```

CAD functions for planes and axis systems:

Planes and axis systems use the shortcut letter R.

Pre-defined planes are:
Vordefinierte Ebenen sind:

RZ   XY (Z=0)  Plane-X = Refsys-X
Plane-Y = Refsys-Y
(Plane-Z = Refsys-Z)

RY   XZ (Y=0)  Plane-X = Refsys-IX
Plane-Y = Refsys-Z
(Plane-Z = Refsys-Y)

RX   YZ (X=0)  Plane-X = Refsys-Y
Plane-Y = Refsys-Z
(Plane-Z = Refsys-X)

RIZ  XY (Z=0)  Plane-X = Refsys-X
Plane-Y = Refsys-IY
(Plane-Z = Refsys-IZ)

RIY  XZ (Y=0)  Plane-X = Refsys-IX
Plane-Y = Refsys-IZ
(Plane-Z = Refsys-IY)

RIX  YZ (X=0)  Plane-X = Refsys-Y
Plane-Y = Refsys-IZ
(Plane-Z = Refsys-IX)

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PLN Z-Axis [X-Axis]
Plane from Z-Axis (normal vector),
optional origin, X-Axis or point on x-axis, offset along z-axis.

[Origin]          optional;
Z-Axis            enter DX or DY or DZ or a vektor;
(the Z-axis of the new plane)
[X-Axis]          optional: the new X-axis; DX or DY or DZ
or a defined vector or a point on the new x-axis.
[offset Z-axis]   optional: distance of the new origin along the
new z-axis

Examples:
# Plane normal to the Z-axis, with distance.
R1=PERP DZ 100
# Plane normal to the Z-axis, through point.
R2=PERP P(0 0 100) DZ
# Plane in point p1; normal to the absolute X-axis;
#   new X-axis direction of absolute Z-axis;
#   distance 10 into direction of new Z-axis.
P1=P(100 0 0)
R3=PERP P1 DX DZ 50

# Level from origin, normal vector and a point on the x-axis of the new plane
R11 = PERP P(100 100 100) D(0 0 1) P(101 100 100)

R12=PERP P(100 150 0) D(ANG(90) ANG(45))

PLN X-Axis [Y-Axis]
Plane from X-Axis,
optional origin, Y-Axis or point on y-axis, offset along z-axis.

[Origin]          optional;
X-Axis            Vector or point on the new X-axis
[Y-Axis]          optional: Vector or point on the new y-axis
[offset Z-axis]   optional: distance of the new origin along the
new z-axis

Examples:
# origin, X-axis, Y-axis.
R12=P(100 100 100) D(1 0 0) D(0 1 0)

# Level/reference system through three 3D points;
#  po = the origin,
#  px = a point on the x-axis of the new plane
#  pt = a point in the plane (must not be on the line po-px).
R4 = P(100 100 100) P(101,100,100) P(100,101,100)

R20=P(100 100 25) DX DY
R10 = P(100 100 100) DZ
R11 = P(100 100 100) D(0 0 1) P (101 100 100)
R13 = P(100 100 100) L(P(0 0 0) P(0 0 100))

PLN PT Plane Offset Angle
Move, rotate a plane/reference system
Set new origin,
move the origin along X/Y/Z-axis,
rotate the X-axis and Y-axis around the Z-axis
All parameters are optional.

[Origin]         the new orgin
[Refsys]         plane to be moved
[offset-X-axis]  move the new origin along the X-axis
[offset-Y-axis]  move the new origin along the Y-axis
[offset-Z-axis]  move the new origin along the Z-axis
[Angle-around-Z] rotate the reference system around Z-axis (degree)
[Angle-around-Y] rotate the reference system around Y-axis (degree - tilt-angle)

Example:
#
# R20 - set new orgin
R21=RSYS P(100 100 50) R20
# R20 - move orgin, rotate axes
R22=RSYS R20 X(100) Y(100) ANG(180)

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MAN functions for planes and axis systems (further functions):

Plane parallel to the XY plane, all axis directions are the same as
the main axis. The distance on the Z-axis is specified.
R = Z (Z_distance)
R5 = Z(100)

Plane parallel to the YZ plane, and the new X-axis corresponds
to the 3D Y-axis, the new Y-axis corresponds to the 3D Z-axis.
The new Z-axis is the axis-X.
R = X(X_distance)

Plane parallel to the XZ plane, and the new X-axis corresponds to the
3D X-axis,
The new Y-axis corresponds to the 3D Z-axis.
The new Z-axis is the axis-Y.
R = Y(Y_distance)

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```