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@q curves.web @>

@q * (0) Copyright and License.@>

@q This file is part of GNU 3DLDF, a package for three-dimensional drawing. @>
@q Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, @>
@q 2011, 2012, 2013 The Free Software Foundation @>

@q GNU 3DLDF is free software; you can redistribute it and/or modify @>
@q it under the terms of the GNU General Public License as published by @>
@q the Free Software Foundation; either version 3 of the License, or @>
@q (at your option) any later version. @>

@q GNU 3DLDF is distributed in the hope that it will be useful, @>
@q but WITHOUT ANY WARRANTY; without even the implied warranty of @>
@q MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the @>
@q GNU General Public License for more details. @>

@q You should have received a copy of the GNU General Public License @>
@q along with GNU 3DLDF; if not, write to the Free Software @>
@q Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA @>

@q GNU 3DLDF is a GNU package.  @>
@q It is part of the GNU Project of the  @>
@q Free Software Foundation @>
@q and is published under the GNU General Public License. @>
@q See the website http://www.gnu.org @>
@q for more information.   @>
@q GNU 3DLDF is available for downloading from @>
@q http://www.gnu.org/software/3dldf/LDF.html. @>

@q (``@@'' stands for a single at-sign in the following paragraph.) @>

@q Please send bug reports to Laurence.Finston@@gmx.de @>
@q The mailing list help-3dldf@@gnu.org is available for people to @>
@q ask other users for help.  @>
@q The mailing list info-3dldf@@gnu.org is for sending @>
@q announcements to users. To subscribe to these mailing lists, send an @>
@q email with ``subscribe <email-address>'' as the subject.  @>

@q The author can be contacted at: @>

@q Laurence D. Finston                 @> 
@q c/o Free Software Foundation, Inc.  @>
@q 51 Franklin St, Fifth Floor         @> 
@q Boston, MA  02110-1301              @>
@q USA                                 @>

@q Laurence.Finston@@gmx.de (@@ stands for a single ``at'' sign.)@>


@q * (0) Curves.@>
@** Curves\quad ({\tt curves\PERIOD web}).\hfil

\LOG
\initials{LDF 2003.11.12.}  
Removed the version control identifiers from the CWEB
files for the distribution of 3DLDF 1.1.  They're still used in my
development versions.

\initials{LDF 2003.12.10.}  
Put the version control identifiers back
into my release versions for 3DLDF 1.1.4.  I've already put some of
them back in, now I'm doing the rest of them.  However, the release
versions are now in their own RCS repository.
\ENDLOG

@f Curve Path

@q * Include files.@>
@ Include files.

\LOG
\initials{LDF 2004.05.09.}  Now including \filename{creatnew.h}. 

\initials{LDF 2004.05.21.}  Now including \filename{pens.web}.
\ENDLOG 

@<Include files@>=
#include "loader.h++"
#include "pspglb.h++"
#include "io.h++"
#include "creatnew.h++"
#include "pntrvctr.h++"
#include "primes.h++"
#include "complex.h++"
#include "matrices.h++"
#include "colors.h++"
#include "transfor.h++"
#include "pens.h++"
#include "dashptrn.h++"
#include "shapes.h++"
#include "pictures.h++"  
#include "points.h++"
#include "lines.h++"
#include "planes.h++"
#include "nurbs.h++"
#include "paths.h++"

@q * (0) Regular closed plane curve.@>
@** Regular closed plane curve.
\initials{LDF Undated.}

\LOG
\initials{LDF 2002.11.12.}  
Changed the name ``|Regular_Closed_Plane_Curve|'' to 
``|Reg_Cl_Plane_Curve|'', because the former caused too many
``Overfull boxes'' when running \cweave/.
\ENDLOG 

@q * (1) Reg_Cl_Plane_Curve class definition.@>
@* {\bf Reg\_Cl\_Plane\_Curve} class definition.
\initials{LDF Undated.}

A |Reg_Cl_Plane_Curve| is assumed to be closed, planar, convex, and
have at least 3  points. The functions that create and modify\newline  
|Reg_Cl_Plane_Curves|
must ensure that these assumptions are correct!
\initials{LDF Undated.}

|Reg_Cl_Plane_Curve| is intended to be used as a base
class.  No objects of type |Reg_Cl_Plane_Curve| should be defined, however,
it is not an abstract class, so it is possible to do so.
\initials{LDF 2002.11.05.}  

@f Reg_Cl_Plane_Curve Curve

@<Define |class Reg_Cl_Plane_Curve|@>=

class Reg_Cl_Plane_Curve : public Path
{
  protected:
    Point center;
    unsigned short number_of_points;
  public:
    @<Declare |Reg_Cl_Plane_Curve| functions@>@;
};

@q * (1) Reflection in a |Plane|.@> 
@ Reflection in a |Plane|.
\initials{LDF 2004.10.03.}
@^\cfunc{Reg\_Cl\_Plane\_Curve}{reflect\_in}@>

Please note that this function tries to allocate memory on the free 
store for the |Reg_Cl_Plane_Curve| pointed to by the pointer to
|Shape| which is its return value.  Therefore, programmers who use
this function must ensure that this memory is freed.
\initials{LDF 2004.10.03.}

If allocation fails, this function throws a |bad_alloc| exception.  
If the reflection of |*this| cannot be found in the |Plane|, 
this function returns 0.
\initials{LDF 2004.10.03.}

\LOG
\initials{LDF 2004.10.03.}
Added this function.

\initials{LDF 2004.10.12.}
Rewrote this function.
Following a system update, 
having |Shape*| as the return value no longer worked.
\ENDLOG

@<Declare |Reg_Cl_Plane_Curve| functions@>=
virtual 
int
reflect_in(const Plane& p, 
           void* v,
           const Scanner_Node scanner_node = 0) const;


@q ** (2) Definition.@>

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
int
Reg_Cl_Plane_Curve::reflect_in(const Plane& p,
                               void* v,
                               const Scanner_Node scanner_node) const


{

@q *** (3) Preliminaries.@> 

  bool DEBUG = false; /* |true|  */

  using namespace Scan_Parse;

  stringstream cerr_strm;

  bool error_stop_value   = true;
  bool warning_stop_value = true;
  string thread_name      = "";

  if (scanner_node)
     scanner_node->get_thread_name_and_stop_values(&thread_name,
                                                   &error_stop_value,
                                                   &warning_stop_value);


@q *** (3).@> 

  Reg_Cl_Plane_Curve* reg_cl_plane_curve_reflection = static_cast<Reg_Cl_Plane_Curve*>(v);  

@q *** (3) If |reg_cl_plane_curve_reflection == static_cast<Reg_Cl_Plane_Curve*>(0)|, @>
@q *** (3) try to allocate memory on the free store for it.                           @> 

@ If |reg_cl_plane_curve_reflection == static_cast<Reg_Cl_Plane_Curve*>(0)|, 
try to allocate memory on the free store for it.                            
\initials{LDF 2004.10.12.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

 if (reg_cl_plane_curve_reflection == static_cast<Reg_Cl_Plane_Curve*>(0))
 {
  try
     {
       reg_cl_plane_curve_reflection = create_new<Reg_Cl_Plane_Curve>(0, scanner_node);
     }

