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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Tue Jun 19, 2012 11:28 pm Post subject: starfish basics 


Have you ever tried to create a starfish?
May be this could be a basic formula to create some variants...
Code:  0.05  sqrt(x^2+y^2)  4*z^2
+(1.0  0.1*acos(cos(5*atan2(y,x))))^2 
Gerd 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Thu Jun 21, 2012 10:18 am Post subject: 


Hi,
In fact no Gerd but why not let's try to do something , it's a very good idea, thanks and thanks for the formula too, that was a nice star , I will try but really I hope to see something from others, anything will be good I'm sure _________________ My YouTube channel 

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Furan
Joined: 05 Oct 2010 Posts: 64 Location: Prague, Czech Republic

Posted: Fri Jun 22, 2012 5:36 pm Post subject: 


Here you go:
Code:  x^2+y^2+(1+(pi/2+atan(30*z30))*(0.03*sin(1+7*x+21*y)+0.06*sin(0.7+22*x+5*y)+0.02*sin(3+25*x)+0.04*sin(25*y)))*(41/(1+10*(x^2+y^2)))*6*(z1/(1+0.15*(x^2+y^2)))^2=(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z0.21/(1+1.5*(x^2+y^2)))^4))*4(0.2+sin(6*atan(y/x)))*(x^2+y^2)
Box 5;5 5;5 0;1.8
Grid 150 150 50

It really feels alive. What a hideous creature.
If you got atan2 and good luck (for some unknown reason not working for me), try this change:
Code:  sin(6*atan(y/x)) to sin(0.2*sqrt(x^2+y^2) + 5*atan2(y,x)) 
Spent last two hours on that, perfecting it, now I'm too tired to render it. Maybe you guys have a nice texture for it. 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Fri Jun 22, 2012 6:40 pm Post subject: 


this is very beautiful Furan but I think you meant:
Code:  x^2+y^2+(1+(pi/2+atan(30*z30))*(0.03*sin(1+7*x+21*y)+0.06*sin(0.7+22*x+5*y)+0.02*sin(3+25*x)+0.04*sin(25*y)))*(41/(1+10*(x^2+y^2)))*6*(z1/(1+0.15*(x^2+y^2)))^2(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z0.21/(1+1.5*(x^2+y^2)))^4))*4(0.2+sin(6*atan(y/x)))*(x^2+y^2) 
I made some changes and got this:
Code:  x^2+y^2+(1+(pi/2+atan(30*z30))*(0.03*sin(1+7*x+21*y)+0.06*sin(0.7+22*x+5*y)+0.02*sin(3+25*x)+0.04*sin(25*y)))*(41/(1+10*(x^2+y^2)))*6*(z1/(1+0.15*(x^2+y^2)))^2(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z0.21/(1+1.5*(x^2+y^2)))^4))*4(0.2+sin(6*atan(y/x)))*(x^2+y^2) +((x^2+y^2)/8)^2
Box 6;6 6;6 0.4;1.8 
It's not time for tiredness we need more Furan and as I see you added one more leg too, we need to solve this problem as well _________________ My YouTube channel
Last edited by abdelhamid belaid on Mon Jun 25, 2012 12:06 am; edited 1 time in total 

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Furan
Joined: 05 Oct 2010 Posts: 64 Location: Prague, Czech Republic

Posted: Sat Jun 23, 2012 12:15 pm Post subject: 


