Since d > 0 for m = 0 (object at infinity or at a distance >> f = 0.165 m), the slight distortion is pincushion. For closer objects the distortion decreases, passing through zero just above the unit magnification (m~1.1, at distance ~ 310-320 mm), and for very close objects (m = 4 with distance  ~ (1+1/m) f = 206 mm, where d < 0) it becomes “barrel” distortion.

For ordinary photography with a 6½ inches Dagor ( m≲0.2 , i.e. subject distances beyond about 1 meter), the distortion stays well under 0.25% over the field actually used on 4×5 in ( θ≤25° , giving ~0.15% at the corners, i.e. about 3 pixels max error for a 4K image at its corners). The same θ≤25° holds for slightly smaller European standard 90×120 mm. Only if the lens is pushed toward the limit of its ~72–80° coverage circle ( θ→36 – 40° ) does the pincushion distortion rise to roughly 0.45–0.66%. Near the center of view, this distortion is negligible. At θ = 20°, it is less than 0.1%. The determination of the vanishing points is therefore virtually unaffected by this radial distortion for the Dagor lens, particularly when the angles of the lines’ projection directions differ greatly.

Practical rule of thumb: for VP work, the error in a vanishing point scales roughly as the line-fitting residual divided by the angular span of the line segments used. Short segments near the frame edge are the worst case. So, try to find long segments near the center of view or near VP, the vanishing point. Segments close to the VP are much more accurate even when they are short.

Evaluating the max distortion

A python script used by Claude Opus 5 ® AI computes the k[i]  and the distortion values from Magill's measurements using a 6th order even power polynomial regression (non-zero coefficients of r2, r4, r6). The max distortion d at 36° field angle (the documented limit of rectilinearity in the coverage circle) is also evaluated for various magnification values. You can use it in a Jupyter notebook or a .py file.