Shap3d42.dat, 42nd 'shape' file for CPO3D

A very small hole in a circular disc, by users equation.

For information on the option for users equations, see users equations.

Here the radius of the inner hole is r = 0.1 and the outer radius is R = 10.

If this is created in the normal way the program will reject it because R/r > 10. The program rejects for the good reason that it is unable to make the segments at the inner edge sufficiently small, even with the option of 'unequal radial distribution'.

But setting up the disc with 'users equations' we can circumvent this restriction.

The equations, say g1(x,y,z), for the inner circular edge are

x = r*cos(phi), y = r*sin(phi), z = b.

The equations, say g2(x,y,z), for the outer square edge are

x = R*cos(phi), y = R*sin(phi), z = b.

2 symmetry planes are in use here, so phi goes from 0 to pi/2.

In the usual fashion we can combine these by using the general equation

g(x,y,z) = (1 - f)*g1 + f*g2,

where f goes from 0 to 1.

This reproduces g1 when f = 0, and g2 when f = 1.

The equations, as they appear in the data file, are:

f 0 1 name of variable number 1 and its limits

phi 0 1.570796 name of variable number 2 and its limits

r 0.1 name of parameter number 1 and its fixed value

R 10.0 name of parameter number 2 and its fixed value

z 1 name of parameter number 3 and its fixed value

n 3 name of parameter number 4 and its fixed value

(r*(1-f^n)+R*f^2)*cos(phi)

(r*(1-f^n)+R*f^2)*sin(phi)

z

1 1 numbers of 2 applied voltages (can be same)

20 5 numbers of subdivisions of variables 1 and 2

(The program has corrected the less accurate value that was entered for pi/2.)

To concentrate the segments near the inner edge, we have used f^n instead of f, where n is typically 2, but is 3 in the present example.