Mathematical calculation of a point of intersection

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  • Mathematical calculation of a point of intersection

    Good day
    I hope you can help me, I would like to know how to mathematically calculate the point of intersection of two lines.
    You build the LIN-A-, as well as the LINR and intersect them to generate the PNT132.
    The software generates an intersection point between those two lines (a point in the middle).
    How does the software do this calculation?
    ThanksWhatsApp Image 2020-12-15 at 18.34.22.jpeg

  • #2
    It's workplane dependent.

    Look what workplane you are in, then set the graphics window to that view, you should see the intersection point is where the two lines intersect..

    I believe it's at the mid point between the lines (in the workplane view) so if one line was at z=10 and one was at z=0 then the point would be at z = 5.


    Does that make sense?

    Automettech - Automated Metrology Technology

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    • #3
      If the lines doesn't intersect phisicaly, I believe that the software calculates the mid point between lines along the common perpendicular line.
      You could :
      Code:
      ASSIGN/V1=CROSS(LIN_A.IJK,LINR.IJK)........................vector perp to both lines - don't use minus in the feature names.
      ASSIGN/V2=DOT(LIN_A.XYZ-LINR.XYZ,V1).....................distance between lines (not a real distance, can be negative)
      ASSIGN/V3=CROSS(V1,LIN_A.IJK)..................................vector perp to LIN_A and V1
      F1=GENERIC/PLANE,DEPENDENT,CARTESIAN,$
      NOM/XYZ,<LIN_A.TX,LIN_A.TY,LIN_A.TZ>,$
      MEAS/XYZ,<LIN_A.X,LIN_A.Y,LIN_A.Z>,$
      NOM/IJK,<V3.I,V3.J,V3.K>,$
      MEAS/IJK,<V3.I,V3.J,V3.K>
      PNT1=FEAT/POINT,CARTESIAN,NO
      THEO/<-3.873,1,0>,<1,0,0>
      ACTL/<-3.873,1,0>,<1,0,0>
      CONSTR/POINT,PIERCE,LINR,F1
      ASSIGN/V4=PNT1.XYZ+V2/2*V1...........................................................I'm not sure of the "+", maybe it's "-", I'm not at the cmm...
      F2=GENERIC/POINT,DEPENDENT,CARTESIAN,$
      NOM/XYZ,<V4.X,V4.Y,V4.Z>,$
      MEAS/XYZ,<V4.X,V4.Y,V4.Z>,$
      NOM/IJK,<V1.I,V1.J,V1.K>,$
      MEAS/IJK,<V1.I,V1.J,V1.K>
      F2 should be the point given by PC-DMIS...

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