4D parametrics fonctions examples

 
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Wed Oct 16, 2013 7:41 pm    Post subject: 4D parametrics fonctions examples Reply with quote

i post some parametrics examples in 4D , to illustrate the fonction.


i start very simple with curves , because with one more dimention ,

the result will be planes in 3d


1 example

the parabole cubique

in 2D




y=x^3

in 4D

X = u
Y = v
Z = u^3 - 3*u*v^2
W = 3*u^2*v - v^3
With U[ -1, 1] And V[ -1, 1]









what do you mind of that?

cheers

denisc


Last edited by denisc on Fri Oct 18, 2013 10:59 pm; edited 1 time in total
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Fri Oct 18, 2013 6:41 pm    Post subject: Reply with quote

hello all

In my first post , i am inspired of this site;


http://la-dimension4.com/Fonctions%20complexes.html


if my first read, i am not understamd all.





and now , a new curve


sigmoide




En mathématiques, la fonction sigmoïde (dite aussi courbe en S) est définie par :
f(x)=1/1 + e^(- x) pour tout réel x\,
mais on la généralise à toute fonction dont l'expression est :
f(x)=1/1 + e^(-lambda* x)



y=1/(1 +1/exp(x))
[x]: -8 , 8
[y]: -8 , 8
[z]: -0 , 0
;

and in 4D

X = u
Y = v
Z = (exp(-u)* cos(v)+1)/(exp(-2 *u)* sin(v)^2+(exp(-u)* cos(v)+1)^2)
W = exp(-u)* sin(v)/(exp(-2* u) *sin(v)^2+(exp(-u)* cos(v)+1)^2)

U[ -pi, pi]
V[ -pi, pi]




another

Courbe de Gauss y = exp(-x*x)




in 4D


X = u
Y = v
Z = exp(v^2-u^2)* cos(2 *u *v)

W = -exp(v^2-u^2)* sin(2* u *v)

U[ -1, 1]
V[ -1, 1]





for end

Chaînette

y = cosh(x)=exp(x)+exp(-x)/2




in 4D

X = u

Y = v

Z = 1/2* exp(-u)* cos(v)+1/2* exp(u)* cos(v)

W = 1/2* exp(u) *sin(v)-1/2* exp(-u)* sin(v)
U[ -pi, pi]
V[ -pi, pi]



the probeme is , it's seem a same curve , but not same formula and

calculs can a little bit different.

more after

cheers

denisc
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Sat Oct 19, 2013 4:18 pm    Post subject: Reply with quote

hello

one more

Cuspide
cissoid of diocles

You can see that on my site examples but less soution.


y^2=x^3



4d:

X=u*cos(v) ;
Y=u*sin(v) ;
Z=u^1.5*(cos(1.5*v)
w=u^1.5*sin(1.5*v)





and export in obj, make probleme

i am plenty of v nan

a+
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Thu Nov 07, 2013 10:56 pm    Post subject: Reply with quote

hello all.


now, a few example of 3D to 4d


hopf in 3D


X():cos(u)/2
Y():sin(u)/2
Z():(cos(u)*sin(v)-sin(u)*sin(v)*cos(v))/2
[u]:-pi, pi
[v]:-pi, pi




hopf in 4D


X = cos(u)/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v)))
Y = sin(u)/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v)))
Z = (cos(u)*sin(v)-sin(u)*sin(v)*cos(v))/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v)))
W = (cos(u)*sin(v)*cos(v)+sin(u)*sin(v)*cos(v))/sqrt(1+sin(v)*sin(v)*(1+cos(v)*cos(v)))
With U[ -pi, pi] And V[ -pi, pi]





cheers

denisc
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ufoace



Joined: 11 Mar 2013
Posts: 46

PostPosted: Wed Dec 11, 2013 12:58 am    Post subject: Reply with quote

intresting. still i have to say mandelbulb3d has more varied results:D
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Fri Dec 13, 2013 11:13 am    Post subject: Reply with quote

hello uoface

you can explain me a little, please?

cheers

denisc
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