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## Sinusoid, hypotrochoid, guilloche and other parametric curves in AutoCAD.

With the free utility CADstudio 2DPlot you can easily use your AutoCAD to generate 2D curve from any mathematical function (XY) - ie. create a curve (2D polyline) representing results of the function. The function has to be defined as XY=f(U) - i.e. returning a (X Y) list as a result of one variable parameter.

On the homepage of 2DPlot you can find several examples of definitions of mathematical functions and specifying intervals of input values and precision of the resulting curve.

With parametrization you can use 2DPlot also for creating guilloches, strophoids, curves based on the hypotrochoide and epitrochoide functions, resp. on Farrel wheels.

General format of 2DPlot calls:

```(2dplot fXY u-from u-to ustep)
```

Example - sinusoide (from -PI to PI, 100 steps):

```(defun fSin(u)(list u (sin u)))
(2DPlot fSin (- pi) pi (/ (* 2 pi) 100))
```

or a parabolic curve (from -2 to 2, 200 steps):

```(defun fParabola(u)(list u (* u u)))
(2DPlot fParabola -2.0 2.0 (/ 4.0 200))
```

The interactive command 2DPLOT offers several samples (sinusoid, catenary...). You can use the job #8) for interesting parametric Farrel wheel curves.

You can use 2DPlot as a replacement of the old tool FPLOT.LSP.

 See also: Tip 11727: Animated drawing of a curve shape in AutoCAD. Tip 9829: DrGrid - parametric grid for AutoCAD drawings. Tip 9743: How to use XY coordinates from Excel as polyline vertices in AutoCAD? Tip 9711: 3DConstruct - converting a 3D mesh to a frame construct Tip 9651: Convert a DWG 3D mesh model to an Inventor 3D solid part.