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:

QA-P1, QA-P5, QA-P10, QA-P16, QA-P19, QA-P20, QA-P21, QA-P22, QA-P25, QA-P26, QA-P31.

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, relating to QA-P1, QA-P5, and 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,
• etc.

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