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CAD tip CAD tip # 13847:

Question CAD 
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Q - question

Pringles in AutoCAD - a hyperbolic paraboloid.

A - answer The typical saddle shape of Pringles potato chips is referred to as a hyperbolic paraboloid. In AutoCAD, you can create this mathematical 3D shape using the freeware utility 3DPlot - see 3DPlot and see Download.

The mathematical definition of a symmetric hyperbolic paraboloid is:

Z = A * X^2 - A * Y^2.

then in LISP:

(defun pringle (u v)(list u v (- (* 0.5 u u)(* 0.5 v v))))

Plot this function using 3DPlot over the X and Y coordinate interval (-1 to 1), with a step size of 0.1:

(3dplot pringle -1 1 0.1 -1 1 0.1)

And to make the shape of the chip perfect, trim the resulting surface to a circular plan-shape. To do this, we must first convert the initial shape from the original polyline mesh to a 3D mesh (MESHSMOOTH) and then to a 3D surface (CONVTOSURFACE). This can then be trimmed with an auxiliary circle (SURFTRIM).

See the video demonstration of this procedure:

And see the finished DWG file Pringle.DWG available for download from the Block Library.

This approach is of course also applicable to other mathematical forms for architecture and design.

100% *  CAD 
30.8.2023    995×  

See also:
Tip 12749:Generate parametric mathematical 3D surfaces (meshes) in Fusion 360.
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.
Tip 9625:How to color 3D topo surface model by slope?
Tip 8903:Draw normals of 3DFaces in AutoCAD DWG.

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