Important Notice:
We regret to inform you that our free phpBB forum hosting service will be discontinued by the end of June 30, 2024.
If you wish to migrate to our paid hosting service, please contact billing@hostonnet.com.
View previous topic :: View next topic |
Author |
Message |
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 |
|
Back to top |
|
|
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://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 |
|
Back to top |
|
|
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+ |
|
Back to top |
|
|
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 |
|
Back to top |
|
|
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 |
|
Back to top |
|
|
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 |
|
Back to top |
|
|
|
|
You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum
|
2005 Powered by phpBB © 2001, 2005 phpBB Group
|