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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sun Jun 05, 2011 12:40 pm Post subject: 


It's not a new idea, any time my friends, I welcome your ideas and suggestions, I will be very glad to do something for others
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Last edited by abdelhamid belaid on Sun May 19, 2013 5:39 pm; edited 1 time in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Mon Jun 06, 2011 11:41 pm Post subject: 


a torus:
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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Thu Jun 09, 2011 12:31 am Post subject: 


Hi all,
for me this is the first pattern making over z=x*y surface
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Last edited by abdelhamid belaid on Sun May 19, 2013 5:48 pm; edited 2 times in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sat Jun 11, 2011 1:47 pm Post subject: 


here are patterned surfaces ( pattern(x,y)^2+f(x,y,z)^2R^2=0 or generally F(pattern(x,y) , f(x,y,z))=0 )
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Last edited by abdelhamid belaid on Sun May 19, 2013 5:50 pm; edited 2 times in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Fri Jun 17, 2011 11:44 am Post subject: 


Hi all,
It's just over new surfaces
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Last edited by abdelhamid belaid on Mon Nov 07, 2011 12:20 pm; edited 1 time in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Tue Jul 12, 2011 5:52 pm Post subject: 


a torus:
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Last edited by abdelhamid belaid on Sun May 19, 2013 5:56 pm; edited 3 times in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sun Jul 24, 2011 5:16 pm Post subject: 


Hi all,
A dodecahedron, of course we can get as much as we want faces (F(x,y,z,n)=0)
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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sat Aug 06, 2011 2:40 am Post subject: 


taking straight lines instead of a single curved line:
over z = sin(x)
z = x^2
z = x*sin(x/3)/3
z = y*x^2/5
z = y*x^2/10
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Last edited by abdelhamid belaid on Sun May 19, 2013 6:08 pm; edited 4 times in total 

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Sat Aug 06, 2011 11:05 pm Post subject: 


this is more explanation about my last method to make patterns over a z = f(x,y) surface:
Let's call our step h, the new normal dimension N or N(f) or N(f, h) , we have z = 3/(1.5+x^2) (of course our formula is N(f, h)^2+y^2R^2=0) I will every time change h (1, 1/2, 1/6, 1/10, 1/20, 1/100), I will get more and more a smooth shape (curved line), that means I will get a normal dimension (section is always orthogonal to the tangent or we can say to our surface) :
h=1
h=0.5
h=0.25
h=0.166666666
h=0.1
h=0.05
h=0.01
more works:
z = y*(x/4)^3
z= 3/(1.5+x^2+y^2)
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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Mon Aug 08, 2011 12:06 am Post subject: 


normal dimension:
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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Wed Aug 10, 2011 1:59 am Post subject: 


a tetrahedron :
Code:  max( z2+tan(pi/3)*abs(x) , tan(pi/3)*abs(y)z2 )
[x]: 3 , 3
[y]: 3 , 3
[z]: 2 , 2
I mean generally:
max( zh+tan(pi/3)*abs(x) , tan(pi/3)*abs(y)zh )

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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Wed Aug 10, 2011 6:14 pm Post subject: 


Also other patterned surfaces by the same method:
z = 2*sin(x)^3*cos(y)
z = sin(x)^3*cos(y)+cos(2*sqrt(x^2+y^2))/2
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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170


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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170


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abdelhamid belaid
Joined: 13 Aug 2009 Posts: 170

Posted: Tue Aug 16, 2011 1:02 pm Post subject: 


The same pattern but it's around the origin this time
It's over: z  cos(sqrt(x^2+y^2))*sin(x) = 0
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