Some pictures of 3D representations by K3DSurf 0.62 Goto page Previous  1, 2, 3, 4, 5, 6, 7, 8  Next
Author Message
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
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
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*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

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.
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*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
_________________

Last edited by abdelhamid belaid on Mon Jun 25, 2012 12:06 am; edited 1 time in total
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*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)
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 channelLast edited by abdelhamid belaid on Mon May 20, 2013 12:39 am; edited 1 time in total
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)*(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

_________________
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
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 channelLast edited by abdelhamid belaid on Thu Jul 05, 2012 9:28 am; edited 1 time in total
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/Red-knobbed.starfish.arp.jpg btw. Some starfishes have more that 5 arms, e.g. the Crown-of-thorns starfish with 16 arms.
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Tue Apr 09, 2013 4:10 pm    Post subject: What an awesome thread, amazing work!!!
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?
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Wed Apr 10, 2013 12:55 pm    Post subject: If you are interested in the stars and geodes, i made a infinite star pattern generator some time ago, and i also did it in 3d so here is some pics. ive kind of lost the files somewhere now but they are kind of fun: press next and previous to see all thanks!http://www.facebook.com/photo.php?fbid=10150419926384575&set=a.10150419924499575.416402.569539574&type=3&l=1af80de565&permPage=1 http://www.facebook.com/photo.php?fbid=10150419925959575&l=31a2d57014
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

_________________
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 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
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMTGoto page Previous  1, 2, 3, 4, 5, 6, 7, 8  Next Page 7 of 8

 Jump to: Select a forum MathMod----------------MathMod Progress & featuresMathematical Models CollectionHow toBugsMathMod for WindowsMathMod for Linux/UnixMathMod For MACOSXMathMod TutorialsOther Mathematical ToolsOpen Discussion K3DSurf----------------K3DSurf Discuss/DiscussionsHow toK3DSurf math related questionsK3DSurf for WindowsK3DSurf for MacOSK3DSurf for LinuxOnline K3DSurf: J3DSurfNewsBugsOnline DocumentationAccount Activation Issue ?/ Problème d'activation de votre compte ?
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