53rd shape file -rectangular hole in a sphere, by users equations

Adapted from shap3d47, square hole in a sphere.

This supersedes shap3d24 and shap3d25.

The sphere has a radius of R, and so z = sqrt(R^2 - x^2 - y^2), always.

The equations, say g1(x,y,z), for the inner straight edge of the first electrode are

x = sx, y = sy*tan(phi), where phi = 0 to pi/4.

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

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

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.

To concentrate the segments at the inner edges we have used f^2

g(x,y,z) = (1-f^2)*g1+f^2*g2

Here sx = 0.25, sy = 0.1, r = 0.75, R = 1 and 2 symmetry planes are used.

The equation for z looks complicated, but is essentially sqrt(R^2 - x^2 - y^2).

It has been necessary to disable the 'aspect ratio' check by entering a large negative number.