Re: 4D Visualisierung

Op 16-9-2024 om 21:49 schreef Chris M. Thomasson:

Trajectory bundles: now these, being curves, can be done in 4D as well...
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I need to study existing your work to see where I should/could plot all of my vectors that have non-zero 4d w's as in (x, y, z, w). That would be interesting. I just need to find some time to give it a go, been really busy lately. Shit... Well... Now, when I do it, I will start small and create 4 axes in the 3d plane. Ask you a lot of questions... ;^) It would be a learning experience for me.
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Also, I think it might help a bit if I colored any vector with a non-zero w with a special color spectrum... Humm... Keep in mind that I am only plotting the (x, y, z) parts of the vectors that my field algorithm generates. So, I can see how non-zero w's cast an influence upon the field wrt the (x, y, z) parts of an n-ary vector.
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I can do the coloring thing in my current work. If any vector has a non-zero w, make its color _unique_ among all colors used in the field render. Humm...

I propose you try this example file.
bolnorm4D. Parabola | Desmos <https://www.desmos.com/3d/igi6shir3e?lang=nl>
A graph of the complex Parabola w=z^2.
The axes can modified/put to rotation with one of two angle control sets (or both;-) :
1. "initial axis position controls", a 'spherical coordinate'-like set of angles α,β,γ,δ; and
2. "axis plane rotation controls", a set of angles for the six possible axis-plane rotations: ζ1,η1,ζ2,η2,ζ3,η3.
The resulting projected axis points are called X,Y,Z,V, defined by 3D coordinates.
A 4D coordinate (a,b,c,d) is graphed as a point
E(a,b,c,d)=aX+bY+cZ+dV.
The graph w=f(z) or u+iv=f(x+iy) is produced by the 4D points
E(x,y,u,v)
The function definitions are stated apart, eg,
Fre(x,y)=xx-yy, Fim(x,y)=2xy
(Desmos lacks yet complex function handling)
A surface is defined with variables u,v (not to be confused with variables u+iv=w!!).
A curve is defined with variable t. Parameter curves are obtained using a parm list L=[a,b...c]
The parabola is rendered by
E(u,v,Fre(u,v),Fim(u,v))
In polar coordinates we'd have
E(u cos v, u sin v, Gre(u,v),Gim(u,v))
You can try out 4D rendering right away with this file!
If you have a function definition with parms u and v, or t and L,
or x,y,z,w, making z a 3D-function z=f(x,y) and w a list or a slider parm),
all you need to render is
E(u,v,F1(u,v),F2(u,v)) or
E(t,L,F1(t,L),F2(t,L)) and another by swapping t and L, or
E(u,v,f(u,v),w)
...
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guido wugi