@q **** (4) Error handling:  |new Reg_Cl_Plane_Curve| failed.  Rethrow |bad_alloc|.@> 

@ Error handling:  |new Reg_Cl_Plane_Curve| failed.  Rethrow |bad_alloc|.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>=


  catch (bad_alloc)
     {

       cerr_strm << thread_name << "ERROR! In `Point::reflect_in()':" 
                 << endl
                 << "`create_new<Reg_Cl_Plane_Curve>()' failed. "
                 << "Rethrowing `bad_alloc'.";

       log_message(cerr_strm);
       cerr_message(cerr_strm, error_stop_value);
       cerr_strm.str("");

       throw;

       
     } /* |catch (bad_alloc)|  */

  
@q *** (3).@> 

  } /* |if (reg_cl_plane_curve_reflection == static_cast<Reg_Cl_Plane_Curve*>(0))|  */

@q *** (3) Call |Path::reflect_in()|.@> 

@ Call |Path::reflect_in()|.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

  Path path_reflection;

  int status;


  try
     {
       status = Path::reflect_in(p,
                            static_cast<void*>(&path_reflection),
                            scanner_node);  
     }

@q **** (4) Error handling:  |Path::reflect_in()| threw |bad_alloc|.@> 

@ Error handling:  |Path::reflect_in()| threw |bad_alloc|.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

  catch (bad_alloc)
     {
       cerr_strm << thread_name << "ERROR! In `Reg_Cl_Plane_Curve::reflect_in():'"
                 << endl 
                 << "`Path::reflect_in()' threw `bad_alloc'."
                 << endl << "Deleting `reg_cl_plane_curve_reflection' and "
                 << "rethrowing `bad_alloc'.";

       log_message(cerr_strm);
       cerr_message(cerr_strm, error_stop_value);
       cerr_strm.str("");

       delete reg_cl_plane_curve_reflection;

       throw;

     } /* |catch (bad_alloc)|  */

@q **** (4) Error handling:  |Path::reflect_in()| returned 1.@> 

@ Error handling:  |Path::reflect_in()| returned 1.
\initials{LDF 2004.10.12.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

  if (status == 1)
    {

      cerr_strm << thread_name << "ERROR! In `Reg_Cl_Plane_Curve::reflect_in():'"
                << endl 
                << "`Path::reflect_in()' failed and returned 1."
                << endl << "Deleting `reg_cl_plane_curve_reflection' "
                << "and exiting function with return value 1.";

      log_message(cerr_strm);
      cerr_message(cerr_strm, error_stop_value);
      cerr_strm.str("");
  
      delete reg_cl_plane_curve_reflection;

      return 1;

      
    }  /* |if (status == 1)|  */

@q **** (4) |Path::reflect_in()| succeeded.@> 

@ |Path::reflect_in()| succeeded.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

#if DEBUG_COMPILE
   if (DEBUG)
     {
        cerr_strm << thread_name << "In `Reg_Cl_Plane_Curve::reflect_in()':"
                  << endl << "`Path::reflect_in()' succeeded.";

        log_message(cerr_strm);
        cerr_message(cerr_strm);
        cerr_strm.str("");

     }
#endif /* |DEBUG_COMPILE|  */ 

   reg_cl_plane_curve_reflection->Path::operator=(path_reflection);

@q *** (3) Set other data members of |*reg_cl_plane_curve_reflection|.@> 

@ Set other data members of |*reg_cl_plane_curve_reflection|.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

  reg_cl_plane_curve_reflection->center  = center; 
  reg_cl_plane_curve_reflection->number_of_points  = number_of_points; 

@q *** (3) Exit function successfully with   @> 
@q *** (3) return value 0.@> 

@ Exit function successfully with return value 0.
\initials{LDF 2004.10.05.}

@<Define |Reg_Cl_Plane_Curve| functions@>= 

#if DEBUG_COMPILE
   if (DEBUG)
     {
        cerr_strm << thread_name << "In `Reg_Cl_Plane_Curve::reflect_in()':"
                  << endl << "Exiting function successfully with "
                  << "return value 0.";

        log_message(cerr_strm);
        cerr_message(cerr_strm);
        cerr_strm.str("");

     }
#endif /* |DEBUG_COMPILE|  */ 

  return 0;

} /* End of |Reg_Cl_Plane_Curve::reflect_in()| definition.  */





@q * Returning elements and information.@>
@* Returning elements and information.
\initials{LDF 2002.11.05.}  The |virtual| functions in this section
are meant to be overloaded by member
functions of types derived from |Reg_Cl_Plane_Curve|.

\LOG
\initials{LDF 2002.11.03.}  Removed
|Reg_Cl_Plane_Curve::is_planar()|.\newline   
A |Reg_Cl_Plane_Curve|
can be manipulated into a non-planar state, so it's safer to use the |Path|
version, which tests whether it's really planar or not.  
\ENDLOG 

@q ** Is quadratic.@>
@ Is quadratic.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{is\_quadratic}@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
inline
virtual 
bool
is_quadratic() const
{
  return false;
}

@q ** Is cubic.@>
@ Is cubic.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{is\_cubic}@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
inline
virtual 
bool
is_cubic() const
{
  return false;
}

@q ** Is quartic.@>
@ Is quartic.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{is\_quartic}@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
inline
virtual 
bool
is_quartic() const
{
  return false;
}

@q ** Get coefficients.@>
@ Get coefficients.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{get\_coefficients}@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
inline
virtual 
Real_Triple 
get_coefficients(real, real) const
{
  return Real_Triple(INVALID_REAL, INVALID_REAL, INVALID_REAL);
}

@q * Solve.@>
@* Solve.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{solve}@>
\initials{LDF 2002.11.05.}  This |virtual| function is meant to be overloaded by
member functions of types derived from |Reg_Cl_Plane_Curve|.
@<Declare |Reg_Cl_Plane_Curve| functions@>=
inline
virtual 
pair<real, real> 
solve(char, real) const
{
    return pair<real, real>(INVALID_REAL, INVALID_REAL);
}

@q * (1) Location of a point.@>
@* Location of a point.  
@^\cfunc{Reg\_Cl\_Plane\_Curve}{location}@>
|location()| returns a |signed short|
indicating the location of its |Point| argument with respect to the
|Reg_Cl_Plane_Curve|.   

\initials{LDF 2002.11.05.}  @:!! TO DO@> TO DO: 
Currently, the programmer must ensure that a
|Reg_Cl_Plane_Curve| is planar.  It might be worthwhile to check that it
really is by using |Path::get_normal()|, since some manipulations may
cause a |Reg_Cl_Plane_Curve| to become non-planar.  

\initials{LDF 2002.11.05.}  
The number of |Points| in a |Reg_Cl_Plane_Curve| must be a multiple of
4, and that the |Point| |number_of_points@t$/4$@>| 
must be at $90^\circ$ to |Point| 0.
Also, |ref_pt| can't be |Point| 0.

\initials{LDF 2003.07.16.}  |Reg_Cl_Plane_Curve| now has a data member named
|center|.  However, a\newline
|Reg_Cl_Plane_Curve| need not have a meaningful
center.  Usually, when an object of a class derived from
|Reg_Cl_Plane_Curve| calls this function, its |center| will
be passed as the |ref_pt| argument.  However, this need not be the
case. 

