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Someone just asked me what the mathematical name for the shape of an egg
was, since eggs aren't ellipsoidal, there must be another term, so I
thought. I did find these pages and I wonder how the math relates to the
blob function, or how shapes like the demonstration for Cassini's oval
might be done as an isosurface (which I should probably post to p.u.p, I
know) and generalized into 3D space... it might make them easier (for me
at least) to understand.
http://new.math.uiuc.edu/eggmath/Shape/cassini.htm
http://new.math.uiuc.edu/eggmath/Shape/descartes.html
--
Josh English -- Lexiphanic Lethomaniac
eng### [at] spiritone com
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/
"He who hebetates is last."
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On Thu, 08 Feb 2001 14:37:12 -0800, Josh English wrote:
>Someone just asked me what the mathematical name for the shape of an egg
>was, since eggs aren't ellipsoidal, there must be another term, so I
>thought.
I should think that the term is "ovoid." It even has the same root word
as other egg-related words, like "ovary" and "ovum."
--
Ron Parker http://www2.fwi.com/~parkerr/traces.html
My opinions. Mine. Not anyone else's.
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Josh English wrote:
>
> Someone just asked me what the mathematical name for the shape of an egg
> was, since eggs aren't ellipsoidal, there must be another term, so I
> thought. I did find these pages and I wonder how the math relates to the
> blob function, or how shapes like the demonstration for Cassini's oval
> might be done as an isosurface (which I should probably post to p.u.p, I
> know) and generalized into 3D space... it might make them easier (for me
> at least) to understand.
>
> http://new.math.uiuc.edu/eggmath/Shape/cassini.htm
>
> http://new.math.uiuc.edu/eggmath/Shape/descartes.html
That's some interesting pages !
But you left out the last l in the first link.
This link works:
http://new.math.uiuc.edu/eggmath/Shape/cassini.html
See my example code below for such iso-surface eggs.
(Requires MegaPOV)
--
Best regards,
Tor Olav
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
// Cassini and Descartes Eggs
// By Tor Olav Kristensen
// mailto:tor### [at] hotmailcom
// http://www.crosswinds.net/~tok
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
#version unofficial MegaPov 0.5;
#include "colors.inc"
#include "textures.inc"
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
$ P1 = <-1, 1, 0>;
$ P2 = < 1, -1, 0>;
$ P1x = P1.x;
$ P1y = P1.y;
$ P1z = P1.z;
$ P2x = P2.x;
$ P2y = P2.y;
$ P2z = P2.z;
/*
$ P3 = <-1, -1, -1>/3;
$ P3x = P3.x;
$ P3y = P3.y;
$ P3z = P3.z;
*/
$ SphereFunction = function { sqrt(x*x + y*y + z*z) }
$ CassiniEggs =
isosurface {
function {
SphereFunction(x - P1x, y - P1y, z - P1z)
*SphereFunction(x - P2x, y - P2y, z - P2z)
// *SphereFunction(x - P3x, y - P3y, z - P3z)
// +0.15*noise3d(30*x, 30*y, 30*z)
}
threshold 1.95 // Also try 2.00 and 2.20
contained_by { sphere { <0, 0, 0>, 10 } }
method 1
}
object {
CassiniEggs
texture {
pigment { color (White + Blue)/2 }
finish { Dull }
}
}
/*
$ DescartesEgg =
isosurface {
function {
SphereFunction(x - P1x, y - P1y, z - P1z)
+2*SphereFunction(x - P2x, y - P2y, z - P2z)
// +0.05*noise3d(4*x, 4*y, 4*z)
}
threshold 5
contained_by { sphere { <0, 0, 0>, 10 } }
method 1
}
object {
DescartesEgg
texture {
pigment { color Gray30 }
finish { Dull }
}
}
*/
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7 =
background { color Magenta/4 }
light_source {
<5, 0, -1>*10
color White/2 + Red
}
light_source {
<1, 0, -5>*10
color White
}
camera {
location <0, 0, -5>
look_at <0, 0, 0>
}
// ===== 1 ======= 2 ======= 3 ======= 4 ======= 5 ======= 6 ======= 7
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On Thu, 08 Feb 2001 14:37:12 -0800, Josh English
<eng### [at] spiritonecom> wrote:
>Someone just asked me what the mathematical name for the shape of an egg
>was, since eggs aren't ellipsoidal, there must be another term, so I
"Oblate spheroid," isn't it?
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