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inode
Joined: 27 Jan 2007
Posts: 127
Location: Austria
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 Posted: Tue Jun 19, 2012 11:28 pm Post subject: starfish basics |
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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
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| Posted: Thu Jun 21, 2012 10:18 am Post subject: |
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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
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Fri Jun 22, 2012 5:36 pm Post subject: |
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Here you go:
| Code: | x^2+y^2+(1+(pi/2+atan(30*z-30))*(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)))*(4-1/(1+10*(x^2+y^2)))*6*(z-1/(1+0.15*(x^2+y^2)))^2=(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z-0.2-1/(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
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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
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| Posted: Fri Jun 22, 2012 6:40 pm Post subject: |
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this is very beautiful Furan but I think you meant:
| Code: | | x^2+y^2+(1+(pi/2+atan(30*z-30))*(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)))*(4-1/(1+10*(x^2+y^2)))*6*(z-1/(1+0.15*(x^2+y^2)))^2-(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z-0.2-1/(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*z-30))*(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)))*(4-1/(1+10*(x^2+y^2)))*6*(z-1/(1+0.15*(x^2+y^2)))^2-(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z-0.2-1/(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
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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
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| Posted: Sat Jun 23, 2012 12:15 pm Post subject: |
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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*z-30))*(
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:
))*(4-1/(1+10*(x^2+y^2)))*
Local vertical displacement of the body:
6*(z-1/(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*(z-0.2-1/(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*z-30))*(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)))*(4-1/(1+10*(x^2+y^2)))*6*(z-1/(1+0.15*(x^2+y^2)))^2-(1+1000/(1+40*(x^2+y^2)^2)/(1+20000*(z-0.2-1/(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
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| Posted: Sat Jun 23, 2012 7:28 pm Post subject: |
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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)
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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
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| Posted: Sun Jun 24, 2012 11:23 pm Post subject: |
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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)*(z-cos(sqrt(x^2+y^2))/4)^2-1 )
*
( (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+(z-1.1+sqrt(x^2+y^2)/18-cos(1.15*sqrt(x^2+y^2))/4)^2-0.01 )-0.1
[x]: -8 , 8.5
[y]: -8 , 8
[z]: -1.3 , 2
Cnd: x^2+y^2<8.5^2 |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Mon Jun 25, 2012 5:46 am Post subject: |
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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
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| Posted: Mon Jun 25, 2012 1:04 pm Post subject: |
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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 !
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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
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| Posted: Mon Jun 25, 2012 1:15 pm Post subject: |
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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/Red-knobbed.starfish.arp.jpg
btw. Some starfishes have more that 5 arms, e.g. the Crown-of-thorns starfish with 16 arms.
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Tue Apr 09, 2013 4:10 pm Post subject: |
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| What an awesome thread, amazing work!!! |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Wed Apr 10, 2013 4:46 am Post subject: |
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These are parametric formulas? isometric? Only the curves is parametric like sin, cos, etc?
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ufoace
Joined: 11 Mar 2013
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abdelhamid belaid
Joined: 13 Aug 2009
Posts: 170
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| Posted: Thu Apr 11, 2013 8:15 pm Post subject: |
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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 |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Sun Apr 14, 2013 8:41 am Post subject: |
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| 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:
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That is amazing, Thank you for the amazing formula. I didn't realise it was so confusing , using only 3-4 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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