@:!! TO DO@> TO DO: 
Check whether it will work if |pt0.x < 0|.  
I think it should.

\initials{LDF 2003.06.14.}  !! CHECK.  Bug, when |Reg_Cl_Plane_Curve| is 
rotated about x and z-axes only.  

@q ** Return values.@>
The following values are returned if the |Point| is in the same plane
as |*this| and this function has worked properly:

\BRVS{-1}

\RV{-1}\relax  The |Point| lies outside the |Reg_Cl_Plane_Curve|.

\RV{0}\relax   The |Point| lies on the perimeter of the |Reg_Cl_Plane_Curve|.

\RV{1}\relax   The |Point| lies inside the perimeter of the |Reg_Cl_Plane_Curve|.
  
\ERVS

\noindent
These values are returned in cases where errors have occurred:

\BRVS{-5}\relax

\RV{-2}\relax  The |Point| is not in the same plane as the
|Reg_Cl_Plane_Curve|.  

\RV{-3}\relax  Something has gone terribly wrong.

\RV{-4}\relax  The normal to the |Reg_Cl_Plane_Curve| has 0 magnitude,
  i.e., the |Points| on the\newline
  |Reg_Cl_Plane_Curve| are colinear.

\RV{-5}\relax  An error occurred in putting the |Reg_Cl_Plane_Curve|
  in one of the major planes.

\RV{-6}\relax  The |Reg_Cl_Plane_Curve| is non-planar.
\ERVS

\LOG
\initials{LDF 2002.04.03.}  Added  and tested all cases.  Seems to work properly.  

\initials{LDF 2002.11.12.}  Added ``\.{\char`\\relax}'' after the arguments to
``\.{\char`\\RV}'' in the {\TeX} code above in order to suppress a
space at the beginning of the first line of the following indented
paragraph.  I couldn't figure out a way of suppressing the space
within the definition of \.{\char`\\RV} (which is currently 
``\.{\char`\\let}'' to \.{\char`\\ARG}).


\initials{LDF 2003.06.03.}  Changed the line where |Plane::get_distance()| is
called below.  It now returns a\newline
|Real_Short|, so ``|.first|'' has to
be added, in order to get the |real| value.

\initials{LDF 2003.06.13.}  Changed |pt0.epsilon()| to |Point::epsilon()|.

\initials{LDF 2003.06.14.}  Added error handling code for the case that
|get_plane()| fails.

\initials{LDF 2003.06.14.}  No longer taking absolute value of the |real| value
|r0| returned by |Plane::get_distance()|, since it will always be
positive, anyway.  Comment at place below, where I made this change. 

\initials{LDF 2003.07.01.}  Added argument |suppress_warnings|.


\initials{LDF 2003.07.16.}  Changed name of |center| argument to |ref_pt|,
because I've made |center| a data member of |Reg_Cl_Plane_Curve|.


\initials{LDF 2004.05.25.}  
Commented-out some drawing commands.  This was necessary, because
|current_picture| is no longer a global 
variable, and drawing requires a |Picture|.  

\initials{LDF 2004.06.08.}  Changed |origin| to |origin_pt|, because I've
removed the global variable |origin|.  I'm replacing it with a predefined
variable defined in |Scanner_Type::create()|.

\initials{LDF 2007.08.26.}
Added optional |Scanner_Node| argument with default $0$.
\ENDLOG 


@q ** (2) Declaration.@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
virtual
signed short
location(Point ref_pt, 
         Point pt0, 
         const bool suppress_warnings = false) const;
   
@q ** (2) Definition.@>
@
@<Define |Reg_Cl_Plane_Curve| functions@>=
signed short
Reg_Cl_Plane_Curve::location(Point ref_pt, Point pt0, const bool suppress_warnings) const
{

    bool DEBUG = false; /* |true| */

    if (DEBUG)
      {
        cerr << "Entering Reg_Cl_Plane_Curve::location()\n";
        ref_pt.show("ref_pt");
        pt0.show("pt0");
      }

    Point origin_pt(0, 0, 0);


    unsigned short orientation;
    const unsigned short X_Y = 0;
    const unsigned short X_Z = 1;
    const unsigned short Z_Y = 2;

    Plane pl(get_plane());
    
    if (pl == INVALID_PLANE) /* LDF 2003.06.14.  Added this error 
                                handling code.  */
      {
        cerr << "ERROR! In Reg_Cl_Plane_Curve::location():"
             <<  "The Reg_Cl_Plane_Curve is non-planar.\n"
             << "Returning -6\n\n";
        return -6;
      }

    real r0 = pl.get_distance(pt0).first;  

    if (r0 > Point::epsilon())      /* LDF 2003.06.14.  Changed.
                                       |r0| will always be positive, 
                                       so I now longer take its 
                                       absolute value.  */
      {
        if (!suppress_warnings)
          cerr << "WARNING! In Reg_Cl_Plane_Curve::location().\n"
               << "Point is not in plane of regular closed plane curve.\n"
               << "Returning -2.\n\n";
          return -2;
      }

    Reg_Cl_Plane_Curve copy(*this);

    if (ref_pt != origin_pt)
      pt0 *= ref_pt *= copy.shift(-ref_pt);  /* LDF 2002.11.05.
                                                Simplified.  */

    Point copy_normal = copy.get_normal();

    if (DEBUG)
      copy_normal.show("copy_normal");

    if (copy_normal.magnitude() == ZERO_REAL)
      {
          cerr << "ERROR! In Reg_Cl_Plane_Curve::location().\n"
            << "Normal has no magnitude. Returning -4\n\n";
              
          return -4;
      }
    
    else if (fabs(copy_normal.get_x()) < Point::epsilon()
             && fabs(copy_normal.get_y()) < Point::epsilon())
      {
          if (DEBUG)
            cerr << "Regular closed plane curve is already in x-y plane.\n";
          orientation = X_Y;
      }

    else if (fabs(copy_normal.get_x()) < Point::epsilon()
             && fabs(copy_normal.get_z()) < Point::epsilon())
      {
          if (DEBUG)
            cerr << "Regular closed plane curve is already in x-z plane.\n";
          orientation = X_Z;
      }
    else if (fabs(copy_normal.get_z()) < Point::epsilon()
             && fabs(copy_normal.get_y()) < Point::epsilon())
      {
          if (DEBUG)
            cerr << "Regular closed plane curve is already in z-y plane.\n";
          orientation = Z_Y;
      }
    else
      {
          if (DEBUG)
            cerr << "Putting regular closed plane curve into x-z plane.\n";
          Transform t1;
          t1.align_with_axis(ref_pt, copy.get_point(0), 'x');
          
          copy *= ref_pt *= pt0 *= t1;

          Point pt_c4(copy.get_point(number_of_points / 4));

          Transform t2;
          t2.align_with_axis(ref_pt,
                             pt_c4,
                             'z');

          copy *= ref_pt *= pt0 *= t2;
          orientation = X_Z;
      }
    if (DEBUG)
      {
          cerr << "orientation == " << orientation << endl;
#if 0 