No, that is not correct. I'm not using K3DSurf so I don't have to use F(x,y,z)=0 I can also use F(x,y,z)=Threshold(x,y,z)
Let me correct it:
Code:  Beginning of ellipsoid
x^2+y^2+
Function for allowing bumps only on the top of the starfish:
(1+(pi/2+atan(30*z30))*(
Bumps:
0.03*sin(1+7*x+21*y)+0.06*sin(0.7+22*x+5*y)+0.02*sin(3+25*x)+0.04*sin(25*y)
Vertical thickness of the starfish:
))*(41/(1+10*(x^2+y^2)))*
Local vertical displacement of the body:
6*(z1/(1+0.15*(x^2+y^2)))^2
end of ellipsoid
Radial size of the membrane:
(1+1000/(1+40*(x^2+y^2)^2)/
Membrane function with local vertical displacement
(1+20000*(z0.21/(1+1.5*(x^2+y^2)))^4))*4
Cutting the ellipsoid into 5 legs
+(0.2+sin(5*atan2(y,x)))*(x^2+y^2)
Box 5;5 5;5 0;1.8
Grid 150 150 50 
I used 6 legs because I don't have the atan2 function so I needed some plane symmetry.
This version has curved legs:
Code:  x^2+y^2+(1+(pi/2+atan(30*z30))*(0.03*sin(1+7*x+21*y)+0.06*sin(0.7+22*x+5*y)+0.02*sin(3+25*x)+0.04*sin(25*y)))*(41/(1+10*(x^2+y^2)))*6*(z1/(1+0.15*(x^2+y^2)))^2(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z0.21/(1+1.5*(x^2+y^2)))^4))*4+(0.2+sin(0.2*sqrt(x^2+y^2)+sin(5*atan(y,x)))*(x^2+y^2)



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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sat Jun 23, 2012 7:28 pm Post subject: 


aha Furan I'm sorry I thought you are using k3dsurf, and I was just kidding about the sixth leg and of course wanted to see more beautiful work of you, anyway I've heard that Taha will pay 10000 $ for the first one who makes the more realistic starfish (a k3dsurf award) _________________ My YouTube channel
Last edited by abdelhamid belaid on Mon May 20, 2013 12:39 am; edited 1 time in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sun Jun 24, 2012 11:23 pm Post subject: 


this is my first own attempt, of course I'm waiting for your suggestions
Code:  ( (sqrt(x^2+y^2)/(3+exp(1.5*cos(5*atan2(y,x)))) )^2+(1+sqrt(x^2+y^2)/10)*(zcos(sqrt(x^2+y^2))/4)^21 )
*
( (sqrt(x^2+y^2)*cos(sin(2.5*atan2(y,x))/2.5)floor(1*sqrt(x^2+y^2)*cos(sin(2.5*atan2(y,x))/2.5)+0.5)/1)^2+(sqrt(x^2+y^2)*sin(sin(2.5*atan2(y,x))/2.5))^2+(z1.1+sqrt(x^2+y^2)/18cos(1.15*sqrt(x^2+y^2))/4)^20.01 )0.1
[x]: 8 , 8.5
[y]: 8 , 8
[z]: 1.3 , 2
Cnd: x^2+y^2<8.5^2 
_________________ My YouTube channel 

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Furan
Joined: 05 Oct 2010 Posts: 64 Location: Prague, Czech Republic

Posted: Mon Jun 25, 2012 5:46 am Post subject: 


Also a very hideous one indeed. Good job !!!
I can see you used totally different equations than me and that brings a question:
What if we modeled a specific Starfish according a picture. How would our different approaches cope with the problem?
I'm gonna have to install K3DSurf for that 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Mon Jun 25, 2012 1:04 pm Post subject: 


I haven't an exact answer how but okay let's try and see, there are many picturs I saw, I'm not sure which one is good so please Furan (or anyone) feel free to choose a picture, for a starfish or anything you like and let us know.
finally, that's a good news Furan , Taha didn't deny what I heard, I began to believe that ! _________________ My YouTube channel
Last edited by abdelhamid belaid on Thu Jul 05, 2012 9:28 am; edited 1 time in total 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Mon Jun 25, 2012 1:15 pm Post subject: 


Wooow, suprise, suprise..
That's really fantastic work!
It looks like this one...
If you add some poisonous coloring, the starfish would look a litte bit more dangerous.
Cnd: 0.8*sin(x*x+y*y) + sin(1.57+10*atan(x/y)) > 0
I'm inquiring, about what forms  especially starfishes  can still be expressed by mathematical formulas.
The fantasy of nature seems to be endless... humans too ?
http://upload.wikimedia.org/wikipedia/commons/c/c8/Redknobbed.starfish.arp.jpg
btw. Some starfishes have more that 5 arms, e.g. the Crownofthorns starfish with 16 arms.


