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<PRE>
CAD functions for Splines (Curves)
<A HREF="CAD_using_en.htm">See operation CAD ..</A>
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See also codes for curves
Shortcut key is S (Spline)
Polygon
Ellipse
Clothoid (spiral-form curve)
Contour (compound curve)</PRE>
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<h2>S Ellipse Center AxisEndPoints ELL</h2>
Ellipse from centre, end point main axis, end point minor axis:
S1 = P ELL(100 0) P(150 0) P(100 20)
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<h2>S Ellipse Center Axes [EndPoints] ELL</h2>
Limited ellipse from
center,
vector main axis, length can be added
vector secondary axis, length can be added
[startpoint]
[endpoint]
Example:
# Vectors + length and endpoints
S1=ELL P(0 0) D(DX 100) D(DY 80) P(10 0) P(-10 0)
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<h2>S Polygon < Points... POL</h2>
Polygon from points
2D-Polygon from points:
S# = POL2, 2D-point1, 2D-point2, <2D-point3, ...2D-pointN>
Example:
P20 = 10.10
S20 = POL2, P20, P(10.0) P(20.10) P(30.30)
3D-Polygon from points:
S#= POL, point1, point2, <point3, ...pointN>
Example:
P20 = P(10.10)
P21 = P(20,20,15)
P22 = P(25.20)
S24 = POL P20 P21 P22 P(30,12,0) P(30,10,10) P(40,30,10)
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<h2>S Polygon < Rectangle REC</h2>
Parallelogram from a corner and 2 vectors:
CornerPoint lower left point
DX horizontal vector; you can add the length
DY vertical vector; you can add the length
Example:
S20 = REC P(100 0 0) D(50 0 0) D(DY 12)
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<h2>S BSpline < Points... BSP</h2>
B-Spline from points
S-bsp = BSP {points} [,degree] [,CTRL]
CTRL - whether the defined points are transit points or check points.
Example:
P20 = P(78.9)
P21 = P(66.28)
P22 = P(44,9,25)
P23 = P(9.12)
P24 = P(6.34)
# B-Spline from Points
S20 = BSP, P20, P21, P22, P23, P24
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<h2>S BSpline < Polygon... BSP</h2>
B-Spline from polygon:
S-bsp = BSP S-polygon [,degree] [,CTRL]
CTRL - whether the defined points are transit points or check points.
Example:
# Poly from points
P20 = P(78.9)
P21 = P(66.28)
P22 = P(44,9,25)
P23 = P(9.12)
P24 = P(6.34)
# Poly ← Points
S20 = POL, P20, P21, P22, P23, P24
# BSpl <- Poly
S21 = BSP, S20
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<h2>S BSpline < convert & join objects BSP1</h2>
Convert and connect one or more objects into a B-Spline curve,
with or without rounding.
Input elements: Points, lines, arcs,
polygons, ellipses, clothoids or B-Spline-curves.
smoothFactor: 0 = no rounding, max. 1.
only for polygons:
-1 = no rounding
0 = through points,
1 = through controlpoints.
Example:
# convert polygon into B-Spline-curve
S21=BSP1 S20
# Connect Linie20 and Linie21 to a curve with rounding.
S20 = BSP1 L20 L21 0.1
Example Model see sample_curv_bsp_join1.gcad
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<h2>S Clothoid (spiral-form curve) CLOT</h2>
Clothoid spiral-form curve: generate (a planar spiral through Fresnel-Integral).
StartPoint starting point
StartVector launch direction (vector or angle)
Angle difference angle from direction towards the end point, positive is clockwise (CW), negative is counter-clockwise (CCW).
StartRadius radius at the starting point, or 0 for infinite
EndRadius radius at the end point, or 0 for infinite
[Z-Axis] normal vector, optional.
Auxiliary functions to create a clothoidal spiral-form curve
Creation of the start point with "PT cartes"
Select the end of the previous element.
Generating the start vector "VEC tangent"
Select the end of the previous element and the previous element. With "OK", the discharge (outlet) vector will be generated.
Example:
S20 = CLOT P(0 0 0) ANG(0) ANG(30) 0 10
Example Model see sample_cloth1.gcad
Export of a clothoidal spiral-form curve:
DXF: Issue as POLYLINE.
IGES: Issue as Entity 106 (Copious Data, Form 12 = 3D polygon).
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<h2>S connection-lines < Points... MSH</h2>
Creates connection-lines between points (e.g. for schematics).
Position and direction of the connection-line can be defined
(select "Line")
Connection-lines can have relative distances to themselves
(select line and key "distance")
Points
select all points
Vector/Line
None: mid-line vertical, between first / last point.
Define the direction of the mid-line:
select a line or key direction (eg DX or DY)
Distance: none.
Define the direction and position of the mid-line:
select a line or select point and direction
and key Distance (0 = exactly through line)
Distance
key offset from line
None: mid-line between first / last point.
Examplemodel sample_connLn1.gcad
Example:
P21=P(-1.94 -1.26 0)
P22=P(-1.69 0.15 0)
P24=P(9.05 -3.25 0)
P25=P(4.86 -2.46 0)
#
# connection-line P21-P25
S20=MSH U(P21 P25)
# connection-line P22-P24 with a distance of 0.2 to connection-line S20
S23=MSH U(P22 P24) L(S20 MOD(3)) VAL(.2)
# connection-line through line outside
P26=P(0 -5)
P27=P(1 -6)
S23=MSH U(P26 P27) L(P(6 0) DY) VAL(0)
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<h2>S Contour(CCV) <- PT/LN/CIR/CRV CCV</h2>
Contour ("Composite (compound, concatenated) curve" - CCV)
A contour consists of the elements of points, lines, circles, curves.
The outline should start at a point and end at a point.
The rotational direction (CW or CCW) is defined following circles and curves.
Lines and arcs are automatically connected with normal elements;
Points are directly connected;
Intersections between elements are automatically formed.
Format:
S# = CCV {contour elements}
Example:
C20 = P(39.26) VAL (22)
S20 = CCV P(7.25) C20 CW P(35.58)
A 2D composite curve from 2D polygon
A 2D composite curve consists of circles/lines
S# = CCV2, 2D polygon, tolerance
Example:
P20 = P(78.9)
P21 = P(66.28)
P22 = P(44,9,25)
P23 = P(9.12)
P24 = P(6.34)
# Poly from Points
DRAW OFF
S20 = POL, P20, P21, P22, P23, P24
# BSpline from Poly
DRAW ON
S21 = BSP, S20, 2
# Poly from BSpline
DRAW OFF
S22 = POL, S21, 0.05
# 2DPoly from Poly
DRAW OFF
S23 = POL2 S22 R22 0.05
# 2DCircle/Line from 2DPoly
DRAW ON
S24 = CCV2 S23 0.05
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