QA-5: List of QA-Crosspoints

When 3 lines connecting QA-points concur, the point of concurrence is called a QA-Crosspoint.
In this list all possible non-registered QA-Crosspoints are listed originating from at least 3 connecting lines of QA-points in the range QA-P1QA-P34.
QA-points are mentioned without prefix “QA-”.
Lines are defined by the first 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.
When there are no fixed ratios this is indicated by the remark “x : y”.
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.
        P1.P4 ^ P3.P6 ^ P20.P28                                        1 : 2 / 2 : 1 / 4 : -1
        P1.P4 ^ P5.P28 ^ P6.P34                                        1: 4 / 4 : 1 / 3 : 2
        P1.P8 ^ P2.P23 ^ P4.P33                                        x : y / x : y / x : y
        P1.P8 ^ P2.P32 ^ P7.P33                                        x : y / x : y / x : y
        P1.P11 ^ P3.P30 ^ P12.P20 ^ P13.P22                 Infinity Point
        P1.P11 ^ P5.P12 ^ P13.P20 ^ P30.P34                 -1 : 2 / 1 : 1 / -1 : 2 / 3 : -1
        P1.P12 ^ P5.P13 ^ P24.P32                                     1 : 4 / 4 : 1 / 4 : 1
        P1.P12 ^ P11.P26 ^ P14.P32                                   1 : 6 / 9 : -2 / 4 : 3
        P1.P13 ^ P5.P12 ^ P11.P20                                     Infinity Point
        P1.P13 ^ P11.P22 ^ P12.P20                                   2 : -1 / 2 : -1 / 1 : 1
        P1.P16 ^ P19.P20 ^ P22.P31                                  Infinity Point
        P1.P17 ^ P10.P16 ^ P18.P21                                   x : y / x : y / x : y
        P1.P17 ^ P10.P27 ^ P16.P18                                  -1 : 4 / x : y / x : y
        P1.P19 ^ P5.P16 ^ P10.P27                                    -1 : 3 / 2 : 1 / x : y
        P1.P19 ^ P5.P31 ^ P10.P21                                     1 : 4 / 4 : 1 / 2 : 3
        P1.P28 ^ P5.P6 ^ P12.P24                                      x : y / x : y / x : y
        P1.P29 ^ P2.P20 ^ P3.P5                                       Infinity Point
        P1.P29 ^ P3.P10 ^ P20.P34                                   1 : 1 / 3 : 1 / 3 : 1
        P1.P29 ^ P6.P20 ^ P12.P24                                   x : y / x : y / x : y
        P1.P31 ^ P5.P17 ^ P10.P27 ^ P16.P20                 Infinity Point
        P1.P31 ^ P16.P22 ^ P19.P20                                  2 : -1 / 2 : -1 / 1 : 1
        P1.P32 ^ P2.P4 ^ P7.P8 ^ P12.P24                      Infinity Point
        P1.P32 ^ P3.P6 ^ P4.P34                                       x : y / 1 : 1 / 3 : 1
        P2.P5 ^ P3.P20 ^ P10.P34                                    Infinity Point
        P2.P7 ^ P3.P23 ^ P6.P34                                       x : y / x : y / x : y
        P2.P7 ^ P3.P33 ^ P32.P34                                     x : y / 2 : 3 / 9 : -4
        P2.P7 ^ P6.P32 ^ P23.P33                                     x : y / x : y / x : y
        P2.P8 ^ P3.P4 ^ P7.P34                                         x : y / x : y / x : y
        P2.P8 ^ P4.P33 ^ P7.P23                                       x : y / x : y / x : y
        P2.P16 ^ P3.P21 ^ P29.P31                                   Infinity Point                    
        P2.P16 ^ P19.P29 ^ P21.P34                                 2 : -1 / 2 : -1 / 3 : -2
        P2.P20 ^ P3.P10 ^ P22.P29                                  1 : 1 / 3 : -1 / -1 : 2    
           (Center QA-DT-P2-P20 Conic; note Randy Hutson)
        P2.P20 ^ P3.P22 ^ P10.P34                                  2 : 1 / 4 : -1 / -1 : 2
        P2.P26 ^ P10.P34 ^ P25.P29                                6 : -1 / 2 : 3 / 2 : 3
        P2.P32 ^ P3.P6 ^ P23.P34                                     x : y / x : y / x : y
        P3.P5 ^ P4.P20 ^ P12.P24                                     x : y / x : y / x : y
        P4.P11 ^ P6.P30 ^ P12.P28                                   2 : 1 / 1 : 2 / 4 : -1
        P5.P12 ^ P13.P20 ^ P30.P34                                1 : 1 / -1 : 2 / 3 : -1
        P5.P16 ^ P10.P21 ^ P19.P20                                 2 : -1 / -2 : 3 / 2 : -1
        P5.P17 ^ P10.P27 ^ P16.P20                                 Infinity Point
        P5.P29 ^ P12.P24 ^ P20.P28                                x : y / x : y / x : y
        P5.P31 ^ P10.P27 ^ P19.P20                                 4 : -1 / x : y / 2 : 1
        P10.P14 ^ P11.P33 ^ P20.P24                               Infinity Point
        P10.P21 ^ P16.P18 ^ P17.P20                                x : y / x : y / x : y
        P10.P21 ^ P16.P20 ^ P22.P31                               -1 : 3 / 1 : 1 / -1 : 2
        P10.P21 ^ P16.P26 ^ P19.P25                                1 : 1 / 3 : -1 / 3 : 1
        P10.P21 ^ P19.P26 ^ P25.P31                                2 : 5 / 6 : 1 / 4 : 3
        P10.P27 ^ P16.P22 ^ P20.P21                                x : y / 4 : -1 / 1 : 2
        P10.P27 ^ P16.P25 ^ P19.P26                                x : y / 3 : 2 / 6 : 1
        P10.P27 ^ P19.P25 ^ P26.P31                                x : y / 3 : -1 / -2 : 3
        P10.P33 ^ P11.P14 ^ P26.P32                                2 : 3 / 3 : 2 / -4 : 9
        P11.P16 ^ P12.P19 ^ P13.P31                                  Infinity Point
        P11.P31 ^ P12.P19 ^ P13.P16                                  2 : -1 / 1 : 1 / -1 : 2
        P16.P17 ^ P18.P21 ^ P19.P20                                 x : y / x : y / x : y