Gaudi's fantastic spires

 
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Tue Mar 06, 2007 10:30 am    Post subject: Gaudi's fantastic spires Reply with quote

Hi all
Do you know the brilliant architect Antoni GAUDI i Cornet ?
He was creating many spires with fantastic varieties of shapes.
I think he would like my spires too!

Code:
function name = spire1 x^5+x^8+y^5+z^5+z^8-(0.00017^(cos(2*x)*cos(2*y)+cos(2*y)*cos(2*z)+cos(2*z)*cos(2*x)))
[x]:-4,  4
[y]:-8,  8
[z]:-4,  4


Spire1 picture see https://www.flickr.com/search/?text=Surface_PG_Spire_1

Code:
function name = spire2
x^5+x^8+y^5+z^5+z^8-(0.00017^(cos(3*x)*cos(3*y)+cos(3*y)*cos(3*z)+cos(3*z)*cos(3*x)))
[x]:-4,  4
[y]:-8,  8
[z]:-4,  4


Wink Gerd


Last edited by inode on Thu Aug 24, 2017 7:53 pm; edited 4 times in total
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Tue Mar 06, 2007 11:09 pm    Post subject: Reply with quote

Hi all,
waw Gerd Shocked , really fantastic spires!
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Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Mar 19, 2007 1:08 pm    Post subject: Reply with quote

If you reduce the peroidic gyroid function in y-direction
you'll get my socalled "Gyroid Hedge"...
Code:
 Name: PG_GyroidHedge_1
/* Isosurface: PG_GyroidHedge_1 3/2007 Gerd Platl */
F(): -1.2 -0.015*y*y -cos(x)*sin(y) -cos(y)*sin(z) -cos(z)*sin(x)
-0.05*(cos(2*x)*cos(2*y) -cos(2*y)*cos(2*z) +cos(2*z)*cos(2*x))
[x]: -11 , 11
[y]: -5 , 5
[z]: -11 , 11
;


And because a picture says more than 1000 words here the belonging PovRay3.5 picture...

"PG_GyroidHedge_1"


Last edited by inode on Sun Dec 30, 2007 1:03 pm; edited 3 times in total
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jotero



Joined: 27 Jan 2007
Posts: 153
Location: Germany Hannover

PostPosted: Tue Mar 20, 2007 10:24 am    Post subject: Reply with quote

WOW... nice demo- data of k3dsurf Smile

ciao
torolf
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nextstep
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PostPosted: Tue Mar 20, 2007 9:37 pm    Post subject: Reply with quote

inode wrote:
If you reduce the peroidic gyroid function in z-direction
you'll get my socalled "Gyroid Hedge"...

Hi all,
Very impressive Gerd Smile . I'm wondering if it's possible to make some "closed" shapes in all 3 directions (like the Isocaedron example in K3DSurf! It should be wonderful Very Happy
PS: you can use this website for hosting your images :
http://imagehost.bizhat.com/
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Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Thu Mar 22, 2007 1:09 pm    Post subject: Reply with quote

TaHa wrote:
Quote:
I'm wondering if it's possible to make some "closed" shapes in all 3 directions (like the Isocaedron example in K3DSurf! It should be wonderful Very Happy


Yes, sure it's possible! If you combine a sphere formula with the gyroid grid you'll get this...


But in the meantime it's an "old hat" as torolf showed us with his examples at
http://www.evolution-of-genius.de/3d/Data/page.htm?164,0.

Wink Gerd

PS. torolf I have a question. Can your "twisted torus buildings" be described in a surface formula for K3DSurf or are they only possible to describe within the maxwell render ?

pps. Thanx TaHa for your hint to upload picture to bizhat.
I have an account, but uploading ends for me mostly with an time out error message. I think the server is located somewhere on the west cost of florida...


Last edited by inode on Sun Dec 30, 2007 1:09 pm; edited 2 times in total
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jotero



Joined: 27 Jan 2007
Posts: 153
Location: Germany Hannover

PostPosted: Fri Mar 23, 2007 7:18 am    Post subject: Reply with quote

inode wrote:
TaHa wrote:
Quote:
I'm wondering if it's possible to make some "closed" shapes in all 3 directions (like the Isocaedron example in K3DSurf! It should be wonderful Very Happy


Yes, sure it's possible! If you combine a sphere formula with the gyroid grid you'll get this...


But in the meantime it's an "old hat" as torolf showed us with his examples at
http://www.evolution-of-genius.de/3d/index.htm?144,0.

Wink Gerd

PS. torolf I have a question. Can your "twisted torus buildings" be described in a surface formula for K3DSurf or are they only possible to describe within the maxwell render ?

pps. Thanx TaHa for your hint to upload picture to bizhat.
I have an account, but uploading ends for me mostly with an time out error message. I think the server is located somewhere on the west cost of florida...


