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CAD tip CAD tip # 13960:

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Q - question

Fermat's spiral in AutoCAD.

A - answer Using the LISP tool 2DPlot you can easily generate the shape of a Fermat's spiral in AutoCAD or AutoCAD LT (2024+). In a Fermat's spiral, the distance between turns grows in inverse proportion to their distance from the spiral center.

The Cartesian definition of the drawing function is in this case:

X = +a √φ cos(φ)
Y = +a √φ sin(φ)
and a symmetrical branch:
X = -a √φ cos(φ)
Y = -a √φ sin(φ)

So in the LISP notation for 2DPlot:

(defun fXYfermat (f)
  (* fCa (sqrt f)(cos f))
  (* fCa (sqrt f)(sin f))
, where fCa is a parameter for the distance between turns.

In the 2DPlot app, this curve has the internal preset of 13.

After capping both ends of the spiral branches and hatching the areas you can (by looking in the hatch properties) verify one of the properties of Fermat's spirals - divides the plane into two connected regions with the same area. Or that the area between any two consecutive full turns around the spiral is invariant.

See the DWG Block 22784.

100% *  CAD 
14.12.2023    36465×  
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applies to: AutoCAD · AutoCAD LT ·

See also:
Tip 14061:Animated drawing of geometry in AutoCAD.
Tip 12600:Parametric 3D curves in Fusion 360.
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?

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