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ufoace
Joined: 11 Mar 2013 Posts: 46

Posted: Tue Apr 09, 2013 4:10 pm Post subject: 


What an awesome thread, amazing work!!! 

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ufoace
Joined: 11 Mar 2013 Posts: 46

Posted: Wed Apr 10, 2013 4:46 am Post subject: 


These are parametric formulas? isometric? Only the curves is parametric like sin, cos, etc?


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ufoace
Joined: 11 Mar 2013 Posts: 46


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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Thu Apr 11, 2013 8:15 pm Post subject: 


Thanks ufoace, yes they are parametric formulas (x=f(u,v) , y=g(u,v) , z=h(u,v)) and the using of sin and cos functions is necessary, this is an example:
Code:  X():cos(v)*(5+2*cos(10*v)+cos(u)*cos(10*v))sin(v)*sin(u)
Y():sin(v)*(5+2*cos(10*v)+cos(u)*cos(10*v))+cos(v)*sin(u)
Z():2*sin(10*v)cos(u)*sin(10*v)
[u]:0, 2*pi
[v]:0, 2*pi 
Quote:  what is confusing me is the mathematical complexity of bending an isosurface cylinder around the line made by a circle or a parabola 
yes ufoace that is still unknown for an arbitrary curve, I am looking from time to time for new tricks to open this door and write a general cartesian formula, I did it just for some basic shapes like (the helical torus for example), as an isosurface for the previous example (the helical torus), this is a very very close formula to the parametric shape:
Code:  Name: AB_HelixTorus1x17
F(): (sqrt((sqrt(x^2+y^2)3)^2+z^2)1)^2 + (x^2+y^2)
* (atan2(sqrt((sqrt(x^2+z^2)3)^2+z^2) * sin(atan2(z,sqrt(x^2+y^2)3)17*atan2(y,x))
,sqrt((sqrt(x^2+z^2)3)^2+z^2) * cos(atan2(z,sqrt(x^2+y^2)3)17*atan2(y,x))
) / 17)^2 0.09
[x]: 4.5 , 4.5
[y]: 4.5 , 4.5
[z]: 1.5 , 1.5 
for a parametric formula that's very simple as Furan had explained, I will show you some other examples soon .
about two weeks ago I reached a trick where I could to do this as an isosurface:
Code:  Name: AB_HelixTorus6x17
F(): (sqrt((sqrt(x^2+y^2)3)^2+z^2)1)^2 + (x^2+y^2)
* (atan2(sqrt((sqrt(x^2+z^2)3)^2+z^2) * sin(6*atan2(z,sqrt(x^2+y^2)3)17*atan2(y,x)) ,sqrt((sqrt(x^2+z^2)3)^2+z^2) * cos(6*atan2(z,sqrt(x^2+y^2)3)17*atan2(y,x))
) / 23)^2 0.04
[x]: 4.5 , 4.5
[y]: 4.5 , 4.5
[z]: 1.5 , 1.5 
_________________ My YouTube channel 

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ufoace
Joined: 11 Mar 2013 Posts: 46

Posted: Sun Apr 14, 2013 8:41 am Post subject: 


abdelhamid belaid wrote:  Thanks ufoace, yes they are parametric formulas (x=f(u,v) , y=g(u,v) , z=h(u,v)) and the using of sin and cos functions is necessary, this is an example:

That is amazing, Thank you for the amazing formula. I didn't realise it was so confusing , using only 34 trigonometry functions in 2d... However in 3d and without parametric it is a construct far removed from the laws of nature, for example orbital forces only trace a line in 3d, whereas an isometric spirograph is a very confusing volume! Sorry for asking such a complicated question! anyways when i have my program completed for walking in the formulas, ill send you a copy maybe you can send me some crazy formulas 

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