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Define Line

A line is a straight one-dimensional geometric object that extends infinitely in both directions.  It is uniquely determined by passing through 2 points.  A line may be defined by any of the following:

Rectangular Coordinates
Through 2 Points
Through a Point and Tangent to a Circle
Tangent to 2 Circles
Through a Point and at an Angle or Slope with the X or Y Axis
The X or Y Axis
Through a Point and Having a Slope with Respect to Another Line
Through a Point at an Angle with a Line
Through a Point and Parallel or Perpendicular with a Line
Parallel to a Line at a Distance
Intersection of 2 Planes
Angle or Slope and Axis Intercept
Tangent to a Circle at an Angle to the X-Axis
Angle with a Line and Tangent to a Circle
Offset from the X or Y Axis


Rectangular Coordinates

LINE/x1,y1,z1,x2,y2,z2
The line is defined as passing through 2 points which are defined by their coordinates.  The coordinate of the first point is at x1, y1, z1.  The coordinate of the second point is at x2, y2, z2.


L1=LINE/-6.0,0,0,0,11.0,0
L2=LINE/10.0,3.0,4.0,0,0,13.0


Through 2 Points

LINE/point1,point2
The line is defined as passing through the 2 named points point1 and point2.


L1=LINE/P1,P2
L2=LINE/P3,P4


Through a Point and Tangent to a Circle

LINE/point,modifier,TANTO,circle
modifier: LEFT | RIGHT
The line is defined as passing through point and tangent to circle.  The modifier is determined by looking from the point toward the center of the circle.  LEFT is specified when the line passes to the left of center; RIGHT otherwise.


L1=LINE/P1,LEFT,TANTO,C1
L2=LINE/P1,RIGHT,TANTO,C1
L3=LINE/P2,RIGHT,TANTO,C2
L4=LINE/P2,LEFT,TANTO,C2


Tangent to 2 Circles

LINE/modifier1,TANTO,circle1,modifier2,TANTO,circle2
modifier1: LEFT | RIGHT
modifier2: LEFT | RIGHT
The line is defined as tangent to the circles circle1 and circle2.  The modifiers are determined by looking along the line in relation to the circle centers.  LEFT is specified when the line passes to the left of the given circle's center; RIGHT otherwise.


L1=LINE/LEFT,TANTO,C2,LEFT,TANTO,C1
L2=LINE/RIGHT,TANTO,C2,RIGHT,TANTO,C1
L3=LINE/RIGHT,TANTO,C1,LEFT,TANTO,C2
L4=LINE/LEFT,TANTO,C2,RIGHT,TANTO,C1


Through a Point and at an Angle or Slope with the X or Y Axis

LINE/point,ATANGL,angle,axis
LINE/point,SLOPE,slope,axis
axis: XAXIS | YAXIS
The line is defined as passing through point and at an angle or slope relative to the specified axis.  Slope is the tangent of the angle.


L1=LINE/P1,ATANGL,45.0,XAXIS
L2=LINE/P2,ATANGL,22.5,XAXIS
L3=LINE/P3,ATANGL,30.0,YAXIS
                         or
L1=LINE/P1,SLOPE,1.0,XAXIS
L2=LINE/P2,SLOPE,0.4142,XAXIS
L3=LINE/P3,SLOPE,0.5774,YAXIS


The X or Y Axis

LINE/axis
axis: XAXIS | YAXIS
The defined line is the XAXIS or the YAXIS.  The line may also be offset from and parallel to axis by a specified distance.


Through a Point and Having a Slope with Respect to Another Line
Through a Point at an Angle with a Line

LINE/point,ATANGL,angle,line
LINE/point,SLOPE,slope,line
The line is defined as passing through point and at an angle or slope relative to line.  The angle or slope is measured from the given line to the line being defined.  Slope is the tangent of the angle.


L1=LINE/P1,SLOPE,0.5774,L2
L3=LINE/P3,SLOPE,-1.5051,L2
                      or
L1=LINE/P1,ATANGL,30.0,L2
L3=LINE/P3,ATANGL,-56.4,L2


Through a Point and Parallel or Perpendicular with a Line

LINE/point,PARLEL,line
LINE/point,PERPTO,line
The line is defined as passing through point and parallel (PARLEL) or perpendicular (PERPTO) to line.


L2=LINE/P2,PARLEL,L1
L3=LINE/P3,PERPTO,L1


Parallel to a Line at a Distance

LINE/PARLEL,line,modifier,offset
modifier: XLARGE | XSMALL | YLARGE | YSMALL
The line is defined as parallel to line and offset from it by distance offset.  The modifier specifies the direction of the offset.


L1=LINE/PARLEL,L2,XLARGE,4.0
L3=LINE/PARLEL,L2,XSMALL,6.0
                           or
L1=LINE/PARLEL,L2,YLARGE,4.0
L3=LINE/PARLEL,L2,YSMALL,6.0

The directional modifiers are defined here.


Intersection of 2 Planes

LINE/INTOF,plane1,plane2
The line is defined as the intersection of plane1 with plane2.


L1=LINE/INTOF,PL2,PL3


Angle or Slope and Axis Intercept

LINE/ATANGL,angle,INTERC,axis,intercept
LINE/SLOPE,slope,INTERC,axis,intercept
axis: XAXIS | YAXIS
The line is defined as having an angle or slope with the given axis and intersects the given axis at intercept.  Slope is the tangent of the angle.


L1=LINE/ATANGL,-45.0,INTERC,XAXIS,5.92
L2=LINE/ATANGL,-65.0,INTERC,YAXIS,3.54
                                     or
L1=LINE/SLOPE,-1.0,INTERC,XAXIS,5.92
L2=LINE/SLOPE,-2.1445,INTERC,YAXIS,3.54


Tangent to a Circle at an Angle to the X-Axis

LINE/modifier,TANTO,circle,ATANGL,angle
modifier: XLARGE | XSMALL | YLARGE | YSMALL
The line is defined as tangent to circle and at an angle with the X-axis.  The modifier specifies which of the 2 possible lines is required.

L1=LINE/YSMALL,TANTO,C1,ATANGL,45
L2=LINE/XSMALL,TANTO,C1,ATANGL,120

The directional modifiers are defined here.


Angle with a Line and Tangent to a Circle

LINE/ATANGL,angle,line,TANTO,circle,modifier
modifier: XLARGE | XSMALL | YLARGE | YSMALL
The line is defined as tangent to circle and at an angle to line.  The angle is measured from the given line to the line being defined.  The modifier specifies which of the 2 possible lines is required.


L2=LINE/ATANGL,55.0,L1,TANTO,C1,YLARGE
L3=LINE/ATANGL,55.0,L1,TANTO,C1,YSMALL

The  directional modifiers are defined here.


Offset from the X or Y Axis

LINE/axis,offset
axis: XAXIS | YAXIS
The line is defined as parallel to and offset from the given axis.


L5=LINE/XAXIS,5.0
L6=LINE/YAXIS,-7.0