \begin{bmatrix}
   c_x  \\
   c_z
\end{bmatrix}.
</math>

While orthographically projected images represent the three dimensional nature of the object projected, they do not represent the object as it would be recorded photographically or perceived by a viewer observing it directly. In particular, parallel lengths at all points in an orthographically projected image are of the same scale regardless of whether they are far away or near to the virtual viewer. As a result, lengths are not foreshortened as they would be in a perspective projection.

====Multiview projection====
{{Main|Multiview projection}}
[[File:Convention placement vues dessin technique.svg|thumb|right|Symbols used to define whether a multiview projection is either First Angle (left) or Third Angle (right).]]
With ''multiview projections'', up to six pictures (called ''primary views'') 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. Although six different sides can be drawn, ''usually'' three views of a drawing give enough information to make a 3D object. These views are known as ''front view'', ''top view'', and ''end view''. The terms ''elevation'', ''plan'' and ''section'' are also used.