QL-5: List of QL-Crosspoints

 
When 3 lines connecting QL-points concur, the point of concurrence is called a QL-Crosspoint.
In this list all possible non-registered QL-Crosspoints are listed originating from at least 3 connecting lines of QL-points in the range QL-P1QL-P26.
QL-points are mentioned without prefix “QL-”.
Lines are defined by 2 points on it with lowest serial number.
There are regularly recurring crossing lines with these Crosspoints. This is an indication for the occurrence of Perspective Fields (see QA-PF-1).
When the intersection points have fixed ratios of the distances to the defining points on the defining lines, then they are mentioned. There are many of them.
For point P on line P1.P2 the ratio d1 : d2 means that d(P,P1) : d(P,P2) = d1 : d2, where:
  • d1 is positive when P is positioned wrt P1 at the same side of the line as P2. If not then d1 is negative.
  • d2 is positive when P is positioned wrt P2 at the same side of the line as P1. If not then d1 is negative.
 
        P2.P5   ^ P3.P20   ^ P4.P12                                1 : 1 / 1 : 1  / 3 : -1
        P2.P5   ^ P4.P20   ^ P6.P22                               Infinity point
        P5.P8   ^ P14.P22 ^ P18.P20                            -3 : 4 / -8 : 9 / -2 : 3
        P5.P14 ^ P8.P22   ^ P18.P20                             9 : -4 / 8 : -3 / 2 : 3
        P5.P15 ^ P8.P20   ^ P18.P22                             9 : -4 / 2 : 3  / 8 : -3
        P5.P18 ^ P8.P20   ^ P15.P22                             4 : -3 / -2 : 3 / -8 : 9
        P9.P12 ^ P10.P14 ^ P11.P18                               6 : -1 / 9 : 1 / 3 : 2
        P9.P15 ^ P10.P12 ^ P11.P18                               9 : -2 / 6 : 1 / 3 : 4
        P9.P18 ^ P10.P12 ^ P11.P15                               3 : 2 / 6 : -1 / 9 : -4
        P9.P18 ^ P10.P14 ^ P11.P12                               3 : 1 / 9 : -1 / 3 : -1

 

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