Wednesday, June 6, 2012

Creating An Ellipsoid in a 3D Grapher

When creating an Ellipsoid in a 3D Grapher, whether it be online or Apple's Grapher that comes with Mac, or using a formula inside of a 3D graphics program such as Blenders Add Mesh Math Addon, use this formula.
X function is:   a(cos(u))*cos(v)
Y function is:   b(cos(u))*sin(v)
Z function is:   c(sin(u))

U min: -Pi/2
U max: Pi/2
V min: -Pi
V max: Pi
a = Some number or function greater than 0
same for b and c function, or some constant n.


  • a>b>c — tri-axial or (rarely) scalene ellipsoid;
  • a=b>c — oblate ellipsoid of revolution (oblate spheroid);
  • a=b<c — prolate ellipsoid of revolution (prolate spheroid);
  • a=b=c — the degenerate case of a sphere;

In Apple Grapher I used this:


The 3,2,2 after the [x,y,z] is where you would put the a,b,c if you like.

This took me all day to figure out.  You got it in 2 secs.  Use carefully with beer.