Eiffel Tower and other works
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Wed Jun 29, 2011 12:03 am    Post subject: Reply with quote

Hi all,
It's a Wonderful flower Abdelmajid . That's the proof that a mathematician can be a romantic person Very Happy
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Abderrahman
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Phil999



Joined: 08 Feb 2007
Posts: 24

PostPosted: Thu Jun 30, 2011 3:36 am    Post subject: Reply with quote

indeed phantastic work. And next to the romantic side I also like the humour!
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sat Jul 02, 2011 1:43 am    Post subject: Reply with quote

Hi all,
Sure it's a crazy attempt, he looks like if I made it of wood by a knife Very Happy (we still need reality and claws as well)




Code:
(min(
((
(   abs(x)^2.8+ 7*((y/(1-(x-0.5)^2/9))^2+((z-(1-cos(2*x))/5)/(1+x/8))^2)-4   )*
(

(((x+1.95)-max(sin(1.7*(z+1.3)+0.3)/8,1.5-(2*(z+1.3)+
0.3-2.5)^2/4)/2 )/(1+3.8*max(0,2-((z+1.3)-2.6)^2/4
)))^2+((abs(y)-0.32)/(1+2.0*max(0,(z+1.15)/6+1.7-((z+1.3)-2.6)^2/4
) ))^2+(((z+1.6)+0)/20)^2-0.01
  )-0.002)*
(
(   ((x-1-sin(z)/8)/1.2)^2+2*((abs(y)-0.35))^2+(z/(1.8-(x-1-sin(z)/8)/1.2))^2-0.16   )*
max( 2*(((x-1.19-sin(z-0.08)/8)+0.35)/(1+(z-0.08)/12))^2+4*(abs(y)-0.3)^2-0.0225, abs((z-0.08)+1.8)-0.8)-0.01          ) -0.0009        )*
(  max( (z*cos(pi/3)-(x-0.9)*sin(pi/3))^2+y^2-0.1 , (abs(z+x-2.5)-0.5) )   )-0.001
,
min(
((  ((2.5*(x-1.8))/(1+(2.5*(z-1.35))^2/8))^2/1.3+((abs(2.5*y)-0.05)/(1+((2.5*(z-1.35))-0.3)^2/4))^2+(2.5*(z-1.35))^2-1  )*
(
(((2.5*(x-1.8))-(2*(2.5*(z-1.35))+sin(2*(2.5*(z-1.35))))/16-1.2)/(1+2*(2.5*(z-1.35))^2))^2/1.5+1.5*((2.5*y)/(1+1.5*((2.5*(z-1.35))-0.15)^2+exp(-(2.5*(z-1.35)))/5))^2+(abs((2.5*(z-1.35)))-(1-cos(10*(2.5*y)/(1+((2.5*(z-1.35))-0.5)/12)))/45)^2/1-0.25    )-0.01  )*
(  ((2.5*(x-1.8))-0.6)^2/1.5+(abs(2.5*y)-0.4)^2/1.3+((2.5*(z-1.35))-0.45)^2-0.09 )-0.001    ,

4*( sqrt((1.3*(abs(2.5*y)-0.5))^2+((2.5*(z-1.35))+(2.5*(x-1.8))^2/2+0.3)^2)-1)^2+((atan2(1.3*(abs(2.5*y)-0.5),(2.5*(z-1.35)))-pi/6)/7)^2+((2.5*(x-1.8))/2/(1+((2.5*(z-1.35))-0.5)^2))^2-0.04    )    ) )*
(max(5.35*( sqrt((x+2.6)^2+(z-0.45)^2)-1)^2+((atan2((x+2.6),-(z-0.45))-pi/4)/7)^2+(2*y)^2-0.04 , z-0.45))-0.02


[x]: -3.5 , 3.3
[y]: -1.3 , 1.3
[z]: -2.5 , 2



more details:

F(x,y,z)= (min(
((   /* middle body */
(   abs(x)^2.8+ 7*((y/(1-(x-0.5)^2/9))^2+((z-(1-cos(2*x))/5)/(1+x/8))^2)-4   )*
(
/* back legs */
(((x+1.95)-max(sin(1.7*(z+1.3)+0.3)/8,1.5-(2*(z+1.3)+
0.3-2.5)^2/4)/2 )/(1+3.8*max(0,2-((z+1.3)-2.6)^2/4
)))^2+((abs(y)-0.32)/(1+2.0*max(0,(z+1.15)/6+1.7-((z+1.3)-2.6)^2/4
) ))^2+(((z+1.6)+0)/20)^2-0.01
  )-0.002)*
(
/* front legs */
(   ((x-1-sin(z)/8)/1.2)^2+2*((abs(y)-0.35))^2+(z/(1.8-(x-1-sin(z)/8)/1.2))^2-0.16   )*
max( 2*(((x-1.19-sin(z-0.08)/8)+0.35)/(1+(z-0.08)/12))^2+4*(abs(y)-0.3)^2-0.0225, abs((z-0.08)+1.8)-0.8)-0.01          ) -0.0009        )*
/* neck */
(  max( (z*cos(pi/3)-(x-0.9)*sin(pi/3))^2+y^2-0.1 , (abs(z+x-2.5)-0.5) )   )-0.001
,

/* head */
min(
((  ((2.5*(x-1.8))/(1+(2.5*(z-1.35))^2/8))^2/1.3+((abs(2.5*y)-0.05)/(1+((2.5*(z-1.35))-0.3)^2/4))^2+(2.5*(z-1.35))^2-1  )*
(
/* mouth */
(((2.5*(x-1.8))-(2*(2.5*(z-1.35))+sin(2*(2.5*(z-1.35))))/16-1.2)/(1+2*(2.5*(z-1.35))^2))^2/1.5+1.5*((2.5*y)/(1+1.5*((2.5*(z-1.35))-0.15)^2+exp(-(2.5*(z-1.35)))/5))^2+(abs((2.5*(z-1.35)))-(1-cos(10*(2.5*y)/(1+((2.5*(z-1.35))-0.5)/12)))/45)^2/1-0.25    )-0.01  )*
(  ((2.5*(x-1.8))-0.6)^2/1.5+(abs(2.5*y)-0.4)^2/1.3+((2.5*(z-1.35))-0.45)^2-0.09 )-0.001    ,
/* ears */
4*( sqrt((1.3*(abs(2.5*y)-0.5))^2+((2.5*(z-1.35))+(2.5*(x-1.8))^2/2+0.3)^2)-1)^2+((atan2(1.3*(abs(2.5*y)-0.5),(2.5*(z-1.35)))-pi/6)/7)^2+((2.5*(x-1.8))/2/(1+((2.5*(z-1.35))-0.5)^2))^2-0.04    )    ) )*

/* tail */
(max(5.35*( sqrt((x+2.6)^2+(z-0.45)^2)-1)^2+((atan2((x+2.6),-(z-0.45))-pi/4)/7)^2+(2*y)^2-0.04 , z-0.45))-0.02


I think now with just some modifications we can get easily one like this:





Thanks Phil999, Oh yes Taha mathematicians are not often socially successful Cool thank you Taha that's exactly what I was want to say Twisted Evil
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Last edited by abdelhamid belaid on Sun May 19, 2013 2:14 am; edited 4 times in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sun Jul 10, 2011 1:58 am    Post subject: Reply with quote

Hi all,

Firstly: always, hunting is not allowed here Wink
We have a stringray fish today (I like this fish). We can make it swims some of time using "Morph" :





