Mathematically applying quaternion, octonion, and other alternative algebras to objects (to transform them) using geometry nodes. I'm trying to take different 4D meshes/objects that are generated mathematically and project them "down" from 4D space onto 3D space while making it interactive.
An example of what I'm very loosely trying to reproduce when changing values: Note: I'm trying to be mathematically accurate I'm not just trying to produce a visual effect, hence the calculations.
Calculate the points/vertices of a 4D object using quaternions, in this case a sphere (using geometry nodes) https://eater.net/quaternions https://eater.net/quaternions/video/rotation
Take a 4D sphere and project it into 3D space see example. I'm having issues with mathematically transforming the objects using geometry nodes. I'm not sure how to apply my quaternion calculations to the objects / vertices / edges / faces to create the transformation. I was thinking of using the set position node but it only has a spot for x,y,z, I seem to be missing a step
My ultimate goal is to make these interactive like https://eater.net/quaternions/video/rotation then 3D print these 3D objects that are projected from 4D space showing the various 4D projected stages of "rotation" in 3D.
I created the quaternion math nodes using geometry nodes from "scratch" to have full control over the calculations, This is because I would also like to test out octonions along with other alternative algebras. I'm testing / verifying the images using https://eater.net/quaternions/video/rotation. My question is how does one connect the geometry vertexes of the sphere (x,y,z) or any object and apply quaternion calculations using geometry nodes.
PS: I used ChatGPT to create the formula and WannesMalfait Math Formula free add-on to enter them video.
My attached Blender file is below.