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<a href="CAD_using_en.htm">See operating CAD</a>


<h1>Vectors</h1>


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))"


<u>Example:</u>
# 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)



<p><a name="Copy"></a></p>
  <h2>Vectors from Copy function</h2>
Objectselections create this formats:

# Vector from Line:
D(L{nr})
<u>Example:</u>
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})
<u>Example:</u>
# 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}))


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



<hr>
<a name="F0"></a>
<h2>VEC cartesian</h2>
Definition by entering the components of the axis (eg "0 0 1")
Or input of a standard vector (eg "DX")
Or a defined vector (eg "D20"; with Page Down key)
Or selection of a line or polygonsegment (or polygonsegment in CCV)
  or plane or plain surface.

Optional:
   Definition of vector length
   Reverse Direction ("REV"; with Page Down key)

Standardvectors are DX DY DZ DIX DIY DIZ.

Examples:
D3 = D (0.7 0 0.7) 100



<a name="F1"></a>
<h2>VEC polar      (Angles Length)</h2>
By definition vector rotation angle [tilting angle] [vector length] [REVers]

   Angle-Rot:  rotation around the z-axis of the active construction-plane,
   Angle-Tilt: rotation (tilt) around the new y-axis.





<a name="F2"></a>
<h2>VEC objects</h2>
Vectors parallel or right-angled to existing objects.

Optional for all vectors:
   Definition of vector length
   Reverse Direction ("REV"; with Page Down key)


<b>Parallel Vector:</b>
  Vector between 2 <a href="CAD_Base_en.htm#P">Points</a>; Length optional.

  Vector tangential to curve through point on this curve:
    select circle or ellipse or B-Spline or Clothoid and -
    point on this curve

  Vector parallel to main-axis (U-direction):
    (until now only for plane, B-SplineSurface)
    Plane: result is the X-axis of the plane.
    Surface: direction of the isoparametric U-curve
    Use Modifier "PARL"

  Vector parallel to V-axis (only for plane, surface)               
    (until now only for plane, B-SplineSurface)
    Plane: result is the Y-axis of the plane.
    Surface: direction of the isoparametric V-curve
    Use Modifier "CX"

<b>Normal Vector:</b>
  Normal vector for circle or plane or ellipse
  
  Normal vector surface (until now only B-SplineSurface)
    select surface and -
    point on this surface

  Normal vector to 2 line Segments(<a href="CAD_Base_de.htm#D">Vector</a> or <a href="CAD_Base_en.htm#L">Line</a>):
    3 points
    point, line
    2 lines
    The result (the normal vector) is the cross product of 2 input vectors.



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




<hr>
The following commands must be produced manually:

<h2>Vector-Multiplication / Divison</h2>
D21 = D20 * 2
D22 = D20 / 2






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