Eiffel Tower and other works
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Tue Sep 20, 2011 5:18 pm    Post subject: Reply with quote

Hi all, this is just a grainy surface cube Smile


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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Fri Sep 23, 2011 3:39 pm    Post subject: Reply with quote

Hi,
Two vases are created as always for me by K3DSurf Smile



Code:
max(abs(max(sqrt(x*x+y*y)-1+sin(z/1.5)/1.8  , -(z+4.75) ) )-0.05, z-4.25 )
[x]: -1.85 , 1.85
[y]: -1.85 , 1.85
[z]: -5.01 , 4.251







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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sun Sep 25, 2011 9:18 pm    Post subject: Reply with quote

It seems to me that my previous flowers have withered, we need at least one, as you see all are empty right now Sad



Code:
max(abs(max(sqrt(x*x+y*y)-1.3-(1.5*sin(1.2*z)-z/1.5)/6  , -z-1 ) )-0.07, z-5.5 )
[x]: -1.5 , 1.5
[y]: -1.5 , 1.5
[z]: -1.1 , 5.51



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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Wed Sep 28, 2011 11:07 pm    Post subject: Reply with quote

Just using one of my preferred functions (dimensions) as a pattern Smile


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nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Wed Sep 28, 2011 11:33 pm    Post subject: Reply with quote

Hi all
Very beautiful design Abdelhamid. Your progress in the ray-tracing area is amazing. Keep it up Smile
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sat Oct 01, 2011 6:27 am    Post subject: Reply with quote

Hi all,
Merci Taha, Here is the same vase in another scene, a 100% mathematical scene Very Happy


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Whystler



Joined: 12 Apr 2012
Posts: 7

PostPosted: Fri Apr 13, 2012 7:26 pm    Post subject: Reply with quote

A beautiful vase for certain!

Unfortunately, I cant get it look right in k3dsurf...

Does anyone know why it looks like this on my computer?

[/img]
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Furan



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

PostPosted: Fri Apr 13, 2012 9:32 pm    Post subject: Reply with quote

Actually I have never used this program, however the Grid parameters strikes my eyes at first sight. Try something like Grid=100x100x200
Also specify the limits:
x: -1.5 1.5
y: -1.5 1.5
z: -1.6 5.51
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Whystler



Joined: 12 Apr 2012
Posts: 7

PostPosted: Fri Apr 13, 2012 11:04 pm    Post subject: Reply with quote

Ahh thank you! It was the grid size. I figured out how to change it.

-Whystler
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Fri Jul 13, 2012 6:02 am    Post subject: Hexagonal pattern formula Reply with quote

Hello, I am searching for an efficient short formula for defining a hexagonal pattern on a flat plane similar do this one...

but connected with cylinders.
Is it possible to define it without using min and max functions?
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Furan



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

PostPosted: Fri Jul 13, 2012 5:15 pm    Post subject: Reply with quote

Try this, I made it a year ago, I called it Crysis Very Happy
Code:
0.25+2*z^2+(0.25*(cos(4*y)+cos(2*sqrt(3)*x-2*y)+cos(2*sqrt(3)*x+2*y))+0.03*(cos(4*sqrt(3)*x)+cos(6*y-2*sqrt(3)*x)+cos(6*y+2*sqrt(3)*x)))
Box
-5;5
-5;5
-0.5;0.5
Grid
250;250;25
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Sun Jul 15, 2012 10:45 pm    Post subject: Reply with quote

Hi,
I didn't understand "connected with cylinders" but in addition to Furan's beautiful work I think this can help Very Happy

Code:
( (abs(y-2*floor(y/2+0.5))-1/(1+exp(7*(abs(x-floor(x/3.2+0.5)*3.2)-0.8))))*cos(atan(-7*exp(7*(abs(x-floor(x/3.2+0.5)*3.2)-0.8))/(1+exp(7*(abs(x-floor(x/3.2+0.5)*3.2)-0.8)))^2)) )^2+1.2*z^2-0.04
[x]: -5 , 5
[y]: -5.5 , 5.5
[z]: -0.3 , 0.3


here is I've used this basic pattern:

Code:
( (abs(y)-1/(1+exp(7*(abs(x)-1))))*cos(atan(-7*exp(7*(abs(x)-1))/(1+exp(7*(abs(x)-1)))^2)) )^2+z^2-0.04
[x]: -4 , 4
[y]: -4 , 4
[z]: -0.3 , 0.3


also, we have this (maybe you meant this):


Code:
( (abs(y-floor(y/4+0.5)*4)-(asin(sin(2*abs(x-floor(x/6.5+0.5)*6.5)))-2*abs(x-floor(x/6.5+0.5)*6.5)+2*pi)/pi)*cos(atan( (2*cos(2*abs(x-floor(x/6.5+0.5)*6.5))/sqrt(1-sin(2*abs(x-floor(x/6.5+0.5)*6.5))^2)-2)/pi )) )^2+z^2-0.04
[x]: -8 , 8
[y]: -8.5 , 8.5
[z]: -0.3, 0.3

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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Jul 16, 2012 11:11 am    Post subject: Hexagonal Grid with cylinder parts Reply with quote

Hi all,
I meant that the hexagonal grid can be constructed by connecting cutted cylinder peaces with identical radius and with identical length arrange with 0, 120 and 240°.
Furan, your solution seems to be symmetrical in all 3 directions e.g. if you turn around the grid by 120° around the z axis.
Belaid, your formulas constructions are also very interresting but they seems to disagree 120° symmetry.

Btw. multiplying Furans formula by 4 will make it a little bit shorter ...
Code:
1 + 8*z^2
  + cos(4*y)  +cos(2*sqrt(3)*x-2*y)  +cos(2*sqrt(3)*x+2*y)
  + 0.12*( cos(4*sqrt(3)*x) +cos(6*y -2*sqrt(3)*x)  +cos(6*y +2*sqrt(3)*x))

Wink


Last edited by inode on Thu Jul 19, 2012 5:35 am; edited 1 time in total
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abdelhamid belaid



Joined: 13 Aug 2009
Posts: 170

PostPosted: Wed Jul 18, 2012 1:26 pm    Post subject: Reply with quote

Gerd, would I know why you want a formula without min and max functions?
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Thu Jul 19, 2012 5:49 am    Post subject: without min and max functions? Reply with quote

Hi,
It was only a principle question I ask to me, if repeating patterns can be handled without using min and max functions.
Do you have an example where you use min and max for a hexagon pattern?

Btw. a modification using abs() gives a nice columned hall!
Code:
Name: ColumnedHall1
F(): 1 - 4*z^9
       + cos(             4*y)
       + cos(2*sqrt(3)*x -2*y)     
       + cos(2*sqrt(3)*x +2*y)   
+ abs(0.18*( cos( 4*sqrt(3)*x)           
       + cos(6*y -2*sqrt(3)*x)         
       + cos(6*y +2*sqrt(3)*x)))
[x]: -3 , 3
[y]: -3 , 3
[z]: 0 , 1.1
;
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