OUSPPS ( bs, pts, ncol, nrow, props, pdata, nprops, sense, ifail )
==================================================================
Output B-surface as spline points
Receives:
KI_tag_b_surface *bs --- B-surface
Returns:
KI_tag_list_dbl *pts --- mesh of spline points
KI_int_nitems *ncol --- number of columns of points
KI_int_nitems *nrow --- number of rows of points
KI_tag_list_int *props --- surface properties
KI_tag_list_<list> *pdata --- list of data lists
KI_int_nitems *nprops --- number of surface properties
KI_cod_logical *sense --- surface sense
KI_cod_error *ifail --- failure indicator
Specific errors:
KI_bad_knots surface has unsuitable knot vector
KI_unsuitable_entity more than one patch in linear or quadratic direction
order of surface is greater than four
Description:
This function outputs a B-surface as spline points, boundary conditions and
knot vectors. This constitutes sufficient information to recreate the surface
(via CRSPPS).
Restrictions
. The surface must be bicubic (or lower degree), non-rational and have
continuous first and second derivatives. If a surface is linear or
quadratic the u direction then to satisfy these conditions it must
consist of a single column of patches (similarly for v direction and rows
of patches).
. If the surface is periodic in a particular direction the corresponding
knot vector must not contain any repeated knots.
. If the surface is non-periodic in a particular direction the
corresponding knot vector can only contain repeated knots at the start
and end. Surfaces
. Any surface created using CRSPPS and not subsequently modified will
satisfy these conditions.
Spline points 'pts', 'npts':
The spline points are returned in the list of real data 'pts', in order
along the rows, row by row. 'ncol' * 'nrow' points are returned. They
correspond to corners of the patches in the surface.
Surface properties 'props', 'pdata', 'nprops':
The 'props' array contains 'nprops' tokens from the sequence PAPR00. A
particular property may be associated with additional data; if so, this
is returned in a list. The tag of the list is returned in the 'pdata' list,
in the position corresponding to the token in 'props'.
The table shows which tokens may be present, and the data associated with
them. Some tokens are always present, whereas others are only present if the
surface has a particular property.
In explaining the various properties of splined surfaces the following
notation is used
o bottom boundary - first row of points
o top boundary - last row of points
o left boundary - first col of points
o right boundary - last col of points
token | meaning | real data | always present?
---------------------------------------------------------------------
| | |
PAPRPU | rows are periodic | none | NO - the default is
| | | non-periodic
| | |
PAPRPV | columns are periodic | none | NO - the default is
| | | non-periodic
| | |
PAPRCB | derivatives returned | 'ncol' derivative | present unless
| at start of columns | vectors | columns are periodic
| (clamped boundary | |
| condition) | |
| | |
PAPRCT | derivatives returned | 'ncol' derivative | present unless
| at end of columns | vectors | columns are periodic
| (clamped boundary | |
| condition) | |
| | |
PAPRCL | derivatives returned | 'nrow' derivative | present unless
| at start of rows | vectors | rows are periodic
| (clamped boundary | |
| condition) | |
| | |
PAPRCR | derivatives returned | 'nrow' derivative | present unless
| at end of rows | vectors | rows are periodic
| (clamped boundary | |
| condition) | |
| | |
PAPRBL | bottom left twist | twist vector | present unless rows
| vector returned | | or cols are periodic
| | |
PAPRBR | bottom right twist | twist vector | present unless rows
| vector returned | | or cols are periodic
| | |
PAPRTL | top left twist | twist vector | present unless rows
| vector returned | | or cols are periodic
| | |
PAPRTR | top right twist | twist vector | present unless rows
| vector returned | | or cols are periodic
| | |
PAPRKU | knot vector in u | knot vector | YES
| | |
PAPRKV | knot vector in v | knot vector | YES
| | |
PAPRCU | surface is bicubic | none | NO
| | |
Boundary conditions PAPRPU, PAPRPV, PAPRCB, PAPRCT, PAPRCL, PAPRCR:
Either clamped or periodic boundary conditions may be returned. These apply
to u and v directions (rows and columns) independently. Clamped boundary
conditions refer to either the start or end of the rows or columns.
Periodic boundary conditions apply to both the start and end of rows or
columns simultaneously.
. Clamped boundary conditions return the first derivatives, with respect to a
parameter varying between 0 and 1 over the first or last interval, across
some boundary of the surface. The derivatives are returned in a real list.
. Periodic boundary conditions imply that the rows or columns are closed, so
that the surface meets itself with continuity of tangent and curvature.
Twist vectors PAPRBL, PAPRBR, PAPRTL, PAPRTR:
A twist vector is a derivative with respect to both u and v; i.e. it
is the rate of change of the u derivatives in the v direction, and also
the rate of change of the v derivatives in the u direction (these two
quantities are always equal). The twist vectors are returned at all four
corners, but only if neither the rows nor the columns are periodic.
Knot vector PAPRKU, PAPRKV:
Knot vectors are always returned. They have the following properties:
. The knot values form strictly increasing sequences.
. If the rows are not periodic there will be 'ncol' knot values in the
u knot vector.
. If the rows are periodic there will be ('ncol'+1) knot values in the
u knot vector.
. If the columns are not periodic there will be 'nrow' knot values in
the v knot vector.
. If the columns are periodic there will be ('nrow'+1) knot values in
the v knot vector.
Bicubic surface PAPRCU:
This token indicates that the surface is bicubic.
Surface sense 'sense'
. If 'sense' is KI_true the surface normal is given by the cross product of
the first derivatives of the surface with respect the u and v parameters.
i.e.
normal = Pu X Pv
. If 'sense' is KI_false the surface normal is in opposite to that described
for 'sense' == KI_true.
