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I have a question related to implicit equation in Blender.

I made a project developing about 100 parametric equitation/ or algebraic minimal surfaces, first with xyz math function, later I translated most of them to Geometry Nodes.(example in the Attachment & screenshot).

Now I would like to make the next step and build a collection of the implicit equations like:

$ x^2+y^2+z^2+sin(4x)+sin(4y)+sin(4z)-1 = 0 $

But I don’t find a way, neither any kind of addon, nor a helpful article in this forum or in the www.

So, maybe one of you have an idea how to import implicit equations to blender? I am happy about all hints and inspiring idea’s 😁✌️

scene

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    $\begingroup$ What does "implicit" mean in "implicit equations" exactly? For easy conversions, see How do i convert this equation into the node editor? $\endgroup$
    – Markus von Broady
    Sep 10 at 20:32
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    $\begingroup$ There are addons for creating nodes from equations blendermarket.com/products/node-expressions?ref=165 $\endgroup$
    – taiyo
    Sep 10 at 20:52
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    $\begingroup$ Hi Markus, “ An implicit equation is an equation which relates the variables involved”, so y= … or z=… it includes the relation. Like you see in the example 0= …. $\endgroup$
    – smice
    Sep 10 at 21:38
  • $\begingroup$ Hi Tayio, the problem is not the translation of equitations to proper Nodes, I made this many times. My question is how to integrate „implicit equation“ properly into Geometry Nodes? $\endgroup$
    – smice
    Sep 10 at 21:45
  • $\begingroup$ As you say, it's a relation. So you take all but one variable as an input, and read the output as the remaining value. For example for $y = 2x$ (or $y - 2x = 0$) create a mesh line going from $x=0$ to $x=10$ for example, and then use the Set Position node to set the points' $y$ coordinate based on existing $x$ coordinate. $\endgroup$
    – Markus von Broady
    Sep 10 at 23:03

1 Answer 1

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Here's one way to display:

$$ x^2+y^2+z^2+sin(4x)+sin(4y)+sin(4z)-1 = 0 $$

For a better visual Effect, with a strong PC you can Smooth (modifier) it out decently:

You can add a material connecting Texture Coordinate: Generated to Base Color:

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    $\begingroup$ +1 that's an interesting approach! i didn't know you could plot implicit functions! i double checked and this is correct. snipboard.io/vROzVm.jpg. In the other 3d equation stuff we used Grid and set position. $\endgroup$
    – Harry McKenzie
    Sep 11 at 8:50
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    $\begingroup$ @HarryMcKenzie thanks for checking, because I didn't, and with those Vector Maths optimizations I was worried I could maybe get it wrong 😅 $\endgroup$
    – Markus von Broady
    Sep 11 at 8:57
  • $\begingroup$ this volume cube node is so cool. like holy cow.. finally we can plot any type of equation! really exciting! can i add another +1 vote??? on a side note though, this seems like a workaround? is the topology it generates clean? because you mentioned we need strong pc specs to smooth it out? sorry i didn't try it. $\endgroup$
    – Harry McKenzie
    Sep 11 at 9:09
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    $\begingroup$ @HarryMcKenzie the topology isn't any good, it's remesh. In general plotting is just sampling in a grid, though it can be postprocessed and smoothed out in various ways… $\endgroup$
    – Markus von Broady
    Sep 11 at 9:25
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    $\begingroup$ @MarkusvonBroady - sorry for my fault - works perfect your way ! 😀 i love it - thx so much ! ! $\endgroup$
    – smice
    Sep 11 at 17:47

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