CAD functions for Splines (Curves) See operation CAD .. See also codes for curves Shortcut key is S (Spline) Polygon Ellipse Clothoid (spiral-form curve) Contour (compound curve) ____________________________________________________________________________## S Ellipse Center,AxisEndPoint,Point

Ellipse from center, end point main axis, point on ellipse. Center centerpoint EndPoint MajorAxis endpoint of the main axis Point on Ell. a point on the ellipse Example: S1=ELL P(100 0) P(150 0) P(100 20)## S Ellipse Center Axes [EndPoints] ELL

Limited ellipse from center, vector main axis, vector to point on ellipse. Center centerpoint MajorAxis (VEC) Vector to the endpoint of the main axis Axis (VEC) Vector to a point on the ellipse [StartPoint] Optional: startpoint of ellipse. [EndPoint] Optional: endpoint Example: # Vectors + length and endpoints S1=ELL P(0 0) D(DX 100) D(DY 80) P(100 0) P(-100 0)## S Polygon < Points... POL

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)## S Polygon 4-side quadrilateral REC

Quadrilateral from point and 2 vectors or points: CornerPoint lower left point Vec/Pt first side horizontal vector or point; Vec/Pt last side vertical vector or point; [Type] Typ 1 (default) for parallelogram, rectangle, square Typ 2 for trapezium Typ 3 for rhombus, kite Example: # parallelogram, horizontal, length 100; vertical length 12 S20 = REC P(100 -100 0) D(50 0 0) D(DY 32) # trapezium S21=REC P(100 0 0) D(100 0 0) D(20 60 0) MOD(2) # kite S22=REC P(100 100 0) D(100 0 0) D(-20 60 0) MOD(3)## S BSpline < Points... BSP

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, P24Tangential to a line:(CTRL must be active !) The spline is tangential to the lines defined by the first two and last two points. Example: P21=P(-737.37375 -42.08754 0) L20=P21 P(-13.468014 335.016819 0) P22=P(L20 0.5) L21=P(-457.912466 -159.932652 0) P(390.572397 -149.831643 0) S20=BSP P22 P(L20 0.6) P(-70.7 119 0) P(-67 -58 0) P(L21 0.6) P(L21 0.7) CTRL P23=P(L21 MOD(2))## S BSpline < convert & join objects BSP1

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: negativ value: degree 1 (polygon) positive value: degree 2 or 3; higher values - more 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## S Clothoid (spiral-form curve) CLOT

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).## S Contour(CCV) <- PT/LN/CIR/CRV CCV

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