Shap3d36.dat, 36th 'shape' file for CPO3D
Elliptical electrode by users equation.
For information on the option for users equations, see users equations.
See also shap3d37 and shap3d38.
First, ignore the factors sin(phi) and cos(phi), by putting phi = 0, and consider an ellipse in the xy plane.
Here the ellipse is produced by stretching a circular plate by the factor a = 2.
A circle of radius r could have x = r*cos(theta), y = r*sin(theta).
It can be seen from the first equation above that we have stretched x by the factor a.
The factor f has been used to cover the range from the inside to the outside of the ellipse.
The third equation gives z the constant value b.
The range of theta covers half the complete ellipse, and the symmetry plane x = 0 produces the other half.
Now restore sin(phi) and cos(phi) by making phi non-zero.
Then you will see that the plane of the electrode has been rotated around the x axis by phi.
The equations, as they appear in the data file, are:
f 0 1 name of variable number 1 and its limits
theta -1.570796 1.570796 name of variable number 2 and its limits
a 2 name of parameter number 1 and its fixed value
r 1 name of parameter number 2 and its fixed value
b 1 name of parameter number 3 and its fixed value
phi 0 name of parameter number 4 and its fixed value
f*a*r*cos(theta)
f*r*sin(theta)*cos(phi)
f*r*sin(theta)*sin(phi)+b
1 1 numbers of 2 applied voltages (can be same)
8 12 numbers of subdivisions of variables 1 and 2
(The program has corrected the less accurate value that was entered for pi/2.)