/* Commented-out, because |current_picture| is no longer a global
  variable, and drawing requires a |Picture|.  
  \initials{LDF 2004.05.25.}  */@;

          copy.draw(Colors::blue);
          copy.show("copy");
          ref_pt.dotlabel("C");
          pt0.dotlabel("pt0");
          pt0.show("pt0");
#endif 
      }

    Transform t3;
    Point pt1 = copy.get_point(0);
    pt1 -= ref_pt;
    pt1.unit_vector(true);

    Point x_axis(1, 0, 0);
    Point z_axis(0, 0, 1);

    if (orientation == X_Y || orientation == X_Z)
      {
        if (pt1 != x_axis && pt1 != -x_axis)
          {
            t3.align_with_axis(ref_pt, pt1, 'x');
            copy *= ref_pt *= pt0 *= t3;
          }
      }
    else if (orientation == Z_Y)
      {
        if (pt1 != z_axis && pt1 != -z_axis)
          {
            t3.align_with_axis(ref_pt, pt1, 'z');
            copy *= t3;
            ref_pt *= t3;
            pt0 *= t3;
          }
      }

    Real_Pair rr;
    real pt0_v;  /* \initials{LDF 2002.11.05.}  Vertical.  */
    real pt0_h;  /* \initials{LDF 2002.11.05.}  Horizontal.  */
    
    if (orientation == X_Y)
      {
          pt0_h = pt0.get_x();
          pt0_v = pt0.get_y();
      }
    else if (orientation == X_Z)
      {
          pt0_h = pt0.get_x();
          pt0_v = pt0.get_z();
      }

    else if (orientation == Z_Y)
      {
          pt0_h = pt0.get_z();
          pt0_v = pt0.get_y();
      }

    else
      {
          cerr << "ERROR! In Reg_Cl_Plane_Curve::location().\n"
            << "orientation has invalid value: " << orientation
              << "\nReturning -5\n\n";
          return -5;
      }

    rr = solve('v', pt0_h);  /* \initials{LDF 2002.11.05.}  TO DO:  Explain.  */

    if (rr.first == INVALID_REAL && rr.second == INVALID_REAL)
      {
          if (DEBUG)
            {
              cerr << "Point is outside regular closed plane curve. "
                   << "Returning -1.\n";
              cerr << "Exiting Reg_Cl_Plane_Curve::location()\n";
            }
          return -1;
      }
    
    else if ((fabs(fabs(pt0_v) - fabs(rr.first)) < Point::epsilon())
             || (fabs(fabs(pt0_v) - fabs(rr.second)) < Point::epsilon()))
      {
          if (DEBUG)
            {
                cerr << "Point is on regular closed plane curve. "
                     << "Returning 0.\n"
                     << "Exiting Reg_Cl_Plane_Curve::location()\n";
            }
          return 0;
      }

    else if (fabs(pt0_v) < fabs(rr.first))
      {
          if (DEBUG)
            {
                cerr << "Point is inside regular closed plane curve. "
                     << "Returning 1.\n";
                cerr << "Exiting Reg_Cl_Plane_Curve::location()\n";
            }
          return 1;
      }
    else if (fabs(pt0_v) > fabs(rr.first)) /* This case should never
                                              occur, I believe.  
                                              \initials{LDF 2002.11.05.}  
                                              Why not??  */
      {
          if (DEBUG)
            {
                cerr << "Point is outside regular closed plane curve. "
                     << "Returning -1.\n"
                     << "Exiting Reg_Cl_Plane_Curve::location()\n";
            }
          return -1;
      }
    else
      {
          cerr << "ERROR! In Reg_Cl_Plane_Curve::location().\n"
            << "This can't happen! Returning -3.\n";

          if (DEBUG)
            cerr << "Exiting Reg_Cl_Plane_Curve::location()\n";
          return -3;
        }
  }

@q * Angle point.@>
@* Angle point.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{angle\_point}@>
\initials{LDF 2003.01.05.}  @:!! TO DO@> TO DO:  Find out why this function isn't
|const|! 
@<Declare |Reg_Cl_Plane_Curve| functions@>=
virtual
Point
angle_point(real angle);

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Point
Reg_Cl_Plane_Curve::angle_point(real angle)
{
    cerr << "ERROR! In Reg_Cl_Plane_Curve::angle_point().\n"
         << "This virtual function doesn't have a real definition for "
         << "ordinary Reg_Cl_Plane_Curves.\nReturning INVALID_POINT.\n\n";
    return INVALID_POINT;
}

@q * (1) Intersection points.@>
@* Intersection points.  
\initials{LDF 2002.11.05.}  

Intersection with a line.
|intersection_points()| returns a 
|Bool_Point_Pair|.  The |bool| in a |Bool_Point|
indicates whether the |Point| is on the
line segment in question.  
If one of the |bools| is |false|, but the |Point|
is not |== INVALID_POINT|, then the {\it line\/} (as opposed to the
segment) does intersect the
|Reg_Cl_Plane_Curve|, and the |Point| indicates
one of the intersection points.
So, |intersection_points()| can be
used whether you want to restrict the intersection points to ones that
are actually on a particular line segment or not.  
\initials{LDF 2002.11.05.}  


\TODO
@q { @>
@:TO DO}{{\bf TO DO}@>
@q } @> 
@q !! TO DO:@>  
\initials{LDF 2002.04.12.}  
In the specializations, I should check
whether the intersection points are on the curve in question.  I
should also write a version of this for |Lines|, where there's no test
for whether the intersection points are on the segment, since there's
no segment.
\ENDTODO

The versions of |intersection_points()| belonging to classes derived
from |Reg_Cl_Plane_Curve| will most likely call on the functions
described in this section, passing
|center| as the |ref_pt| argument.  However, this need not be the
case, and |Reg_Cl_Plane_Curves| need not have a meaningful |center|.
|ref_pt| in these functions merely refers to the |Point| which should be placed
at the origin by the transformation.  \initials{LDF 2003.07.16.}

@q ** (2) |Point| arguments.@>
@*1 {\bf Point} arguments.@>
@^\cfunc{Reg\_Cl\_Plane\_Curve}{intersection\_points}@>


\LOG
\initials{LDF 2003.06.20.}  
Rewrote this function.  The perpendicular and
non-parallel, non-coplanar cases are handled in exactly the same way.
In these cases, there can only be one intersection point.\newline
|Plane::intersection_point()| and |Reg_Cl_Plane_Curve::location()| are
now used to find it, if it exists.

\initials{LDF 2003.06.20.}  
The coplanar case was the one that was causing
difficulty.  The copy of |*this| is now always put into the x-z plane,
even if it is in one of the major planes, or in a plane parallel to
one of these.  The advantage of this, is that it simplifies the code.
The disadvantage is, that additional rotations reduce the accuracy of
the calculation of the intersection points.

\initials{LDF 2003.06.20.}  
|Transform::align_with_axis()| is no longer used for
putting the copy of |*this| and the line into the x-z plane.  It might
be possible to use it, but I used |Point::angle()| while debugging, in
order to see what was happening better.  It might be possible to
go back to using |Transform::align_with_axis|, but I don't see any
advantage to doing so.

\initials{LDF 2003.06.20.}  
I've tested this function for coplanar lines for
planes with various orientations.  I hope that it works properly for
all planes now!

