CRSPPC ( npts, pts, nprops, props, pdata, bc, ifail )
=====================================================
Create B-curve by splining
Receives:
KI_int_nitems *npts --- number of points supplied
KI_vec_position pts[npts] --- array of points to spline
<KI_int_nitems> *nprops --- number of curve properties
KI_cod_papr props[nprops] --- array of curve properties
<KI_tag_list> pdata[nprops] --- array of tags of data lists
Returns:
KI_tag_b_curve *bc --- B-curve
KI_cod_error *ifail --- failure indicator
Specific errors:
KI_wrong_number_knots wrong number of knots
KI_repeated_knots repeated knots
KI_bad_knots bad parameterisation
KI_bad_derivative derivative too big
not enough coordinates in derivative
KI_bad_position a spline point lies outside modeller size box
KI_coincident_points repeated spline points
KI_insufficient_points not enough spline points
KI_incompatible_props periodic end condition with coincident end points
incompatible end conditions
KI_bad_parametric_prop inappropriate property
KI_bad_tag_in_list invalid null tag in pdata list
Description:
This function creates a B-curve by splining through a set of points.
The curve will be continuous in slope and curvature. It may be periodic, in
which case the end meets the start with slope and curvature continuity.
Number of points to spline 'npts':
. For non-periodic curves the minimum number of points is 2.
. For periodic curves the minimum number of points is 3.
Points to spline 'pts':
. Consecutive points should not coincide.
. To make a closed non-periodic curve the start point must be repeated at
the end.
. If the curve is periodic the start and end points should not coincide.
Curve properties 'nprops', 'props', 'pdata'
There are several controls that may be applied to the splining operation.
For example, the curve may be periodic or a knot vector may be supplied.
Each action has a default, and each default can be overridden by giving a
token in the 'props' arrray. 'nprops' is the number of tokens that have
been supplied in 'props'.
A particular action may require additional data; if so, this must be
supplied in a list. The tag of the list must be entered in the array
'pdata', in the position corresponding to the token in 'props'. If the
action does not require additional data, then the null tag should be
entered in the appropriate position in 'pdata'.
Property tokens:
The 'props' array contains 'nprops' tokens from the sequence PAPR00. The
table shows which tokens may be used, and the data associated with them.
There are some pairs (or sets) of tokens which are alternatives; if both are
supplied they may be contradictory, and in this case the last one to be
supplied is the one which is used.
There are also cases in which the presence of a token implies a particular
structure, and another implies a different structure. Use of both tokens is
inconsistent, and raises an error.
token | meaning | real data
---------------------------------------------------------------------
| |
PAPRPE | curve is periodic | none
| |
PAPRNS | no curvature at start of curve | none
| i.e. natural end condition |
| |
PAPRNE | no curvature at end of curve | none
| i.e. natural end condition |
| |
PAPRCS | derivative supplied at start | derivative vector
| i.e. clamped end condition |
| |
PAPRCE | derivative supplied at end | derivative vector
| i.e. clamped end condition |
| |
PAPRKT | knot vector supplied | knot vector
| |
PAPRCU | force cubic curve | none
| |
End conditions PAPRPE, PAPRNS, PAPRNE, PAPRCS, PAPRCE:
There are three end conditions available to control the splining: natural,
clamped and periodic. Natural and clamped conditions refer to either the
start or end of the splined curve, whereas the periodic end condition refers
to both.
. Natural end conditions imply that the curve has no curvature at either
the start or end of the curve. Natural end conditions are the default.
. Clamped end conditions allow the user to specify derivatives at either the
start or the end of the curve, or both. Each derivative is supplied in a
real list of length three.
The derivatives should be supplied with respect to a parameter which varies
from 0 to 1 between the first or last two points (as appropriate). In other
words, the derivatives should have dimensions of length. The magnitude is
significant, and supplying vectors which are too large may cause the
curve to loop or kink.
. Periodic end conditions imply that the curve is closed, so that the curve
will return to the start point after the final point has been splined. The
curve will meet itself with continuity of tangent and curvature. If periodic
end conditions are used, then at least three points must be supplied
('npts' >= 3).
Knot vector PAPRKT:
If a knot vector is supplied then it must satisfy the following conditions:
. The knot values must form an increasing sequence; repeated knots are
not permitted.
. For non-periodic splining there must be 'npts' knot values.
. For periodic splining there must be ('npts'+1) knot values.
If the knot vector is not supplied then an accumulated chord length
parameterisation is used.
Curve degree PAPRCU:
In general, the curve will be cubic. However, if only two points are given
and the end conditions are natural, then a straight line (degree 1) will be
produced by default. This default can be overridden by supplying the token
PAPRCU, which forces the curve to be cubic.
