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In Adobe Illustrator, I create a mesh grid, transform it to obtain an isometric perspective, and then apply an Envelope Distort from a mesh to obtain a bulge that resembles a bivariate (3D) Gaussian distribution (a.k.a. bell curve).

enter image description here

Question: How can I remove or hide the "hidden lines", i.e., those that would be hidden anyway if the object had a surface? It's visually unappealing as it is now. Do I have to remove them or did I miss a setting when creating the graph?

Further, if anyone can think of a more appropriate tool to create such a graph, which can then be imported to Illustrator, I'll be glad to hear about.

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  • yup.. give it a surface (white fill behind the grid). Or Expand and manually remove pieces.
    – Scott
    Nov 29, 2022 at 23:59
  • can you elaborate on how to give it a white fill behind the grid?
    – Steve06
    Nov 30, 2022 at 10:45
  • Ermm.. a rectangle behind the grid with a white fill, then group the white rectangle and the grid and then perform your envelope distortion.
    – Scott
    Nov 30, 2022 at 12:05
  • I would point out that this is neither 3D nor a wireframe. This is a series of paths you've distorted, it's quite different.
    – Scott
    Nov 30, 2022 at 21:40

2 Answers 2

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After surveying a couple of programs available, my conclusion is the following:

(1) Gnuplot: A free plotter that allows you to visualize both data series and mathematical functions. Its language is fairly accessible and allows for a high level of customization. It handles vector graphics exports very well (svg, pdf). The resulting shapes are easy to work with. Gnuplot is my winner. Here's an example of what I plotted with it. enter image description here Gnuplot GUI also allows you to rotate the view of your graph with the mouse to find the best angle.

(2) Mathematica: It turns out that, for 3D graphs at least, it only allows rasterized exports.

(3) Matlab: It allows vector graphics output, but I got the impression that they can't be customized to the same degree as in Gnuplot.

(4) Maxima: A free math program with excellent plotting abilities, but these are handled internally by Gnuplot, so it's best to deal with (1) directly.

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  • you can force mathematica to export the edges. though normally its slow but not in this case. But yeah gnuplot is okay.
    – joojaa
    Dec 12, 2022 at 19:29
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No hope to automate it. The drawn image contains no 3D depth information, you are the only one who knows which curves should be removed. Expanding and deleting the unwanted pieces manually is the only way to get it right if one must start from your image.

Mathematics programs, graph generation websites(free ones exist!) and even spreadsheets can generate the wanted image. They insert automatically filled pieces between the lines to hide the unwanted curves. Alternatively you can use a CAD or other 3D modelling program, but they really expect one knows what he does. There you'll get an automatic hidden line removal and (if wanted) a perfect surface shading for plausible 3D appeararance.

In math programs and spreadsheets you must be able to define the surface elevation as a function of X and Y. The same is true in 3D programs if you expect a mathematically sound result. Something resembling can be got easily by revolving a bell-like curve and projecting vertically on it a rectangular xy line grid. 3D-abilities in Adobe's CC-set unfortunately are too poor for the task.

The problem seems to be discussed several times in the past as well here and other places. Search for drawing a 3D Gaussian distribution graph.

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