\initials{LDF 2003.07.01.}  
Added |true| as |silent| argument to |unit_vector()|
when I call it on |cross|.  This prevents |unit_vector()| from issuing
a warning message, when |cross| has magnitude 0, which occurs when 
|surface_vector| and |pt_vector| are colinear.  Since this case is
handled correctly, the warning messages are unnecessary and distracting.

\initials{LDF 2003.07.01.}  
@:BUG FIX@> BUG FIX:  Made changes to the way
|on_segment| is used in the coplanar case.  The way it was before
handled certain cases wrong.

\initials{LDF 2003.07.04.}  
Removed unreachable statement at end of function: 
|return bpp|.  GCC didn't complain, but the DEC compiler issued a
warning. 

\initials{LDF 2003.07.16.}  
Changed name of |center| argument to |ref_pt|,
because I've made |center| a data member of |Reg_Cl_Plane_Curve|.

\initials{LDF 2004.05.25.}  
Commented-out some drawing commands.  This was necessary, because
|current_picture| is no longer a global 
variable, and drawing requires a |Picture|.  

\initials{LDF 2004.06.08.}  Changed |origin| to |origin_pt|, because I've
removed the global variable |origin|.  I'm replacing it with a predefined
variable defined in |Scanner_Type::create()|.
\ENDLOG


@q *** (3) Declaration.@>

@<Declare |Reg_Cl_Plane_Curve| functions@>=

virtual
Bool_Point_Pair
intersection_points(Point ref_pt, Point p0, Point p1) const;

@q *** (3) Definition.@>

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Bool_Point_Pair
Reg_Cl_Plane_Curve::intersection_points(Point ref_pt, Point pt0,
                                       Point pt1) const   
{

  bool DEBUG = false; // true

    if(DEBUG)
      cerr << " *** Entering Reg_Cl_Plane_Curve::"
           << "intersection_points()\n"; 
  Bool_Point_Pair bpp = INVALID_BOOL_POINT_PAIR;

  Point origin_pt(0, 0, 0);

  Plane pl = get_plane();

  if (DEBUG) 
    pl.normal.show("pl.normal");
  
  Point surface_vector = (get_point(0) - ref_pt);
  surface_vector.unit_vector(true);

  Point pt_vector(pt1 - pt0);
  pt_vector.unit_vector(true);

  Point cross = surface_vector.cross_product(pt_vector);
  cross.unit_vector(true, true);


    if (DEBUG)
      {
        surface_vector.show("surface_vector");
        pt_vector.show("pt_vector");
        cross.show("cross");
        pl.normal.show("pl.normal");
      }

  short distance = pl.get_distance(pt0).second;



@q **** (4) Degenerate cases, error handling.@>
@ Degenerate cases, error handling.
@<Define |Reg_Cl_Plane_Curve| functions@>=
  if (pt_vector == INVALID_POINT || 
      pl.normal == INVALID_POINT || 
      pt_vector == origin_pt || 
      pl.normal == origin_pt)
    {
        cerr << "ERROR! In Reg_Cl_Plane_Curve:intersection_points():\n"
             << "Something is wrong with the normals:\n";
        pt_vector.show("pt_vector:");
        pl.normal.show("pl.normal");
        cerr << "Returning INVALID_BOOL_POINT_PAIR.\n\n";
        if (DEBUG) 
          cerr << "Exiting Polygon::intersection_points().\n\n";
        return INVALID_BOOL_POINT_PAIR;
    }

@q **** (4) Parallel and coplanar cases.@>
@ Parallel and coplanar cases.
@<Define |Reg_Cl_Plane_Curve| functions@>=
else if (surface_vector == pt_vector || surface_vector == -pt_vector
         || cross == pl.normal || cross == -pl.normal)
  {
@q ***** (5) Coplanar case.@>
@ Coplanar case.

\LOG
\initials{LDF 2004.05.02.}  Changed |Point x_axis_pt(1)| to 
|Point x_axis_pt(1, 0, 0)| because this |Point| constructor now
requires three explicit |real| arguments.  This is because |CURR_Y| and 
|CURR_Z| are no longer |static| members of |class Point|, but rather 
internal quantities, stored in |Scanner_Type.id_map_node->id_map|.  This way, 
each |Scanner_Node| can its own |CURR_Y| and |CURR_Z|, and code using them 
will be reentrant.
\ENDLOG 
@<Define |Reg_Cl_Plane_Curve| functions@>=

  if (distance == ZERO_REAL)
    {
        if (DEBUG)
          cerr << "Line and Reg_Cl_Plane_Curve are coplanar.\n";
        
        Transform t0;
        
        Reg_Cl_Plane_Curve copy(*this);
        Point curve_0 = copy.get_point(0);

        if (DEBUG)
          {
            cerr << "After copying:" << endl;
            show("this:");
            copy.show("copy:");
            curve_0.show("curve_0");
          }

        t0 *= curve_0 *= pt0 *= pt1 *= copy.shift(-ref_pt);

        if (DEBUG)
          {
            cerr << "After shift:" << endl;
            copy.show("copy:");
            curve_0.show("curve_0");         
            pt0.show("pt0");
            pt1.show("pt1");
          }

        if (curve_0.get_x() < 0)
          {
           
            t0 *= curve_0 *= pt0 *= pt1 *= copy.rotate(0, 0, 180);
          }

        if (DEBUG)
          {
            cerr << "After rotating so curve_0 has positive x:" << endl;
            copy.show("copy:");
            curve_0.show("curve_0");         
            pt0.show("pt0");
            pt1.show("pt1");
          }

        Point trace_x_z_0 = curve_0;
        trace_x_z_0.shift(0, -(curve_0.get_y()));
        Point x_axis_pt(1, 0, 0);

        real ang = trace_x_z_0.angle(x_axis_pt);
        
        if (DEBUG)
          {
            cerr << "ang == " << ang << endl;
          }

        if (ang != ZERO_REAL)
          {
            if (curve_0.get_z() > 0)
              ang *= -1;
            t0 *= curve_0 *= pt0 *= pt1 *= copy.rotate(0, ang);
          }
        if (DEBUG)
          {
            cerr << "After rotating so the trace of curve_0 is on x-axis:" << endl;
            copy.show("copy:");
            curve_0.show("curve_0");         
            pt0.show("pt0");
            pt1.show("pt1");
          }

        ang = curve_0.angle(x_axis_pt);

        if (ang != ZERO_REAL)
          {
            if (curve_0.get_y() > 0)
              ang *= -1;
            t0 *= curve_0 *= pt0 *= pt1 *= copy.rotate(0, 0, ang);
          }

        if (DEBUG)
          {
            cerr << "After rotating so curve_0 is on x-axis:" << endl;
            copy.show("copy:");
            pt0.show("pt0");
            pt1.show("pt1");
          }