Code:
(
(
max(
max(
(
(
sqrt((x-1.5)^2+(y/1.5)^2)-acos(cos(atan2(y/1.5,x-1.5)))+(5*(z+1.5*y^2/20*cos(x-1.5+1.3*pi)))^2 -1       )*
(
(x+0.2)^2/4+(y/(0.9-x/4))^2+(1.5*z/(0.8-(x+0.2)/4))^2-0.9 )/2-0.1        )*
(
(x+1.2)^2/2.5+(abs(y)-0.55)^2/2+(z-0.6)^2-0.02       )-0.01
,
-( (x+1.2)^2+(abs(y)-0.75)^2+(z-0.7)^2/2-0.07)        )
,
-( (x+0.75)^2+(abs(y)-0.75)^2+(z-0.6)^2/2-0.1)        )*
(
((x-7)/6)^2+64*(y^2+1.2*(z-0.18+((x-2)/6)^2*sin((x-2)/1.9)/2.5 )^2)/(1+exp(-0.8*(x-3)) )^2 -1    )-0.04            )*
(
(x+1.2)^2+(abs(y)-0.65)^2+(z-0.6)^2-0.01        )-10^-7       )*
(
(x-3)^2+((abs(y)-0.1+(-(x-3)-1)/3)/(1+(x-3)/2.5))^2+(6*z)^2-0.25
)-0.0001

[x]: -4 , 13
[y]: -4.5 , 4.5
[z]: -0.6 , 1.4



More details:
Let's call
A:  (    sqrt((x-1.5)^2+(y/1.5)^2)-acos(cos(atan2(y/1.5,x-1.5))) +(5*(z+1.5*y^2/20*cos(x-1.5+1.3*pi)))^2 -1     )

B:  (    (x+0.2)^2/4+(y/(0.9-x/4))^2+(1.5*z/(0.8-(x+0.2)/4))^2-0.9     )

C:  (   (x+1.2)^2/2.5+(abs(y)-0.55)^2/2+(z-0.6)^2-0.02   )

D:  -( (x+1.2)^2+(abs(y)-0.75)^2+(z-0.7)^2/2-0.07)

E:  -( (x+0.75)^2+(abs(y)-0.75)^2+(z-0.6)^2/2-0.1)

F:  (   ((x-7)/6)^2+64*(y^2+1.2*(z-0.18+((x-2)/6)^2*sin((x-2)/1.9)/2.5 )^2)/(1+exp(-0.8*(x-3)) )^2 -1   )

G:  (   (x+1.2)^2+(abs(y)-0.65)^2+(z-0.6)^2-0.01        )

H:  (   (x-3)^2+((abs(y)-0.1+(-(x-3)-1)/3)/(1+(x-3)/2.5))^2+(6*z)^2-0.25    )

So   F(x,y,z,t)=((max(max((A*B /2-0.1)*C-0.01,D),E)*F-0.04)*G-10^-7)*H-0.0001



To get animation (Morph use) you can try this:

F(x,y,z,t)= ( ( max( max( ( ( sqrt(((x+3*t)-1.5)^2+(y/1.5)^2)-acos(cos(atan2(y/1.5,(x+3*t)-1.5))) +(5*(z+1.5*y^2/35*cos(8*t+(x+3*t)-1.5+1.3*pi)))^2 -1       )*
(
((x+3*t)+0.2)^2/4+(y/(0.9-(x+3*t)/4))^2+(1.5*z/(0.8-((x+3*t)+0.2)/4))^2-0.9 )/2-0.1        )*
(
((x+3*t)+1.2)^2/2.5+(abs(y)-0.55)^2/2+(z-0.6)^2-0.02       )-0.01
,
-( ((x+3*t)+1.2)^2+(abs(y)-0.75)^2+(z-0.7)^2/2-0.07)        )
,
-( ((x+3*t)+0.75)^2+(abs(y)-0.75)^2+(z-0.6)^2/2-0.1)        )*
(
(((x+3*t)-7)/6)^2+64*(y^2+1.2*(z-0.18+(1-t)*(((x+3*t)-2)/6)^2*sin(((x+3*t)-2)/1.9)/2.5 )^2)/(1+exp(-0.8*((x+3*t)-3)) )^2 -1
     )-0.04            )*
(
((x+3*t)+1.2)^2+(abs(y)-0.65)^2+(z-0.6)^2-0.01        )-10^-7       )*
(
((x+3*t)-3)^2+((abs(y)-0.1+(-((x+3*t)-3)-1)/3)/(1+((x+3*t)-3)/2.5))^2+(6*z)^2-0.25
)-0.0001

