Partial derivatives, Rotor/Curl of a field, Normal of a surface

Two separate-but-related differential operators that seem pretty important/essential to me for 3D math:

1. Rotor/Curl - https://en.wikipedia.org/wiki/Curl_(mathematics)

I’ve managed to get the rotor of a given field at the point [X,Y,Z] in the following example: https://www.math3d.org/MrIboI6x

Notice that I had to define 9 intermediate functions in order to accomplish this… not great fun. I also wasn’t able to use this method to create a generic rotor function, because I had to use the constants X,Y,Z in the intermediate functions.

1. Surface normal - https://en.wikipedia.org/wiki/Parametric_surface#Tangent_plane_and_normal_vector

(note that I mean the un-normalized vector Ru×Rv)

Again, I was able to do this for a single point using two intermediate functions: https://www.math3d.org/3Iqv6XXf

I’ve looked through math in the console and math.js, and wasn’t able to find a ready-made way to calculate these at given coordinates. Please add one, and/or make an example of it so it’s more discoverable!

What these two things have in common: they involve partial derivatives. I’ve tried using diff with functions of multiple variables, but I just can’t find a way to work with them! If you can expose them a little better to the end-used, that might help.

[ChristopherChudzicki]

Note to self: This is implemented but still needs documented examples.

[NeatNit]

I understand that diff(f,x,y,z) returns a matrix, where each partial derivative is a row (or column?) in the matrix, but I can’t find a way to get one row(/column) of the matrix as a 3D vector. There is no row function, see https://github.com/josdejong/mathjs/issues/230

Edit: I can’t tell you how many failed attempts this took me: https://www.math3d.org/UdFijsnH

Apparently I was using subset/index wrong. To get the partial derivative of R(u,v) in regards to u, apparently we use:

Ru(u,v) = flatten(subset(diff(R,u,v),index(1,[1,2,3])))

I was stuck for hours trying to figure out why index(1,[1,3]) wasn’t working. This would have been easier to solve if I could actually see the values that were being output.

This is related to the “see something’s type” topic discussed here: https://github.com/ChristopherChudzicki/math3d-react/issues/193#issuecomment-505530098, but for variables (that aren’t functions) we might as well be able to see the actual output value - preferably as a nicely formatted matrix/table.

I know I’m making a lot of requests, some of which are big, but it’s only because I like this software so much and want to see it improve. 😃

(I will try to make some PRs eventually, but for the next ~month it will definitely not be possible)

Edit: Curl still requires partial derivatives as intermediate functions, but at least it can be made generic: https://www.math3d.org/bNLU7FfY - RotF(x,y,z) here works for any x,y,z.