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## Pringles in AutoCAD - a hyperbolic paraboloid.

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.

 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.