Editing 3D projection (section)

=== Weak perspective projection ===

A "weak" perspective projection uses the same principles of an orthographic projection, but requires the scaling factor to be specified, thus ensuring that closer objects appear bigger in the projection, and vice versa. It can be seen as a hybrid between an orthographic and a perspective projection, and described either as a perspective projection with individual point depths <math>Z_i</math> replaced by an average constant depth <math>Z_\text{ave}</math>,<ref>{{cite web |url = http://www.cse.iitd.ernet.in/~suban/vision/affine/node5.html |title = The Weak-Perspective Camera |author = Subhashis Banerjee |date = 2002-02-18 }}</ref> or simply as an orthographic projection plus a scaling.<ref>{{cite tech report |first = T. D. |last = Alter |title = 3D Pose from 3 Corresponding Points under Weak-Perspective Projection |url = http://dspace.mit.edu/bitstream/handle/1721.1/6611/AIM-1378.pdf |institution = MIT [[AI Lab]] |date=July 1992 }}</ref>

The weak-perspective model thus approximates perspective projection while using a simpler model, similar to the pure (unscaled) orthographic perspective.
It is a reasonable approximation when the depth of the object along the line of sight is small compared to the distance from the camera, and the field of view is small. With these conditions, it can be assumed that all points on a 3D object are at the same distance <math>Z_\text{ave}</math> from the camera without significant errors in the projection (compared to the full perspective model).

'''''Equation'''''
:<math>\begin{align}
& P_x = \frac X {Z_\text{ave}} \\[5pt]
& P_y = \frac Y {Z_\text{ave}}
\end{align}</math>
assuming focal length <math display="inline">f = 1</math>.