[x]: -7 , 13
[y]: -4.5 , 4.5
[z]: -0.8 , 1.6

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Last edited by abdelhamid belaid on Sun May 19, 2013 2:20 am; edited 4 times in total
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nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Jul 10, 2011 4:41 am    Post subject: Reply with quote

Hi all,
Very nice Abdelhamid and It looks really good Shocked
Also the blue color is perfect for it
Thank you again for making our dreams real and for sharing your passion with us Very Happy
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Abderrahman
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Fri Jul 15, 2011 1:51 am    Post subject: Reply with quote

Hi all,
As you see a dangerous white shark now, I am intending to do more nature works and always I welcome your ideas and suggestions (or dreams) creating these works takes some of time but that's so enjoyable Very Happy







Code:
(
(
min(max(max(
((x+0.3)/2.5)^2+(y/1.3)^2+(z+0.1+(x+0.3)/2.8)^2-1  , (x+0.3)^2/3+(y/1.3)^2+(z+(x+0.3)/2.8-0.5)^2-1 ) ,  abs(y/1.2)-0.85-(x-0.3)^2/2     ) ,  (x-0.2)^2+4*(abs(y)-1.1)^2+(z-0.1)^2-0.01     )*
max( (x+1.3)^2/1.3+y^2/1.3+(z+(x+1.3)/2.8+0.3)^2-1.7 , (x+1.3)-2.5*(z+0.2+(x+0.3)/2.8)^2 )-0.05                )*
(
min(min(
((x+5)/5)^2+abs(y/2/(1-z/14))^2.6+((z+0.4)/2.2/(1+((x+5)/15)^2) )^2-1  ,
 (1.2*((x+4)/(1+0.03*exp(-(abs(y)-3.5+(x+4)/1.5))/6)+((abs(y)-3.5+(x+4)/1.2)+0.5)^2/7)/(1-(abs(y)-3.5+(x+4)/1.2)/4.5))^2+((abs(y)-3.5+(x+4)/1.2)/2.3)^2+(3.8*(abs(z+2+(y/5)^2)+0.03)/(1+0.9*((x+4)/(1+0.03*exp(-(abs(y)-3.5+(x+4)/1.2))/5)+((abs(y)-3.5+(x+4)/1.2)+0.5)^2/7)/2))^2-1    ),
   (0.6*((x+7)/(1+0.5*exp(-((1.0*(z-2.3))+(x+7)/1.3))/6)+(((1.0*(z-2.3))+(x+7)/1.2)+0.5)^2/7)/(1-((1.0*(z-2.3))+(x+7)/1.2)/4.5))^2+(((1.0*(z-2.3))+(x+7)/1.2)/2)^2+(4*(abs(y)+0.1)/(1+1.5*((x+7)/(1+0.5*exp(-((1.0*(z-2.3))+(x+7)/1.2))/5)+(((1.0*(z-2.3))+(x+7)/1.2)+0.5)^2/7)/2))^2-1           )*
(
min(min(min(min(
((x+12)/10)^2+(y/(0.8+1.3*sin((x+19)/8)^4)  )^2+((z+0*((x+10)/10)^2+0.4)/(0.8+1.3*sin((x+19)/8)^4) )^2-1 ,       (1.5*(((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/(1+0.5*exp(-((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.3))/6)+(((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.2)+0.5)^2/7)/(1-((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.2)/4.5))^2/2+(((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.2)/2)^2+(4*(abs(y)+0.1)/(1+1.5*(((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/(1+0.5*exp(-((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.2))/5)+(((abs((z+0.3))-1.5)+((x+22+(z+0.3)/12+exp(-((z+0.3)-2.8)^2)/6)/1.5)/1.2)+0.5)^2/7)/2))^2-1        ),        (1.5*(((x+11)-(abs(y)-1.3)/1.8)/(1+0.5*exp(-(3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.3))/6)+((3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.2)+0.5)^2/7)/(1-(3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.2)/4.5))^2+((3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.2)/2)^2+(4*(abs((z+abs(y/3) +1.2))+0.1)/(1+1.5*(((x+11)-(abs(y)-1.3)/1.8)/(1+0.5*exp(-(3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.2))/5)+((3*(abs(y)-1.3)+((x+11)-(abs(y)-1.3)/1.8)/1.2)+0.5)^2/7)/2))^2-1      ),      max(
(((x+16)*cos(pi/3)+(z-0.3)*sin(pi/4))/0.5)^2+ ((z-0.3)*cos(pi/3)-(x+16)*sin(pi/3))^20 +(8*y/(1+x+16))^2-1 , -(z+0.5))       ),        max(
(((x+17.5)*cos(pi/3)-(z+0.85)*sin(pi/4))/0.5)^2+ (-(z+0.85)*cos(pi/3)-(x+17.5)*sin(pi/3))^20 +(8*y/(1+(x+17.5)))^2-1 , z+0.5)     )                     )-0.01      )-0.03             )


