Heart1 (implicit)

 
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Feb 25, 2007 12:48 pm    Post subject: Heart1 (implicit) Reply with quote

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
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Mar 04, 2007 8:50 am    Post subject: Reply with quote

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
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nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Mon Mar 05, 2007 4:59 am    Post subject: Reply with quote

Hi all,
Beautiful Gerd Very Happy .Are you using Pov-Ray to render your models ?
_________________
Cheers,
Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Mar 05, 2007 1:00 pm    Post subject: Reply with quote

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!

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

Cool 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>, <pi-0.001,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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