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Points

Points use the identification letter P.

PT cartes
Create point from cartesian coordinates.

[BasePoint]          optional - BasePoint
[offset X-coord]     optional - set X-offset (value)
[offset Y-coord]     optional - set Y-offset
[offset Z-coord]     optional - set Z-offset

BasePoint:
- key coordinates into field BasePoint (eg "10,10,0")
- or indicate position (left mouse button)
- or select object; the point and the parametric value for the selected
position is generated

Relative:
- select the base point and put the values for the offset distance
into the fields "offset -"

Example :
Specifying an absolute 2D point.
P1 = P(10 20)
Specifying an absolute 3D point.
P2 = P(10 20 30)
Specifying a relative point (at a distance 10,10 from P2)
P3 = P2 X(10) Y(10)

PT polar
Create points from polar coordinates

BasePoint       BasePoint
Angle-Rot.      rotate around the Z-axis of the active construction plane (angle);
[Angle-Tilt]    rotate (tilt) normal to the Z-axis
Dist.           distance from BasePoint

Example:
# P = BasePoint, RotationAngle, [Tilt Angle,] Distance
P5 = P4 ANG(90) 25

PT rotate-Z
Rotate a Point around the Z-axis of the active construction plane

CenterPoint     rotate around this point an d the Z-axis
Point/Vector    set point to be rotated (select point or vector)
Angle-Rot.      rotate around the Z-axis of the active construction plane (angle);
[Angle-Tilt]    rotate (tilt) normal to the Z-axis
[Dist.]         distance from BasePoint

Example:
P3 = P1 P2 ANG(180)
# P2 is turned 180 degrees around P1.

PT rotate-axis
Rotate a Point around a axis

Point to rotate set point point to be rotated
Rot-Axis        select line as rotation-axis
Angle           angle in degree

Example:
# P = point, rot-axis, angle
P21=P20 L20 ANG(30)    # rotate P20 30 degrees around line L20

PT translate
Translate (move) point with a vector

Point            point to move
Direction-VEC    set direction/distance (vector)
[Dist.]          length
[Dist.Normal]    Distance - normal to "Direction" (in the construction plane)

P = BasePoint, Direction, [Distance,] [Normal Distance]

Examples:
# Translate point P1 with vector D1.
D1 = 100 0 0
P2 = P1 D1

# Translate point P1 in the direction of the vector D1 at a distance of 12.
P2 = P1 D1 12

PT endpoints center focus ..
Get the characteristic point of an object.

LN/CI/Curv    select curve
Version       set which type of point

PTS()     default        1         2          3           4
Line:    startpoint, startpoint, endpoint  midpoint.
Circle:  centerpoint,startpoint, endpoint, centerpoint.
Ellipse: centerpoint,startpoint, endpoint, centerpoint, focuspt-1, focuspt-2.
Clothoid startpoint, startpoint, endpoint
Plane:   origin.
Model:   origin.

Beispiele:
P20=C20             # center of circle: or
P20=C20 PTS(1)
P24=L21 PTS(2)      # endpoint of line, or:
P24=P(L21 PTS(2))
P7=S20 PTS(2)       # endpoint of curve S20
P3=P1 P2            # midpoint
P3=L1 PTS(3)        # midpoint

PT control-points
Get control-points of a polygon or spline

LN/CI/Curv    select polygon or spline
point-Nr      set point-number

# get second point of polygon S20
P20=S20 PTI(2)

PT intersect  LN/CIR/CRV/PLN

Create a point at the intersection of two objects

# Intersection of a line with another line
P4 = L1 L2

# Intersection a circle and a line
P5 = L1 C1 page

# Intersection of 2 circles
P6 = C1 C2 side

# Intersection Line X Plane|RuledSurface
P6=L10 R20
P6=INT L10 R20

PT Proj. PT -> LN/CIR/CRV/PLN
Project a point perpendicular onto an object.
Object: line,circle,polgon,ellipsis,b-spline,plane
Version: (1-n, PageUp/dwn-key)

# Project Point onto Line:
P2 = P1, L1
# Line defined by Point + Vector:
P3=P2 P1 DX
# projects P2 onto Line P1-DX (horizontal, unlimited, through P1)

# project Point onto circle
# The standard solution is the nearer point.
P7 = P1 C1 MOD(2)
MOD(2) defines the distant point.

# Projection of the point P10 to the plane R1.
P11 = P10 R1

# Point on curve project.
P11 = P1 S10 MOD(1)
P1-P11 now form a normal to S10 at point P11.
MOD (1) =-first solution.

PT Proj. PT along VC -> PLN
Projects a point along a vector onto a plane.

Example:
R20=P(50 0 0) D(1 0 1)
D20=D(1 0 1)
P28=P(10 0 0) D20 R20

PT parametric on LN/CIR/CRV/SUR
Create a point on Line / Circle / Curve / Surface using parameter/s.

LN/CI/Curv/Surf        select line, cirle or curve (*1)
Parameter along        key parameter (*2)
[Parameter across]

(*2)  Parameters field is 0 to 1; 0.5 defines the middle.

(*1) Surfaces (RuledSurface, RevolvedSurface or B-SplineSurface):
Two parameters are required (U and V), along and across the direction.
Not all types of surfaces supported yet.

Example:
# midpoint of line:
P23 = L20 VAL(.5)

# Point on surface, U-value, V-value; range is 0 - 1 !
P1=A1 0.5 0.5
# or
P1=A1 VAL(0.5) VAL(0.5)

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