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Because I read several times some questions about "XYZ Math & Geometry Nodes", I decided to answer my own questions with this small post.

Since a couple of time I´m working on a project to generate parametric objects, based on mathematical equations in Blender Geometry Nodes. As a mathematical dummy, it was difficult to find a way translating something like [ x= [R + s cos(t/2)] cos(t) - y = [R + s cos(t/2)] sin(t) - z = s sin(t/2) ] in Geometry Nodes like this "Moebius Band" object.

The question is what is the way to reach this?

cornus

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So, this is one way to do it.

The results are looking very similar to the Results of the XYZ Math Function addon. The XYZ Math Surface can be used to construct meshes for parametric surfaces. The parametric surface is defined by three functions of two variables U and V. But maybe the most important difference is, creating the parametric surfaces by Geometry Nodes is non-destructive.

Now the first 75 algebraic objects are ready. To see what´s about and how it could work, have a look on my first three free Objects following with this post.

I want to say thank to @MarkusvonBroady and @HarryMcKenzie for their technical assistance with my last questions. I truly appreciate the time and effort you've dedicated to helping me navigate this complex issues. Thanks also to (https://www.3d-meier.de) & (https://mathcurve.com)


In Addition to the short description above, here some extra Explanations to understand the blend file better.

The first screenshot should explain the base structure of the maths objects.

Overview

The "Basic-Area" controls the Input Geometry, base is the Object on this Grid. (The UV, if needed, is stored in the "store named attribute" Node.)

Second View

The "Geometry Area" controls the Resolution and the extra Geometry inputs and values to controls the objects look. Some are without extra input values, some have a lot of them. One should use the parameter area to change the look.

Third View

The Main Nodes are the dark green "Group Nodes" for the XYZ Orientation. Even if possible to edit the maths nodes behind this group, it can cause unexpected results.

Forth view

The last area is the "Output area", you should keep the "merge by distance" in the front, to keep the object "clean" before subdividing in the next steps. It is important to keep the "realize instance" node at the end.

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