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inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sun Feb 25, 2007 12:48 pm    Post subject: Heart1 (implicit)

Hi all

every men should have it ...
 Code: F(x,y,z,t) = (x*x+9/4*y*y+z*z-1)^3 - (x*x+9/80*y*y)*z^3 = 0  x [ -1.3, 1.3]  y [ -0.7, 0.7]  z [ -1.0, 1.3]

you can find a picture at...
http://mathworld.wolfram.com/HeartSurface.html
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sun Mar 04, 2007 8:50 am    Post subject:

Hi all

There is another formula for a heart like surface defined as parametric surface:

Heart2 (Another heart)

 Code: X = 4*cos(v)*(sin(abs(u))^abs(u))*cos(u)*cos(v)*1.6 Y = 4*cos(v)*(sin(abs(u))^abs(u))*sin(u)*cos(v) Z = 2*sin(v)  With   U[ -pi,  pi] And V[  -pi/2,  pi/2]

there you can find a picture too...
http://www.econym.demon.co.uk/isotut/real.htm#heart1

Last edited by inode on Wed Mar 07, 2007 2:22 pm; edited 3 times in total
nextstep

Joined: 06 Jan 2007
Posts: 538

 Posted: Mon Mar 05, 2007 4:59 am    Post subject: Hi all, Beautiful Gerd .Are you using Pov-Ray to render your models ?_________________Cheers, Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Mon Mar 05, 2007 1:00 pm    Post subject:

Hi Taha

Yes, I am using POV-Ray 3.5 to render the functions because it is a free raytracer that can render Parametric and Algebraic Functions.

You will find a real great surface collection with all it's pov-ray-sources at
http://www.econym.demon.co.uk/isotut/maths.htm

This pages are created by Mike Williams und he has great tutorials how to create your own pov-ray-files!

http://www.econym.demon.co.uk/isotut/maths.zip
first, because you need the file "param.inc" of it.

Gerd
 Code: //********************************************************* // Persistence of Vision Ray Tracer Scene Description File // File: surface_p0200.pov // Vers: 3.5 // Desc: parametric surface: "Another Heart" // Link: http://www.econym.demon.co.uk/isotut/real.htm // Date: 05.March.2007 // Auth: Gerd Platl //********************************************************* #version 3.5; #include "colors.inc" #include "param.inc" //------------------------------------------- background { color White } #declare CamLoc = < 2, 2, -26>; camera { location CamLoc     look_at < 0, -pi/2, 0>     angle 25        } light_source {CamLoc color Red*0.4} light_source {<10, -15,-17> color White} //------------------------------------------- // parametric surface: "Another Heart" //   with  U[-pi, pi] and V[-pi/2, pi/2] #declare F1 = function(u,v) { 4*cos(v)* cos(v) * pow(sin(abs(u)), abs(u)+0.01) } #declare Fx = function(u,v) { F1(u,v) * sin(u) } #declare Fy = function(u,v) { F1(u,v) * cos(u) * -1.6 } #declare Fz = function(u,v) { 2*sin(v) } object {Parametric(Fx,Fy,Fz,<-pi,-pi/2>, , 200,100,"")   pigment {rgb Red}    //  pigment {uv_mapping checker rgb Red rgb Red*0.8 scale 0.1}   finish {phong 0.5 phong_size 10}   no_shadow }
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