yielding,

and

This is simply the perspective equation with individual point depths replaced by an average constant depth

The weak-perspective model is valid when the average variation of the depth of the object along the line of sight is small compared to the and the field of view is small. We see this as follows.

Expanding the perspective projection equation using a Taylor series, we obtain

When only the zero-order term remains giving the weak-perspective projection. The error in image position is then :

showing that a small focal length , small field of view and ) and small depth variation contribute to the validity of the model.

Subhashis Banerjee 2008-01-20