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denisc
Joined: 24 Apr 2013 Posts: 92

Posted: Wed Oct 16, 2013 7:41 pm Post subject: 4D parametrics fonctions examples 


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

Posted: Fri Oct 18, 2013 6:41 pm Post subject: 


hello all
In my first post , i am inspired of this site;
http://ladimension4.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^2u^2)* cos(2 *u *v)
W = exp(v^2u^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

Posted: Sat Oct 19, 2013 4:18 pm Post subject: 


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

Posted: Thu Nov 07, 2013 10:56 pm Post subject: 


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

Posted: Wed Dec 11, 2013 12:58 am Post subject: 


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

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denisc
Joined: 24 Apr 2013 Posts: 92

Posted: Fri Dec 13, 2013 11:13 am Post subject: 


hello uoface
you can explain me a little, please?
cheers
denisc 

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