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    See operating CAD

    Vectors

    Vectors define a direction and do not have a position.

    Vectors use the identification letter D ("Direction").

    There are the following standard vectors:
      DX DY DZ
      corresponding to the absolute directions

      DIX DIY DIZ
      corresponding to the reverse absolute directions

    Display of Vectors:
    - Vectors are only temporarly represented;
    - standard-vectors are displayed in the lower right corner
    - scan through defined vectors with the PageUp or PageDown button
    - Standardized vectors (with length 1) as dashed line, otherwise as full line.

    Define a vector:
    - select a line or 2 points or a polygon
    - select a circle or plane (normal-vector)
    - select one of the standard-vectors from the vectors displayed in
        the lower right corner.
    - select a defined vector with the PageUp or PageDown button
    - key in vector:
      standard-vector DX or DY or DZ or DIX or DIY or DIZ
      or defined-vector eg "D12"
      or the x/y/z-coordinates; eg "D(0 0 1)" defines a Z-vector
      or one or two angles; eg "D(ANG(45))" or "D(ANG(45) ANG(45))"

    Example:
    # Vector 1 = direction negative X-Achse
    D1=DIX
    # Vektor 2 = into direction x=1, y=1 in the XY-plane
    D2=D(1 1 0)

      Vectors from Copy function
    Objectselections create this formats:

    # Vector from Line:
    D(L{nr})
    Example:
    L20=P(0 0 0) P(100 10 0)
    D20=D(L20)

    # Vector from Polygon segment
    # or Vector from Line in CCV:
    D({obj} MOD({SegmentNummer}))

    # Vector on circle, B-Spline, clothoid, ellipse:
     D#={C#|S#}) {lpar})
    Example:
    # Vector on circle:
    C20=P(0 0 0) 12
    D20=D(C20 0.5)

    # Vector from Line in CCV
    # or Vector from Polygonsegment in CCV:
    P({obj} MOD({CCV-SegmentNummer}) MOD({SegmentNummer}))

    Example:
    # Vector from 1.Segment of CCV S26 (a Line):
    P(S26 MOD(1))

    VEC cartesian
    Create vector.

       BaseVector       basevector
       [Angle-Rot.]     rotation around the z-axis of the active construction-plane
       [Angle-Tilt]     tilting angle in the active construction-plane
       [Length]         Definition of vector length
       [REVers]         Reverse Direction ("REV"; also with Page-Down key)

      Definition basevector:
        Definition by entering the components of the axis (eg "0 0 1", a z-vector)

        Or input of a standard vector (eg "DX")
          Standardvectors are DX DY DZ DIX DIY DIZ.

        Or a defined vector (eg "D20"; with Page-Up or Down key or select
          from the objectbrowser (left side))

        Or selection of a line or polygonsegment (or polygonsegment in CCV)
          or plane or plain surface.

    Examples:
    # Vector from X,Y,Z-components:
    D3=D(0.7 0 0.7)

    # X-Vector rotated 30 deg. around the z-axis of the active construction-plane
    #   an then 60 deg. tilted.
    D4=DX ANG(30) ANG(60)

    # Vector reverted
    D5=D4 REV

    VEC objects
    Vectors parallel or right-angled to existing objects.

       Obj1              Line or curve or surface
       [Point (on obj)]  basepoint for vector
       [PT or VC]        additional object (e.g. for normal vector)
       [Length]          Definition of vector length
       [REVers]          Reverse Direction ("REV"; with Page Down key)
       [parallel-across] parallel (tangential) or normal (rectangular)

    Parallel Vector:

      Vector tangential to curve through point on this curve:
       Obj1              Line or curve or surface
       [Point (on obj)]  point on this curve / surface

      Vector parallel to Vector or Line, cornerpoint
        Obj1              direction - Vector or Line
        [Point (on obj)]  Startpoint
        [PT or VC]        point (cornerpoint)
        PARL oder CX      PARL: Vector along Obj1 from Startpoint to cornerpoint
                          CX:   Vector normal to direction
                          default: normal to plane from Obj1 - cornerpoint

      Vector parallel to 2 points, cornerpoint
        Obj1              Startpoint
        [Point (on obj)]  point on Vector / Line
        [PT or VC]        point (cornerpoint)
        PARL oder CX      PARL: Vector along Startpoint - Point-on-OBj to cornerpoint
                          CX:   Vector normal to Startpoint - Point-on-OBj
                          default: normal to plane from 3 points

      Vector in surface parallel to Isoparametric direction U or
                          Isoparametric direction V
        Obj1              surface oder plane
        [Point (on obj)]  point on surface
        PARL oder CX      PARL: vector at Point-on-OBj into direction U
                          CX:   vector at Point-on-OBj into direction V
                          default: vector at Point-on-OBjnormal to surface

    Normal Vector:
      Normal vector for circle or plane or ellipse
        Obj.1                 select  circle, plane or ellipse

      Normal vector to 2 line Segments (crossproduct):
        3 points
        line, point
        2 lines
        The result (the normal vector) is the cross product of 2 input vectors.

      Normal vector surface (until now only B-SplineSurface)
        Obj.1                 select surface and -
        [Point (on Obj)]      a point on this surface

    Examples:

    # Normal vector to circle
    D20=C20

    # Tangential vector to circle
    D21=C20 P(C20 0.2)

    # Vector between points P1, P2; length 100.
    D5=P1 P2 VAL(100)

    # Normal vector to line L20:
    D20=L20 DZ

    # X-axis-Vector of plane R20
    D20=R20 PARL

    The following commands must be produced manually:

    Vector-Multiplication / Divison
    D21 = D20 * 2
    D22 = D20 / 2