Objects and Functions

Scalar:Distance

Scalar:Distance(<point>, <point>)

Distance between 2 Points:

d = Scalar:Distance(P1, P2)

Distances from Point to Point are always positive values.

Scalar:Distance(<point>, <line>)

Abstand zwischen einem Punkt und einer Geraden:

d = Scalar:Distance(P1, L1)

Ergebnis is positiv, wenn der Punkt in Fahrtrichtung rechts der Geraden liegt

Ergebnis ist negativ, wenn der Punkt in Fahrtrichtung links der Geraden liegt

Scalar:Distance(<point>; <circle>)

Abstand zwischen einem Punkt und einem Kreis:

d = Scalar:Distance(P1, C1)

Ergebnis ist positiv, wenn der Punkt ausserhalb des Kreises liegt n

Ergebnis ist negativ, wenn der Punkt innerhalb des Kreises liegt

Scalar:Angle

Scalar:Angle(<line>, <line>)

Angle (in degrees) between 2 lines:

alfa = Scalar:Angle(L1, L2)

Ergebnis ist der erforderliche Winkel, um L1 fahrtrichtungsgleich auf L2 zu drehen.

(-180° <= Ergebnis < 180°).

Point: Direct Creation

Point:Create(<number>, <number>)

Definition using x/y coordinates:

P = Point:Create(x, y)

x: x coordinate

y: y coordinate

Point: Intersections

Intersection of lines

Point:Intersection(<line>, <line>)

Definition by intersection of 2 lines:

P = Point:Intersection(L1, L2)

L1: first line object

L2: second line object

Intersection of line and circle

Point:Intersection(<line>, <circle>, <number>)

Definition by intersection of a line and a circle:

P = Point:Intersection(L1, C1, n)

L1: line object

C1: circle object

n: selected number of intersection: 1 (first), 2 (second)

Intersection of 2 circles

Point:Intersection(<circle>, <circle>, <number>)

Definition by intersection of 2 circles:

P = Point:Intersection(C1, C2, n)

C1: circle object

C2: circle object

n: selected number of intersection: 1 (first), 2 (second)

Reference line is the connection between the center points of the 2 circles.

Point: Perpendiculars

Perpendicular of a point to a line

Point:Perpendicular(<point>, <line>)

Definition by the intersection of perpendicular line from a point to the target line:

Px = Point:Perpendicular(P1, L1)

P1: point object

L1: target line object

Perpendicular of a point to a circle

Point:Perpendicular(<point>, <circle>)

Definition by the intersection of perpendicular line from a point to the target circle:

Px = Point:Perpendicular(P1, C1)

P1: point object

C1: target circle object

Point: Vanishing

Point:Align(<point>, <point>, <number>)

Definition by the vanishing point on the line between 2 points:

P = Point:Align(P1, P2, rdist)

P1: first point object

P2: second point object

rdist: position of target point in relation to distance between P1 and P2

rdist < 0 : before P1

rdist == 0 : P1

0 < rdist < 1 : between P1 and P2

rdist == 1: P2

rdist > 1 : after P2

Point: Reflections

Point:Mirror(<line> [,<line>]*, <point> [,<point]*)

Definition by the reflection point(s) on the line(s):

Pa, Pb, Pc, Pd = Point:Mirror(L1, P1, P2, L2)

Pa: reflected point P1 on line L1

Pb: reflected point P2 on line L1

Pc: reflected point P1 on line L2

Pd: reflected point P2 on line L2

Point:: Tangents

Tangent from a point to a circle

Point:Tangent(<point>, <circle>, <number>)

Definition of a tangent point from a point to a circle:

P = Point:Tangent(P1, C1, n)

P1: point object

C1: circle object

n: integer number 1 (right hand side), 2 (left hand side)

Reference direction is the line from P1 to the center of C1

Tangent between 2 circles

Point:Tangent(<circle>, <circle>, <number>)

Definition of a tangent point of 2 circles:

P = Point:Tangent(C1, C1, n)

C1: first circle object

C2: second circle object

n: integer number

1 right hand side on C1

2 right hand side on C2

3 left hand side on C1

4 left hand side on C2

Reference direction is the line from the center of C1 to the center of C2

Point: Fillets (Rounding of corners)

Rounding between 2 lines

Point:Rounding(<line>, <line>, <radius>, <number>)

Definition of a fillet between 2 lines:

P1, P2, P3 = Point:Rounding(L1, L2, r, n)

P1: center point of arc circle P2: starting point of arc circle P3: ending point of arc circle r: radius of arc circle n: selection of area as shown in figure (returns all results if < 1)

Rounding between line and circle

Point:Rounding(<line>, <circle>, <radius>, <number>)

Definition of a fillet between a line and a circle:

P1, P2, P3 = Point:Rounding(L1, C1, r, n)

P1: center point of arc circle P2: starting point of arc circle P3: ending point of arc circle r: radius of arc circle n: selection of area as shown in figure (returns all results if < 1)

Rounding between 2 circles

Point:Rounding(<circle>, <circle>, <radius>, <number>)

Definition of a fillet between 2 circles:

P1, P2, P3 = Point:Rounding(C1, C2, r, n)

P1: center point of arc circle P2: starting point of arc circle P3: ending point of arc circle r: radius of arc circle n: selection of area as shown in figure (returns all results if < 1)

Line: Create

2 Points

Line:Create(<point>, <point>)

Definition by 2 points:

L = Line:Create(P1, P2)

P1: first point

P2: second point

Point and Angle

Line:Create(<point>, <angle>)

Definition by one point and an angle:

L = Line:Create(P1, alfa)

P1: first point

angle: angle from x-axis in degree

Point and Perpendicular

Line:Create(<point>, <line>)

Definition by a point and a perpendicular line:

L = Line:Create(P1, L1)

P1: point which must not be part of the target line

L1: perpendicular line

Perpendicular of line between 2 Points

Line:Perpendicular(<point>, <point>, <rdist>)

Definition by a point and a perpendicular line:

L = Line:Perpendicular(P1, L1, rdist)

P1: first point

P2: second point

rdist: position of target line rotated by 90 deg in relation to distance between P1 and P2

rdist < 0 : before P1

rdist == 0 : P1

0 < rdist < 1 : between P1 and P2

rdist == 1: P2

rdist > 1 : after P2

Parallel line of point

Line:Parallel(<line>, <point>)

Definition by a parallel line and a point:

L = Line:Parallel(L1, P1)

L1: line

P1: point of the target parallel line

Parallel line with distance

Line:Parallel(<line>, <distance>)

Definition by a parallel line and a distance:

L = Line:Parallel(L1, dist)

L1: line

dist: distance of the target parallel line (>0 right hand side, <0 left hand side)

Circle

Direct construction

Circle:Create(<point>, <radius>)

Definition by center point and radius:

C = Circle:Create(P1, rad)

P1: center point

rad: radius

Center and Radius

Circle:Create(<point>, <radius>)

Definition by center point and radius:

C = Circle:Create(P1, rad)

P1: center point

rad: radius

3 Points

Circle:Create(<point>, <point>, <point>)

Definition by 3 points:

C = Circle:Create(P1, P2, P3)

P1: first point

P2: second point

P3: third point