I need Wink
R= radius of the emphasis circle of the producing surface
r = radius of the produced circle

Code:
(R2 − r2)2 + 2R2(z2 − x2 − y2) − 2r2(x2 + y2 + z2) + (x2 + y2 + z2)2 = 0


ciao
torolf
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inode



Joined: 27 Jan 2007
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PostPosted: Mon Mar 26, 2007 3:26 pm    Post subject: Reply with quote

Hi torolf

using (R2 − r2)2 + 2R2(z2 − x2 − y2) − 2r2(x2 + y2 + z2) + (x2 + y2 + z2)2 = 0
R= 8 r= 2

results in
(8−2)^2+2*8*(z^2−x^2−y^2) −2*2*(x^2+y^2 + z^2)+(x^2+y^2+z^2)^2
which is a simple torus.

What I mean is a twisted torus such as your example at...
http://www.evolution-of-genius.de/3d/Data/page.htm?73,0

Can this "twisted torus" be described in a surface formula for K3DSurf ?

Wink Gerd
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nextstep
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PostPosted: Tue Mar 27, 2007 3:43 am    Post subject: Reply with quote

Gerd wrote:
Can this "twisted torus" be described in a surface formula for K3DSurf ?

Hi all,
This shapes is derived from the Klein shape (see the "Klein_2" parametric example in K3DSurf). torolf is an expert in a great tool called "TopMod" which can make complicated shapes by reworking simple ones like those generated by K3DSurf (since TopMod can load OBJ files) Smile
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Abderrahman
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jotero



Joined: 27 Jan 2007
Posts: 153
Location: Germany Hannover

PostPosted: Tue Mar 27, 2007 6:13 am    Post subject: Reply with quote

inode wrote:
Hi torolf

using (R2 − r2)2 + 2R2(z2 − x2 − y2) − 2r2(x2 + y2 + z2) + (x2 + y2 + z2)2 = 0
R= 8 r= 2

results in
(8−2)^2+2*8*(z^2−x^2−y^2) −2*2*(x^2+y^2 + z^2)+(x^2+y^2+z^2)^2
which is a simple torus.

What I mean is a twisted torus such as your example at...
http://www.evolution-of-genius.de/3d/Data/page.htm?73,0

Can this "twisted torus" be described in a surface formula for K3DSurf ?

Wink Gerd


bend is missing still Wink
Code:
F():(x*cos(0.180*z) - y*sin(0.180*z))^100 + (x*sin(0.180*z) + y*cos(0.180*z))^100 + (z/4.3)^100 -1
[x]:-2,  2
[y]:-2,  2
[z]:-2*4.3*1,  2*4.3*1


ciao
torolf
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inode



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PostPosted: Sun Dec 30, 2007 1:32 pm    Post subject: new spire Reply with quote

Here's a new spire...

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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Sun Oct 05, 2014 10:45 am    Post subject: Reply with quote

hello

it's possible to print that ?


With witch printer you can do that?
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nextstep
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Posts: 538

PostPosted: Sun Oct 05, 2014 1:17 pm    Post subject: Reply with quote

Hi all,
This blog gives,I think, an answer to your questions about the gyroid formula and how to print your model.

Quote:
{
"Iso3D": {
"Cnd": [ "" ],
"Component": [ "SpaceEgg" ],
"Description ": [ "SPACE EGG" ],
"Fxyz": [
"-(cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x))
*(cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x))
+0.05-exp(100.0*(x*x/64+y*y/64 + z*z/(1.6*64)*exp(-0.4*z/8 ) - 1))"
],
"Name": [ "SpaceEgg" ],
"Xmax": [ " 8.5" ],
"Xmin": [ "-8.5 " ],
"Ymax": [ " 8.5" ],
"Ymin": [ "-8.5 " ],
"Zmax": [ " 17" ],
"Zmin": [ "-8.5 " ]
}
}


SpaceEgg by taha_ab, on Flickr



Quote:
{
"Iso3D": {
"Cnd": [ "" ],
"Component": [ "WonderTree" ],
"Description ": [ "Wonder Tree" ],
"Fxyz": [
"cos(4.0*x/(x*x+y*y+z*z+0.0001))*sin(4.0*y/(x*x+y*y+z*z+0.0001))+ cos(4.0*y/(x*x+y*y+z*z+0.0001))*sin(4.0*z/(x*x+y*y+z*z+0.0001))+ cos(4.0*z/(x*x+y*y+z*z+0.0001))*sin(4.0*x/(x*x+y*y+z*z+0.0001))+ exp(0.1*(x*x+y*y+z*z-0.2))- exp(-10.0*(x*x+y*y+z*z-0.15))"
],
"Name": [ "WonderTree" ],
"Xmax": [ " 2" ],
"Xmin": [ "-2 " ],
"Ymax": [ " 2" ],
"Ymin": [ "-2 " ],
"Zmax": [ " 2" ],
"Zmin": [ "-2 " ]
}
}



WonderTree by taha_ab, on Flickr
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Thu Aug 24, 2017 6:49 pm    Post subject: Visit this shape in 3d... Reply with quote

You can visit this red 'WonderTree' shape also known as inverted gyroid shape in 3d at
https://www.shapeways.com/product/XVPTN9XKQ/wondertree
after pressing the (3d) button !

Or look at this anmiation made by Schmiegel...
https://vimeo.com/20417412
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