PK_BSURF_piecewise_sf_t

struct PK_BSURF_piecewise_sf_s
    {
    int                 u_degree;           --- The degree in u = order-1.
    int                 v_degree;           --- The degree in v = order-1.
    int                 n_u_segments;       --- The number of segments in u.
    int                 n_v_segments;       --- The number of segments in v.
    int                 dim;                --- Dimension of coefficient vecs
    PK_LOGICAL_t        is_rational;        --- True if the surface is rational
    PK_piecewise_rep_t  rep;                --- Representation method
    double             *coeffs;             --- Coefficient vectors
    };
typedef struct PK_BSURF_piecewise_sf_s PK_BSURF_piecewise_sf_t;


This data structure is the piecewise standard form of a b-surface.


Specific Errors:
    PK_ERROR_bad_value             unreadable value
    PK_ERROR_bad_dimension         illegal 'dim'
    PK_ERROR_bad_order             hermite basis and degree not 3
    PK_ERROR_discontinuous_surface adjacent segments do not meet.

Used in:

PK_BSURF_ask_piecewise
PK_BSURF_create_piecewise

'u_degree'       This field specifies the degree of the surface in the u
                 direction. The minimum degree is 1.  If the Hermite basis is
                 used ('rep' = PK_piecewise_rep_hermite_c)
                 then the surface must be bicubic ('degree' = 3).

'v_degree'       This field specifies the degree of the surface in the v
                 direction. The minimum degree is 1.  If the Hermite basis is
                 used ('rep' = PK_piecewise_rep_hermite_c)
                 then the surface must be bicubic ('degree' = 3).

'n_u_segments'   The number of segments in the surface in the u direction.
                 This must be greater than or equal to 1. Adjacent segments
                 must meet.

'n_v_segments'   The number of segments in the surface in the v direction.
                 This must be greater than or equal to 1. Adjacent segments
                 must meet.

'dim'            This field gives the number of doubles per coefficient vector
                 in the array 'coeffs'. Allowable values are 3 and 4.

'is_rational'    This field is set to true if the surface is rational.
                 In this case the 'dim' field must be one greater than the
                 dimensionality of the surface.
                 At present, if:

                     'is_rational' == PK_LOGICAL_false then 'dim' must be 3
                     'is_rational' == PK_LOGICAL_true  then 'dim' must be 4.

'rep'            This field defines the representation method.
                 See documentation of PK_piecewise_rep_t.

'coeffs'         Contains
                 ('u_degree'+1)*'n_u_segments'*('v_degree'+1)*'n_v_segments'
                 vectors of dimension 'dim'.
                 If `is_rational` == PK_LOGICAL_false, then the vectors are
                 3-D vectors giving the x, y and z components.
                 If 'is_rational' == PK_LOGICAL_true, then each vector has
                 a weight (w)associated with it, and x, y, z and w components
                 are supplied for each vector. The weights supplied must be
                 greater than zero.
                 The interpretation of 'coeffs' depends on the representation
                 method chosen; this is determined by the value of the field
                 'rep'.
                 The u and v segments divide the surface into a grid of
                 patches. The vectors are ordered such that the coefficients
                 for a given patch are grouped together. The patches are
                 arranged so that the patches vary most quickly with u and then
                 with v.

The 'rep' together with the 'coeffs' define a function for each patch of the
b-surface. For more information about these representations see
Other methods of representing surfaces. Note that the coefficients
are independent of the parameterisation of the b-surface - the u and v
parameters of the function for each patch of the b-surface are parameterised
from 0 to 1.