CFD Utilities Files

   BSPROFILE manipulates and/or displays a B-spline curve representing
an airfoil in wrap-around form.  It provides some of the functionality
of program PROFILE, which deals strictly with discretized (X,Y) airfoil
datasets but should still be of interest to a BSPROFILE user.

   A given B-spline curve may be discretized for plotting purposes, or
for compatibility with other applications.  The plot includes the
control polygon and curve evaluations corresponding to the knots.

   The airfoil is expected to consist of a single curve from the lower
trailing edge, round the leading edge (blunt or sharp), to the upper
trailing edge.  It need not be closed at the trailing edge.

   This version can also discretize an arbitrary curve, which is
distinguished from the wrap-around airfoil case by whether the first
and last control point Xs (almost) match or not.

   Results are in QPLOTable form.  Tailoring to some other plot package
may be required - possibly externally via a translator.  A modified
B-spline airfoil dataset may also be output.

   BSPROFILE also provides for converting a discretized curve into a
B-spline curve, either by standard interpolation (where the number of
control points is determined by the number of data points), or by the
standard linear least squares method (to employ a specified, smaller,
number of control points), or by a nonlinear least squares method which
improves the curve fit attainable with a given number of control points
by iteratively adjusting the knots as well.  This more elaborate method
was developed at Ames to keep the number of control points to a minimum
for design-by-optimization purposes.

   A curve fit may also be performed using a specified set of knots,
since multiple sections of a wing (say) with common knot vectors are
most convenient for a CAD system to convert to NURBS surface form.
Knot commonality also permits spanwise lofting of sections by applying
the lofting to the control points.

   BSPROFILE is built upon the DT_NURBS library of NURBS utilities,
which is the only such package known to be in the public domain and
written in FORTRAN 77.  A collection of higher-level utilities, mostly
airfoil-related, has been developed in the Applied Aerodynamics Division
at Ames as the AA_NURBS library.  Some of these are used by BSPROFILE.
Along with a modest subset of the DT_NURBS package, they have also been
employed in CFD-based design-by-optimization applications with mixed
results.  Whether use of B-spline control points as design variables
is preferable to using conventional perturbing shape functions remains
an open question.  Either way, BSPROFILE enables an aerodynamicist to
interface with a CAD system in what is nowadays the preferred manner.


Data format:
------------

   DT_NURBS employs a compact "C-array" format for 2-space B-spline
curves as follows:

   C(1) = 1 (# parametric variables);
   C(2) = 2 (for X and Y);
   C(3) = polynomial order k (e.g., 4 for cubics);
   C(4) = # control points, N;
   C(5) = pointer for efficient evaluations;
   C(6 : 5 + N + k) = knot vector,
   followed by the X coords. of N control pts.,
   followed by the Y coords. of N control pts.

   Initially, BSPROFILE reads and writes B-spline curves in this format,
which is far more readable and compact than an IGES representation and
may well be preferred for a design application.  Direct I/O of IGES
representations may become an option, but for now, program DTIGES serves
to convert a curve from DT_NURBS to IGES format and vice versa.

   The curve-fitting options expect (X,Y) coordinates forming a single
curve as follows:

   Title  ! Descriptive text
   N      ! # points
   X   Y  ! Coordinates
   :   :

   If a knot vector is specified for the fit, it is extracted from a
B-spline curve file in the DT_NURBS format.  A file of values of the
parametric variable U corresponding to the data points is also required
as input.  It should be in a single-column version of the (X,Y) data
format, as output from the original fitting process which produced the
knot vector being reused.


History:
--------

05/19/92  D.A.Saunders  Adapted from TESTAFGEOM.
05/29/92    "    "      Added area calculation.
06/01/92    "    "      Added option to normalize the chord.
09/19/92    "    "      Made the disretization variable, for possible
                        use of coordinates in a flow solver.
12/21/92    "    "      Provided for discretizing an arbitrary 2-space
                        curve (as needed for a camber line).
02/26/93    "    "      Provided for adjusting chord, leading edge,
                        and thickness of an airfoil curve.
04/05/93    "    "      Provided for adjusting the trailing edge with
                        a shear to compensate for a moved leading edge.
04/26/93    "    "      Provided for discretization according to
                        arc-length.  Introduced display of the leading
                        edge radius of curvature (also used to control
                        the discretization).
06/23/93    "    "      Radius of curvature is units-dependent: needed
                        chord in the empirical formula for unnormalized
                        airfoils.
01/28/94    "    "      Added knot insertion option (mainly to fix a
                        control point at an airfoil leading edge).
02/11/94    "    "      Provided for standard linear transformations.
July '97    "    "      Version 2.0: Installed B-spline curve fitting
                        options originally implemented in a version of
                        SMOOTH; provided for multiple grid distributions.
Apr 2004    "    "      Handle up to 256 points per curve; TOL = 0.01 was
                        too small to identify space shuttle wing sections
                        as airfoils - make it 0.02.
08/13/13    "    "      Resurrecting BSPROFILE on an Intel x86 64-bit
                        processor gave airfoil area trouble, though the
                        nonlinear B-spline curve fit of a 12% oblique wing
                        airfoil appears to work as earlier (degree 4, 16
                        control points, 10,000 iterations, 500 points per
                        surface evaluation of the fit).  The machine-
                        dependent constants are set for an IRIS 4D though,
                        so maybe that's the reason (no time to pursue it).