[x]: -25 , 2
[y]: -6.7 , 6.7
[z]: -6 , 6

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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sun Aug 21, 2011 4:18 pm    Post subject: Reply with quote

Hi all,
These are my first attempts using the ray-tracing to visualize previous K3DSurf works Smile





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Last edited by abdelhamid belaid on Mon Nov 07, 2011 1:34 pm; edited 2 times in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Tue Aug 23, 2011 3:14 pm    Post subject: Reply with quote

Hi all,
Previous patterned torus Smile


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Last edited by abdelhamid belaid on Fri Oct 14, 2011 3:34 pm; edited 1 time in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sat Aug 27, 2011 11:10 pm    Post subject: Reply with quote

Hi all,
a varnished color, only 4 rays at each pixel and more smoothness had cost me about four hours of rendering Smile


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Furan



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

PostPosted: Sun Aug 28, 2011 12:00 pm    Post subject: Reply with quote

Nice one! I'm confused, was that POV-ray or your own rendering program? How many polygons have you used?

4 hours is nothing Smile
I created this one in monstrous 7680x7680xAA4 in about one hundred hours on 20 cores. Enjoy: http://furan.sweb.cz
Hi-res will be available in a month or so.
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sun Aug 28, 2011 10:10 pm    Post subject: Reply with quote

Thank you much Furan your works are always fantastic, I think there is no need to wish to be an actual artist, as I see you are an artist Very Happy

Yes I'm using POV-Ray, just now I've began and there is much to learn, I have no idea about polygons and how to calculate it or to know that (?), and also polygons meshing, also Furan you're right 4 hours is nothing but I meant sure it will be 400 for other complex works.

these are also previous works :




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Last edited by abdelhamid belaid on Sun May 19, 2013 2:33 am; edited 2 times in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Fri Sep 02, 2011 1:30 am    Post subject: Reply with quote

Hi all,
(hexagons patterned helix/torus) Unfortunately it's not real Very Happy

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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Fri Sep 02, 2011 8:01 pm    Post subject: Reply with quote

Again unfortunately it's not real, gold prices are so high these days Very Happy


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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Tue Sep 06, 2011 2:02 pm    Post subject: Reply with quote

Hi all,
How nice to see this isosurface on other images with other tastes:



Code:
max(-( acos(cos(x))+acos(cos(y))+acos(cos(z))+acos(cos(x+y))+acos(cos(x-y))+acos(cos(x+z))+acos(cos(x-z))+acos(cos(y+z))+acos(cos(y-z))-15.5 )
, abs(max(max(abs(x),abs(y)),abs(z))-9.5)-0.5)

x,y,z : -10.1 , 10.1

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Last edited by abdelhamid belaid on Sun May 19, 2013 2:35 am; edited 1 time in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Tue Sep 13, 2011 4:34 pm    Post subject: Reply with quote

Hello all,
The same vase but it's of glass this time Smile

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