        Point curve_4 = copy.get_point(number_of_points / 4);
        Point z_axis_pt(0, 0, 1);
        ang = curve_4.angle(z_axis_pt);

        if (DEBUG)
          {
            curve_4.show("curve_4");
            cerr << "ang == " << ang << endl;
          }


        if (ang != ZERO_REAL)
          {
            if (curve_4.get_y() > 0)
              ang *= -1;
            t0 *= curve_4 *= pt0 *= pt1 *= copy.rotate(ang);
          }

        if (DEBUG)
          {
            cerr << "After rotating so curve_4 is on z-axis:" << endl;
            copy.show("copy:");
            curve_4.show("curve_4");         
            pt0.show("pt0");
            pt1.show("pt1");
          }

        if (DEBUG)
          {

#if 0 
/* Commented-out, because |current_picture| is no longer a global
  variable, and drawing requires a |Picture|.  
  \initials{LDF 2004.05.25.}  */@;

            copy.draw(Colors::blue);
            pt0.draw(pt1, Colors::black, "evenly");
            for (int i = 0; i < 16; i += 4)
              copy.get_point(i).dotlabel(i); 

            pt0.dotlabel("pt0"); 
            pt1.dotlabel("pt1");
            copy.get_center().dotlabel("copy center");

            draw_axes();

#endif 
          } /* |if (DEBUG)|  */@;


        real pt0_h = pt0.get_x();
        real pt0_v = pt0.get_z();

        real pt1_h = pt1.get_x();
        real pt1_v = pt1.get_z();  /* |pt1_v| isn't used.  
                                      Leaving it here, just in case.
                                      \initials{LDF 2003.08.27.}  */

        real Slope = pt1.slope(pt0, 'x', 'z');

        if (DEBUG)
          cerr << "Slope == " << Slope << endl;
        Real_Pair rr;

/* BEGIN */

@q ****** (6) Slope is 0 (line is horizontal).@>
@ Slope is 0 (line is horizontal).
@<Define |Reg_Cl_Plane_Curve| functions@>=


    if (Slope == ZERO_REAL) /* v is known, h is unknown. */
      {
        if (DEBUG)
          {
            cerr << "Slope == ZERO_REAL" << endl;
             
          }
        rr = solve('h', pt0_v);
        if(rr.first != INVALID_REAL)
          {
            bpp.first.pt.set(rr.first, 0, pt0_v);
          }
        else
          bpp.first.pt = INVALID_POINT;

        if(rr.second != INVALID_REAL)
          {
              bpp.second.pt.set(rr.second, 0, pt0_v);
          }
        else
          bpp.second.pt = INVALID_POINT;

        if (DEBUG)
          {
            bpp.first.pt.show("bpp.first.pt");
            bpp.second.pt.show("bpp.second.pt");
             
          }
      } /* End |Slope == ZERO_REAL|. */

@q ****** (6) Slope is undefined (line is vertical).@>
@ Slope is undefined (line is vertical).
@<Define |Reg_Cl_Plane_Curve| functions@>=
    else if (Slope == INVALID_REAL) 
      {
        if (DEBUG)
          {
            cerr << "Line is vertical.\n";
             
          }

        rr = solve('v', pt1_h);   

        if(rr.first != INVALID_REAL)
          {
            bpp.first.pt.set(pt0_h, 0, rr.first);
          }
        else
          bpp.first.pt = INVALID_POINT;
        

        if(rr.second != INVALID_REAL)
          {
              bpp.second.pt.set(pt0_h, 0, rr.second);
          }
        else
          bpp.second.pt = INVALID_POINT;

      } /* End |Slope == INVALID_REAL|. */

@q ****** (6) Slope $\in$ |real| is defined and $\neq0$.@>
@ Slope $\in$ |real| is defined and $\neq0$.
@<Define |Reg_Cl_Plane_Curve| functions@>=
    else
      {
        real v_intercept;
        v_intercept = pt0_v - (Slope * pt0_h);
        if (DEBUG)
          cerr << "v_intercept == " << v_intercept << endl;

        Real_Triple coeffs = get_coefficients(Slope, v_intercept);

        /* New h-values. */
        if (is_quadratic())
          {
            if (DEBUG)
              {
                cerr << "Solving quadratic.\n";
                 
              }
            rr = solve_quadratic(coeffs.first, coeffs.second,
                                 coeffs.third); 
          }
        else
          {
            cerr << "Not a quadratic. "
                 << "Haven't programmed this case yet.\n";
             
          }

          real v_coord;
        
        if(rr.first != INVALID_REAL)
          {
            v_coord = (Slope * rr.first) + v_intercept;
        
              bpp.first.pt.set(rr.first, 0, v_coord);
          }
          else
            bpp.first.pt = INVALID_POINT;
        

        if(rr.second != INVALID_REAL)
          {
            v_coord = (Slope * rr.second) + v_intercept;
            
              bpp.second.pt.set(rr.second, 0, v_coord);
          }
        else
          bpp.second.pt = INVALID_POINT;
      }
@q ***** (5) Common code for the ``coplanar'' case.@>
@ Common code for the ``coplanar'' case.
@<Define |Reg_Cl_Plane_Curve| functions@>=



Bool_Real on_segment;

if (bpp.first.pt == INVALID_POINT)
  {
    on_segment.first = false;
    on_segment.second = INVALID_REAL;
  }
 else 
   on_segment = bpp.first.pt.is_on_segment(pt0, pt1);

if (DEBUG)
  {
    cerr << "on_segment.first == "
      << on_segment.first << endl;
    cerr << "on_segment.second == "
      << on_segment.second << endl;
  }
     

if (on_segment.first == true)
  bpp.first.b = true;
else
  bpp.first.b = false;

Transform t_inverse;
t_inverse = t0.inverse();


if(bpp.first.pt != INVALID_POINT)
  {
          if (DEBUG)
            cerr << "Transforming bpp.first.pt\n";
          bpp.first.pt *= t_inverse;
        }
else
  {
    if (DEBUG)
      cerr << "bpp.first.pt is invalid\n";
  }
        

if (bpp.second.pt == INVALID_POINT)
  {
    on_segment.first = false;
    on_segment.second = INVALID_REAL;
  }
 else 
   on_segment = bpp.second.pt.is_on_segment(pt0, pt1);

if (on_segment.first == true)
  bpp.second.b = true;
else
  bpp.second.b = false;

if (DEBUG)
  {
    cerr << "on_segment.first == "
      << on_segment.first << endl;
    cerr << "on_segment.second == "
      << on_segment.second << endl;
  }
        
if(bpp.second.pt != INVALID_POINT)
  {
    if (DEBUG)
      cerr << "Transforming bpp.second.pt\n";
    bpp.second.pt *= t_inverse;
  }
else 
  {
    bpp.second.pt = INVALID_POINT;
    if (DEBUG)
      cerr << "bpp.second.pt is invalid\n";
  }
        
if(DEBUG)
  {
    cerr << "rr.first == " << rr.first << endl;
    cerr << "rr.second == " << rr.second << endl;
    cerr << "bpp.first.b == "
      << bpp.first.b << endl;
    cerr << "bpp.second.b == "
      << bpp.second.b << endl;
    bpp.first.pt.show("bpp.first.pt");
    bpp.second.pt.show("bpp.second.pt");
  }
return bpp;
} /* End of coplanar case.  */    

@q ***** (5) Parallel case.@>
@ Parallel case.
@<Define |Reg_Cl_Plane_Curve| functions@>=
else
  {
        cerr << "WARNING! In Reg_Cl_Plane_Curve::intersection_points():\n"
             << "Line and Reg_Cl_Plane_Curve are in parallel planes.\n"
             << "No intersections. Returning INVALID_BOOL_POINT_PAIR."
             << endl << endl;
      return INVALID_BOOL_POINT_PAIR;
  }
} /* End of parallel and coplanar cases.  */
  
