Add node that generates geometry using parametric equations

[optozorax]

I wanted to draw this illustration using graphite, but ended up using desmos and screenshotting it, because they support parametric equations. It will be nice to have such a node.

Desmos illustration

I think that in this node we should be able to specify density of the geometry (amount of points), because different equations require different density, and it can affect performance.

I think there also should be density multiplier for the export rendering (if there is such a regime). So that at the editing stage we may see segmented geometry, and for the final render it will be smooth.

Also, unsolved problem: how to make this node accept any amount of variables (so that you can tweak behavior of your equation, like l in my example). This is also the problem for the Math node. Without this, this node will be not as useful is it might be. (#2462, and see also #2459)

[Keavon]

I was overthinking it by trying to consider how a Bezier path might be generated, but you're right that a polyline should be sufficient which would drastically improve the simplicity of this.

Also, unsolved problem: how to make this node accept any amount of variables (so that you can tweak behavior of your equation, like l in my example). This is also the problem for the Math node. Without this, this node will be not as useful is it might be.

I just filed #2462 for this.

[laundmo]

If i understand the feature request correctly, a node like this would be easiest to accomplish using something like https://crates.io/crates/fasteval which parses and evaluates math expressions.

(i'm just passing by, i just noticed this issue and remembered the crate)

[Chen-Hao-WANG]

are this issue be assigned ? i would like to solve this issue as a start for the GSoC

[Keavon]

Feel free to get started with it but you'll probably have to first work with us in Discord to figure out the appropriate design for how it's used and implemented. Like do we use the math expression library we've written for our Math node? Does that require adaption to support equations (not just expressions)?