CRLFPS ( nbcs, bcs, nprops, props, pdata, bs, ifail )
=====================================================
Create B-surface by lofting
Receives:
KI_int_nitems *nbcs --- number of curves supplied
KI_tag_b_curve bcs[nbcs] --- array of B-curves
<KI_int_nitems> *nprops --- number of surface properties
KI_cod_papr props[nprops] --- array of surface properties
<KI_tag_list> pdata[nprops] --- array of tags of data lists
Returns:
KI_tag_b_surface *bs --- B-surface
KI_cod_error *ifail --- failure indicator
Specific errors:
KI_wrong_number_knots wrong number of knots in lofting knot vector
KI_bad_knots curve knot vectors are incompatible
bad lofting knot vector
KI_incompatible_curves curves cannot be matched
KI_bad_curves cannot loft coincident curves
KI_insufficient_curves insufficient curves to loft
KI_bad_index index for degenerate segment out of range
KI_bad_derivative derivative too large
twist vector too large
wrong number of coordinates in twist vector
KI_wrong_number_derivs wrong number of derivatives
KI_incompatible_props incorrect use of degenerate segment property
incorrect use of amalgamate property
incompatible degenerate conditions
incompatible clamping conditions
incompatible boundary conditions
KI_bad_parametric_prop inappropriate property
KI_bad_tag_in_list invalid null tag in pdata list
KI_bad_degen_vertices insufficient vertices for degenerate end curve
insufficient vertices for degenerate start curve
KI_bad_deriv_vertices wrong number of deriv vertices for clamped end
wrong number of deriv vertices for clamped start
Description:
This function creates a B-surface by lofting through a set of
B-curves.
Each curve shall lie along a constant v parameter line. The first curve
shall lie along the v = 0 parameter line and the last curve shall lie along
the v = 'nbcs'-1 parameter line. The parametrisation in the u direction
is derived from the curves being lofted.
Continuity of lofted surface:
The surface is always continuous up to second order in the loft direction.
If the lofted curves were splined or created as B-splines and they all
share the same knot vector, then a surface is produced which is continuous
in the curve direction to the same order as the definition curves.
Otherwise the surface is, in general, only position continuous in the
curve direction.
Dimension of surface:
The surface will be rational if one or more of the B-curves is
rational, otherwise it is non-rational.
B-curves to loft 'nbcs', 'bcs':
. If the surface is to be periodic in the loft direction (see below), at
least three curves ('nbcs' >= 3) must be given.
. If the surface is to be non-periodic in the loft direction (see below), at
least two curves ('nbcs' >= 2), or one curve and a degenerate start or end
(see below) must be given.
. The curves must be in order in the list.
. The curves are unchanged by the operation.
. The curves must have the same number of segments, unless either the
amalgamate option (see below) is used or the number of segments are
equated by adding degenerate segments (see below).
. Consecutive curves must not be coincident.
Surface properties 'nprops', 'props', 'pdata':
There are several controls that may be applied to the lofting operation.
For example, the surface may be periodic in the loft direction; a knot
vector may be supplied, or the surface may degenerate to a point. Each
action has a default, and each default can be overridden by giving a token
in the 'props' array. '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.
In explaining the various controls that may be applied to the lofting
operation the following notation is used :
o bottom left - on the surface at the start of the first curve
o bottom right - on the surface at the end of the first curve
o top left - on the surface at the start of the last curve
o top right - on the surface at the end of the last curve
token | meaning | data
---------------------------------------------------------------------
| |
PAPRPE | surface is periodic in the | none
| loft direction |
| |
PAPRNS | no curvature across start curve | none
| i.e. natural boundary condition |
| |
PAPRNE | no curvature across end curve | none
| i.e. natural boundary condition |
| |
PAPRCS | derivatives supplied | vector at each
| across start curve | spline point
| i.e. clamped boundary condition |
| |
PAPRCE | derivatives supplied | vector at each
| across end curve | spline point
| i.e. clamped boundary condition |
| |
PAPRSD | surface clamped with derivative | b-spline vertices
| curve at start | of derivative curve
| |
PAPRED | surface clamped with derivative | b-spline vertices
| curve at end | of derivative curve
| |
PAPRBL | bottom left twist vector supplied | twist vector
| |
PAPRBR | bottom right twist vector supplied| twist vector
| |
PAPRTL | top left twist vector supplied | twist vector
| |
PAPRTR | top right twist vector supplied | twist vector
| |
PAPRDS | surface is degenerate | degenerate point
| before start curve |
| |
PAPRDE | surface is degenerate | degenerate point
| after end curve |
| |
PAPRSW | degenerate curve supplied | b-spline vertices
| before start curve | of degenerate curve
| |
PAPREW | degenerate curve supplied | b-spline vertices
| after end curve | of degenerate curve
| |
PAPRKT | knot vector supplied | knot vector
| |
PAPRAM | amalgamate option | none
| |
PAPRIS | insert degenerate segment in | segment position
| start curve |
| | segment position
PAPRIE | insert degenerate segment in end |
| curve |
| |
PAPRCU | force cubic lofting | none
| |
Boundary conditions PAPRPE, PAPRNS, PAPRNE, PAPRCS, PAPRCE:
There are three boundary conditions available to control the lofting:
natural, clamped and periodic. Natural and clamped conditions refer to
either the start or end of the lofted surface, whereas the periodic
boundary condition refers to both.
