Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: guido wugi <wugi@brol.invalid>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Tue, 17 Sep 2024 21:46:33 +0200
Organization: A noiseless patient Spider
Lines: 66
Message-ID: <vccmap$3jksm$1@dont-email.me>
References: <vantta$3j6c0$1@dont-email.me> <vc7lqs$2dcna$1@dont-email.me>
 <vc8t2n$2c230$1@dont-email.me> <vca255$314se$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 17 Sep 2024 21:46:34 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="edf4d6bda501b9f402542694adbd18c9";
	logging-data="3789718"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/2JqiMtfhpM/lqXTE/p7OM4Mnfavv2e98="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:XBNT+by9FJiXo1N5F4TS1Qt6rE4=
Content-Language: nl
In-Reply-To: <vca255$314se$1@dont-email.me>
Bytes: 3691

Op 16-9-2024 om 21:49 schreef Chris M. Thomasson:
>> Trajectory bundles: now these, being curves, can be done in 4D as 
>> well...
>>
>
> 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.
>
> 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.
>
> 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)
....

-- 
guido wugi