ENPOPS ( surf, u, v, nudrvs, nvdrvs, nreq, p, norm, ifail )
===========================================================
Evaluate point from surface parameters
Can be called from the GO.
Receives:
KI_tag_surface *surf --- surface
KI_dbl *u --- u parameter of required point
KI_dbl *v --- v parameter of required point
<KI_int_nitems> *nudrvs --- number of derivs wrt u required
<KI_int_nitems> *nvdrvs --- number of derivs wrt v required
KI_cod_logical *nreq --- request for normal
Returns:
KI_vec_derivatives p[(nudrvs+1) * (nvdrvs+1)]
--- point and derivatives
KI_vec_normal norm --- surface normal
KI_cod_error *ifail --- failure code
Specific errors:
KI_at_singularity failure to evaluate normal at singularity
KI_bad_parameter parameter out of range
KI_too_many_derivatives too many derivatives requested
KI_invalid_geometry surface not supported
Description:
Calculates the Cartesian coordinates of the point at the given parameter
values 'u' and 'v', and also the derivatives with respect to 'u' and 'v',
up to order 'nudrvs' and 'nvdrvs' respectively. It also optionally
calculates the surface normal. This normal will be parallel to the
cross product of the derivative with respect to 'u' and the derivative
with respect to 'v'. However, if the surface sense returned by OUTSUR is
false, the sign of the normal will be reversed.
The function works for any type of surface.
Except for B_surfaces and their offsets, which can be evaluated out of range,
if ENSUPA indicates that this surface is not periodic or infinite (in either
u or v), then the corresponding parameter must be in the range specified in
ENSUPA for this surface.
Where derivative discontinuities occur at patch boundaries, the derivatives
just after the discontinuity are returned.
There is a limit on the number of derivatives which may be requested.
In the case of foreign geometry surfaces (type TYSUFG), the maximum
number of derivatives that can be returned by this function is determined
by the surface's external evaluator. The evaluator should, at least, be
able to calculate up to second order derivatives.
The following table shows the derivatives that can be requested for other
surface types.
u derivs
| 0 | 1 | 2 | >2 |
--------------------------------------
0 | A | A | B | D |
--------------------------------------
v derivs 1 | A | A | C | D |
--------------------------------------
2 | B | C | E | D |
--------------------------------------
>2 | D | D | D | D |
--------------------------------------
A - All surface types.
B - All surface types except blend surfaces.
C - All surface types except blend and offset surfaces.
D - B-Surfaces only.
E - All surface types except blend surfaces.
ENPOPS can be called with nudrvs = 2 and nvdrvs = 2 for offset
surfaces, but only zeroth, first and second derivatives will be
calculated. The uncalculated third and fourth derivatives will be
returned in the derivative array as zero vectors.
The return argument 'p' is a vector array returning the point and possibly
derivatives. These are stored as follows:
The point on the surface is the first vector in 'p' (i.e. vector 0)
The i'th derivative ( i <= 'nudrvs' ) wrt u and
the j'th derivative ( j <= 'nvdrvs' ) wrt v is vector
( i + ( 'nudrvs'+1 ) * j ) of 'p'.
The return argument 'norm' contains the surface normal. The normal is only
returned if 'nreq' is true. A value is returned even at a singular point
of the surface, unlike ENPOGS. Note that a singular point has an ambiguous
parametrisation, and different parameter pairs may give different normals,
for the same point.
