QA-PF1: QA-P1-P5-P16-P19 Perspective Field

When we look to all known QA-points we find one prominent Perspective Field (see QA-PF-1) which is defined by the 4 points with lowest serial number, where no three of these points are collinear.
QA-PF1 includes these points:
When we choose QA-P1, QA-P5, QA-P16 and QA-P19 as the defining points of the field we get these Perspective Coordinates for all points:
QA-P1  (1:0:0)
QA-P5 (0:1:0)
QA-P16 (0:0:1)
QA-P19 (1:1:1)
QA-P20 (1:2:0)
QA-P21 (1:0:1)
QA-P22 (3:4:0)
QA-P25 (2:-1:0)
QA-P26 (5:2:0)
QA-P31 (2:2:1)
The standard compliance factors cf1, cf2, cf3 in this field, resp. relating to QA-P1, QA-P5, QA-P16 turn out to be:
cf1 = -(p + q) (p + r) (q + r) (p2 + p q + q2 + p r + q r + r2),
cf2 = p2 + p q + q2 + p r + q r + r2,
cf3 = (p + q) (p + r) (q + r) (p + q + r)
For example it can be checked that:
QA-P31 = 2.cf1.QA-P1 + 2.cf2.QA-P5 + 1.cf3.QA-P16,

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