. Natural boundary conditions imply that the surface has no curvature in the
loft direction, across the start or end curve as appropriate. Natural
boundary conditions are the default.
. Clamped boundary conditions allow the user to specify derivatives across
the start and end curves. There are two methods of supplying these
derivatives. Options PAPRCS and PAPRCE may be used to clamp the surface
with a list of derivative vectors. Similarly, options PAPRSD and PAPRED
may be used to clamp the surface using a derivative b-spline curve.
. If derivative vectors are used then they must be supplied at every
spline point of the corresponding curve (a spline point is a point
between adjacent segments of the curve, or the start or end of the
curve). The derivative vectors must be stored in a real list of length
(3 * 'nsp'), where nsp is the number of spline points on each curve.
The derivatives should be supplied with respect to a parameter which
varies from 0 to 1 between the first or last two curves (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 surface to loop or kink.
. When a derivative b-spline is used to clamp an end of the surface it is
only necessary to supply the control vertices. This is because the knot
vector of the derivative curve will be the same as the knot vector of
the corresponding start or end curve. The vertices should be supplied in
a real list of length :-
('dim' * 'ncrtl')
where,
dim = dimension of vertices on corresponding start or end curve
nctrl = number of vertices on corresponding start or end curve
A derivative b-spline provides a more complete definition of the
start/end derivatives particularly when the curves to be lofted are
either rational or contain multiple knots.
If clamped boundary conditions are used with the insert degenerate segment
option PAPRIS or PAPRIE then it should be noted that for every extra
segment added the end curve will have one extra spline point and one extra
control vertex. This means that if the end is clamped with derivative
vectors one extra vector must be supplied for every segment added.
Similarly if the surface is clamped with a derivative curve one extra
control vertex is required for every segment added.
. Periodic boundary conditions imply that the surface is closed in the loft
direction, so that the surface will return to the first curve in the array
after the final one has been lofted. The surface will meet itself with
continuity of tangent and curvature. If periodic boundary conditions are
used, then at least three curves must be supplied ('nbcs' >= 3). Periodic
boundary conditions cannot be used if either the first or last curve is
degenerate.
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 cross boundary derivatives in the direction of
the curves. The twist vectors may be supplied at any of the four corners,
but only when clamped boundary conditions have been supplied across the
corresponding boundary. Each one should be supplied in a real list of
length 3. If the twist vectors are supplied when they are not required
then they are ignored. If the twist vectors are not supplied then a
suitable default value is used.
Degenerate surface PAPRDS, PAPRDE, PAPRSW, PAPREW:
The lofted surface may degenerate to a point at either the start or the
end of the loft. This degeneracy may be supplied either as a single point
using PAPRDS and PAPRED or as a degenerate b-spline curve using PAPRSW and
PAPREW. A degenerate b-spline curve will provide greater control when
lofting curves that are rational.
. If the degeneracy is supplied as a point then the degenerate point must
be given in a real list of length 3.
. When a degenerate b-spline curve is used to define the degeneracy it is
only necessary to supply the control vertices. This is because the knot
vector of the degenerate curve will be the same as the knot vector of
the corresponding start or end curve. The vertices should be supplied in
a real list of length :-
('dim' * 'ncrtl')
where,
dim = dimension of vertices on corresponding start or end curve
nctrl = number of vertices on corresponding start or end curve
Periodic end conditions cannot be used if either end of the lofted
surface is degenerate, but it is possible to use clamped or natural end
conditions. The insert degenerate segment options PAPRIS and PAPRIE cannot
be used if the corresponding end of the surface is degenerate.
Knot vector PAPRKT:
If a knot vector is supplied then it must be given in a real list, and
must satisfy the following conditions:
. The knot values must form an increasing sequence; repeated knots are
not permitted.
. For non-periodic lofting there must be 'nbcs' knot values.
. For periodic lofting there must be ('nbcs'+1) knot values.
If the knot vector is not supplied then an averaged accumulated chord
length parametrisation is used.
Amalgamation of knot vectors PAPRAM:
An amalgamate property may be supplied for the surface, which will
amalgamate the various knot vectors for the curves, and produce a surface
which is continuous to the same order as the definition curves. However,
this may produce a surface with a large number of patches, and should
only be used on a small number of curves. The amalgamate option cannot
be used in conjunction with inserted degenerate segments.
Insertion of degenerate segments PAPRIS, PAPRIE:
If the first curve has fewer segments than the other curves PAPRIS may be
used add the required number of segments to the first curve. Similarly
PAPRIE may be used to add segments to the last curve. The segments added
using these properties are degenerate, that is they contain the order
of the curve coincident control points. Each degenerate segment added will
cause the lofting process to make a patch with a corresponding degenerate
boundary. Any number of degenerate segments may be added, by supplying the
appropriate token more than once. An integer list containing one value
must be supplied with each token; this specifies the segment preceding the
required degenerate segment. If more than one degenerate segments are
added they should be supplied in ascending order of segment number.
Previously inserted degenerate segments affect the segment number of
subsequent ones.
Degree of lofted surface PAPRCU:
In general, the surface will be cubic in the loft direction. However, if
only two non-rational curves are given and the boundary conditions are
natural, then a ruled surface which is linear in the loft direction will be
produced. The user may force the surface to be cubic in the loft direction
by giving the PAPRCU property.
