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inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Tue Mar 06, 2007 10:30 am    Post subject: Gaudi's fantastic spires

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

Gerd

Last edited by inode on Thu Aug 24, 2017 7:53 pm; edited 4 times in total
nextstep

Joined: 06 Jan 2007
Posts: 539

 Posted: Tue Mar 06, 2007 11:09 pm    Post subject: Hi all, waw Gerd , really fantastic spires!_________________Cheers, Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Mon Mar 19, 2007 1:08 pm    Post subject:

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
jotero

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

 Posted: Tue Mar 20, 2007 10:24 am    Post subject: WOW... nice demo- data of k3dsurf ciao torolf_________________Kontakte
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Tue Mar 20, 2007 9:37 pm    Post subject:

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

Hi all,
Very impressive Gerd . 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
PS: you can use this website for hosting your images :
http://imagehost.bizhat.com/
_________________
Cheers,
Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Thu Mar 22, 2007 1:09 pm    Post subject:

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.

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 ?

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
jotero

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

Posted: Fri Mar 23, 2007 7:18 am    Post subject:

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.

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 ?

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
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
Posts: 127
Location: Austria

 Posted: Mon Mar 26, 2007 3:26 pm    Post subject: 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 ? Gerd
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Tue Mar 27, 2007 3:43 am    Post subject:

 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)
_________________
Cheers,
Abderrahman
jotero

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

Posted: Tue Mar 27, 2007 6:13 am    Post subject:

 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 ? Gerd

bend is missing still
 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

Joined: 27 Jan 2007
Posts: 127
Location: Austria

 Posted: Sun Dec 30, 2007 1:32 pm    Post subject: new spire Here's a new spire...
denisc

Joined: 24 Apr 2013
Posts: 92

 Posted: Sun Oct 05, 2014 10:45 am    Post subject: hello it's possible to print that ? With witch printer you can do that?
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sun Oct 05, 2014 1:17 pm    Post subject:

Hi all,

 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
_________________
Cheers,
Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

 Posted: Thu Aug 24, 2017 6:49 pm    Post subject: Visit this shape in 3d... 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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