@q **** (4) Perpendicular and non-coplanar cases.@>
@ Perpendicular and non-coplanar cases.
\initials{LDF 2003.06.13.}  These cases are handled in exactly the same way.
@<Define |Reg_Cl_Plane_Curve| functions@>=
  else 
    {
        if (pl.normal == pt_vector || pl.normal == -pt_vector)
          {
              if (DEBUG) 
                cerr << "The line is perpendicular to the "
                     << "Reg_Cl_Plane_Curve.\n"; 
          }

        else
          {
              if (DEBUG) 
                cerr << "The line and the Reg_Cl_Plane_Curve "
                     << "are non-coplanar.\n"; 
          }

        Bool_Point bp = pl.intersection_point(pt0, pt1);
        
        if (DEBUG)
          {
              bp.pt.show("bp.pt");
          }

        short s = location(ref_pt, bp.pt);
        
        if (DEBUG) 
          cerr << "location: s == " << s << endl;

        if (s > -1)
          {
            bpp.first.pt = bp.pt;
            bpp.first.b = bp.pt.is_on_segment(pt0, pt1).first;
        
            if (DEBUG)
              cerr << "On segment: == " << bpp.first.b << endl;
            return bpp;

          }
        else
          return INVALID_BOOL_POINT_PAIR;

      } /* End of ``Perpendicular and non-coplanar cases''.  */
}

@q ** (2) |Path| argument.@>
@*1 {\bf Path} arguments.@>
@^\cfunc{Reg\_Cl\_Plane\_Curve}{intersection\_points}@>
\initials{LDF 2003.06.20.}  

\LOG
\initials{LDF 2003.06.20.}  
Added this function.

\initials{LDF 2003.07.16.}  
Changed name of |center| argument to |ref_pt|,
because I've made |center| a data member of |Reg_Cl_Plane_Curve|.
\ENDLOG 

@<Declare |Reg_Cl_Plane_Curve| functions@>=
Bool_Point_Pair
intersection_points(const Point& ref_pt, const Path& p) const;

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Bool_Point_Pair
Reg_Cl_Plane_Curve::intersection_points(const Point& ref_pt, const Path& p) const   
{
  if (!p.is_linear())
    {
      cerr << "ERROR! In Reg_Cl_Plane_Curve::intersection_points():\n"
           << "Path argument p is non-linear. "
           << "Returning INVALID_BOOL_POINT_PAIR.\n\n";
      return INVALID_BOOL_POINT_PAIR;
    }
  return intersection_points(ref_pt, p.get_point(0), p.get_last_point());
}

@q * (1) |Reg_Cl_Plane_Curve| segments. @>
@* {\bf Reg\_Cl\_Plane\_Curve} segments.
The functions in this section require that the\newline 
|Reg_Cl_Plane_Curve|
have a meaningful |center|, in order to make it possible to rotate the
segments.  \initials{LDF 2003.07.16.}

\LOG
\initials{LDF 2003.07.16.}  
Added this section and its subsections, including the
declarations and definitions of |segment()|, |half()|, and
|quarter()|.  They were formerly members of |Circle|.
\ENDLOG 

@q ** (2) Segment.@>
@*1 Segment.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{segment}@>
\initials{LDF 2002.11.10.}  

|segment()| returns a subpath of the
|Reg_Cl_Plane_Curve| representing a segment of |*this|.  
\initials{LDF 2002.11.10.}  

\BARGS{|bool closed|}
\ARG{|int factor|}\relax
   Determines how large a segment of the |Reg_Cl_Plane_Curve| is returned.
   |factor| must be $>1$ and less than or equal to the number of points on the
   |Reg_Cl_Plane_Curve|.   

\ARG{|real angle|}\relax
   Optional, with 0 as the default.  If|angle| is $\neq 0$, a |Point| is
   found in the direction of the normal to the |Reg_Cl_Plane_Curve| 
   from the center of the
   |Reg_Cl_Plane_Curve|, and the segment is rotated around the center and this
   |Point|.  

\ARG{|bool closed|}\relax
  If |true|, the |Path| is made a ``{\bf cycle}'' and the ends of the
  segment are joined by concatenating the curved |Path| with the
  straight line segment from its last to its first |Point| using the
  connector |"&"|. 
\EARGS

\initials{LDF 2003.07.27.}  @:!! TO DO@> TO DO:  Make arguments |const|, if
possible.  |angle| can't be, though.  If |factor == number_of_points|,
return |*this|, cast to a |Path|, with warning.

\LOG  
\initials{LDF 2002.11.12.}  
Added ``\.{\char`\\relax}'' after the arguments to
``\.{\char`\\ARG}'' in the {\TeX} code above in order to suppress a
space at the beginning of the first line of the following indented
paragraph.  I couldn't figure out a way of suppressing the space
within the definition of \.{\char`\\ARG}.

\initials{LDF 2003.05.20.}  
Changed the way the last connector is set when
|closed == true|. 

\initials{LDF 2003.07.27.}  
Made |const|.

\initials{LDF 2003.08.20.}  
@:BUG FIX@> BUG FIX: 
Added |unsigned short subpath_size|.  Changed the way the subpath is
created, when |closed| is |true|.  Now concatenating the curved
subpath with the straight line segment from the last to the first
|Points| of the subpath using |"&"|.

\initials{LDF 2004.11.26.}
Rewrote this function.  Replaced the |int factor| argument with the
|unsigned int| arguments |start| and |end|.  Added the optional 
|Scanner_Node scanner_node| argument with default 0.  Made the debugging
output thread-safe.
\ENDLOG 

@q *** Declaration.@>
@<Declare |Reg_Cl_Plane_Curve| functions@>=
Path
segment(unsigned int start = 0,
        unsigned int end = INT_MAX,
        real angle = 0,
        bool closed = false,
        Scanner_Node scanner_node = 0) const;

@q *** (3) Definition.@> 

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Path
Reg_Cl_Plane_Curve::segment(unsigned int start,
                            unsigned int end,
                            real angle,
                            bool closed,
                            Scanner_Node scanner_node) const 
{

@q **** (4) Preliminaries.@>

#if DEBUG_COMPILE
   bool DEBUG = false; /* |true| */ @; 
#endif /* |DEBUG_COMPILE|  */@; 

   stringstream cerr_strm;

   bool error_stop_value   = true;
   bool warning_stop_value = true;
   string thread_name      = "";

   if (scanner_node)
      scanner_node->get_thread_name_and_stop_values(&thread_name,
                                                    &error_stop_value,
                                                    &warning_stop_value);

   using namespace Scan_Parse;

@q **** (4).@>

   Path p;


@q **** (4) |start >= points.size()|.@> 
@ |start >= points.size()|.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

    
    if (start >= points.size())
       {

@q ***** (5) |is_cycle()|.@> 

@ |is_cycle()|.  Normally, |Reg_Cl_Plane_Curves| will be cyclical, 
but it is possible to make them non-cyclical.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

          if (is_cycle())
              {

                 start %= points.size();               

