PK_TORUS_sf_t

struct PK_TORUS_sf_s
    {
    PK_AXIS2_sf_t basis_set;    --- centre, axis and a reference direction
    double        major_radius; --- the major radius of the torus(!=0)
    double        minor_radius; --- the minor radius of the torus(>0)
    };

typedef struct PK_TORUS_sf_s PK_TORUS_sf_t;



Specific Errors:
PK_ERROR_radius_sum_le_0        sum of radii less than or equal to zero
PK_ERROR_radius_le_0           'minor_radius' less than or equal to zero
PK_ERROR_radius_eq_0           'major_radius' equals zero

Used in:

PK_TORUS_ask
PK_TORUS_create

The parameterisation of the torus 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 = major_radius
    r = minor_radius

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

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

For certain choices of 'major_radius' and 'minor_radius' the torus will
self-intersect.  There are two cases for self-intersecting surfaces.

    The first case produces an inner and an outer surface.  The inner surface
    is called a lemon, while the outer surface is called an apple.  Each
    surface is bounded by two singular points, where the normal is undefined,
    and treated as a separate surface.

    The second case produces an outer surface only.  This apple has only one
    singular point, on its axis of rotation.

An apple is created by setting 'major_radius' positive and less than or equal
to 'minor_radius'.  If, on the other hand, 'major_radius' is negative and the
sum of the radii is positive then a lemon is produced.