Calculation example – Central projection and projective transformation of a plane

Calculate the maximum offset value ΔΖmax of an extrusion or intrusion detail from a reference plane (mainly flat object) so that the maximum error on the image plane due to radial shift does not exceed a certain limit Δρmax. (optical axis perpendicular to object plane)

1. From the geometry of the scene applies:

where m_b is the image scale (constant for a flat object face parallel to image plane).

From these equations, it follows that Δρ value is proportionate to ρ– as well as to ΔΖ. Thus, for a given ρ– value, radial error Δρ reaches its unfavorable value when ΔΖ=ΔΖmax , that is along the limits of the image.

   2. Given the previous equation, for Δρmax:

concluding that, in order to maintain an orthoimage's accuracy inside the limits of the default graphical accuracy, the object must not reveal extruded or intruded faces larger than 12 cm.