struct PK_SPHERE_sf_s
    {
    PK_AXIS2_sf_t basis_set; ---a cartesian point, a ref_direction and a normal
    double        radius;    ---the radius of the sphere(>0)
    };

typedef struct PK_SPHERE_sf_s PK_SPHERE_sf_t;



Specific Errors:
PK_ERROR_radius_le_0            radius less than or equal to zero



The parameterisation of the sphere is as follows:

    C = basis_set.location
    x = basis_set.ref_direction
    y = basis_set.axis X basis_set.ref_direction ( cross product )
    z = basis_set.axis
    R = radius

    S( u, v) = C + R( cos v )( ( cos u )x + ( sin u )y ) + R( sin v )z

                            where  ( 0 <= u < 2PI; -PI/2 <= v < PI/2 )

Radius must be larger than zero.

The surface normal points away from the centre.