              }  /* |if (is_cycle())|  */

@q ***** (5) |!is_cycle()|.@> 

@ |!is_cycle()|.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

 
          else /* |!is_cycle()|  */
             {
                

                 cerr_strm << thread_name 
                           << "WARNING!  In `Reg_Cl_Plane_Curve::segment():"
                           << start << "`start' >= `points.size()' and "
                           << "the `Reg_Cl_Plane_Curve' isn't cyclical."
                           << start << "Setting `start' to 0 "
                           << "and continuing.";

                log_message(cerr_strm);
                cerr_message(cerr_strm, warning_stop_value);
                cerr_strm.str();

                start = 0;

             }  /* |else| (|!is_cycle()|)  */             

@q ***** (5) .@> 

       }  /* |if (start >= points.size())|  */


@q **** (4) |end >= points.size()|.@> 
@ |end >= points.size()|.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=
    
    if (end >= points.size())
       {

@q ***** (5) |is_cycle()|.@> 

@ |is_cycle()|.  Normally, |Reg_Cl_Plane_Curves| will be cyclical, 
but it is possible to make them non-cyclical.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

          if (is_cycle())
              {

                 end %= points.size();               

              }  /* |if (is_cycle())|  */

@q ***** (5) |!is_cycle()|.@> 

@ |!is_cycle()|.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=

 
          else /* |!is_cycle()|  */
             {
                
                 end = points.size() - 1;

                 cerr_strm << thread_name 
                           << "WARNING!  In `Reg_Cl_Plane_Curve::segment():"
                           << endl << "`end' >= `points.size()' and "
                           << "the `Reg_Cl_Plane_Curve' isn't cyclical."
                           << endl << "`end' has been set to " 
                           << end
                           << " (`points.size()' - 1).  Continuing.";

                log_message(cerr_strm);
                cerr_message(cerr_strm, warning_stop_value);
                cerr_strm.str();

             }  /* |else| (|!is_cycle()|)  */             

@q ***** (5) .@> 

       }  /* |if (end >= points.size())|  */


#if DEBUG_COMPILE
   if (DEBUG)
     {
         cerr_strm << thread_name << "start == " << start 
                   << ", end == " << end << ".";

         log_message(cerr_strm);
         cerr_message(cerr_strm, true);
         cerr_strm.str("");
     }
#endif /* |DEBUG_COMPILE|  */@; 
 


@q **** (4) WARNING:  |start == end|.@> 

@ WARNING:  |start == end|.
Issue a warning and return a degenerate |Path| with a single |Point| 
and no connectors.
\initials{LDF 2004.11.25.}

@<Define |Reg_Cl_Plane_Curve| functions@>=
 
    if (start == end)
      {
     
                 cerr_strm << thread_name 
                           << "WARNING!  In `Reg_Cl_Plane_Curve::segment():"
                           << endl << "`start' == `end' == " << start 
                           << "." << endl 
                           << "Returning a degenerate `Path' with one "
                           << "`Point' and no connectors.";
                            
                 log_message(cerr_strm);
                 cerr_message(cerr_strm, warning_stop_value);
                 cerr_strm.str();

                 p += get_point(start); 
                
                 return p;

      } /* |if (start == end)|  */


@q **** (4) |start > end|.@> 

@ |start > end|.
Copy |*this|, reverse the copy, exchange the values of |start| and |end|, 
and extract a subpath from the copy using these values.
\initials{LDF 2004.11.25.}

\LOG
\initials{LDF 2009.09.15.}
Changed ``\.{&}'' to ``\.{..}''.
\ENDLOG 

@<Define |Reg_Cl_Plane_Curve| functions@>=

   Path q;
  
   const Path* ptr;


   if (start > end)
      {
         unsigned int temp = start;
         start = end;
         end = temp;
       
         q = *this;
         q.reverse(true, scanner_node);
         ptr = &q;

      }  /* |if (start > end)|  */

   else
     ptr = this;


@q **** (4).@> 


    for (int i = start; i <= end; ++i)
        {
           p += ptr->get_point(i);
           p += ptr->get_connector(i);
        }
 
    p.set_cycle(false);

    if (closed)
      {
        p += "..";
        p += p.get_last_point();
        p += "--";
        p += p.get_point(0);
        p += "..";
        p.set_cycle();
      }

    angle = fmod(angle, 360);

    if (angle != ZERO_REAL)
      {
          Point normal = ptr->get_normal();
          normal.shift(center);
          p.rotate(center, normal, angle);
      }
      
    return p;

} /* End of |Reg_Cl_Plane_Curve::segment()| definition.  */


@q ** (2) Half.@>
@*1 Half.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{half}@>
\initials{LDF Undated.} 

|half()| creates a curve using half of the points in |points|
starting from point 0.  If the argument |angle| is not zero, the
resulting |Path| is rotated by that amount about a line from |center|
in the direction of the normal to the |Reg_Cl_Plane_Curve|.
If the argument |closed| is |true|, then the segment is closed and can
be filled using |fill()| or |filldraw()|.
\initials{LDF Undated.} 


\LOG
\initials{LDF 2004.11.26.}
Changed the call to |Reg_Cl_Plane_Curve::segment()| to reflect
its new calling convention.

\initials{LDF 2004.11.26.}
Rewrote this function and made it virtual and non-inline.
Added the optional arguments |vector<Point*>::size_type start| 
and |Scanner_Node scanner_node|, both with default 0.

\initials{LDF 2007.07.09.}
Changed call to |Path::get_size| to a call to |Path::size|.  
Removed the former function, since it simply duplicated the latter one.
\ENDLOG 

@q *** (3) Declaration.@> 

@<Declare |Reg_Cl_Plane_Curve| functions@>=
virtual
Path
half(vector<Point*>::size_type start = 0,
     real angle = 0, 
     bool closed = true,
     Scanner_Node scanner_node = 0) const; 

@q *** (3) Definition.@> 

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Path
Reg_Cl_Plane_Curve::half(vector<Point*>::size_type start,
                         real angle, 
                         bool closed,
                         Scanner_Node scanner_node) const 
{

    vector<Point*>::size_type path_size = size();
    vector<Point*>::size_type half_size = path_size / 2;
    vector<Point*>::size_type end = start + half_size;
    
@q **** (4) @>   

    if (start < half_size)
      {
         return segment(start, end, angle, closed, scanner_node);
      }

@q **** (4) @>   

    else /* |start >= half_size|  */
     {
        Path p;

        vector<Point*>::size_type i = start;
        vector<Point*>::size_type j = i;

@q ***** (5) @>   

        for (; i <= end; ++i, ++j)
           {
              if (j == path_size)
                 j = 0;
                                
              p += get_point(j);
              if (i != end)
                 p += get_connector(j);

           } /* |for|  */

@q ***** (5) @>   
@
\LOG
\initials{LDF 2009.09.15.}
Changed ``\.{&}'' to ``\.{..}''.
\ENDLOG 

@<Define |Reg_Cl_Plane_Curve| functions@>=

        if (closed)
           {
              p += "..";
              p += p.get_last_point();
              p += "--";
              p += p.get_point(0);
              p += "..";
              p.set_cycle(true);

           } /* |if (closed)|  */
       

@q ***** (5) @>   
@
@<Define |Reg_Cl_Plane_Curve| functions@>=

        if (angle != ZERO_REAL)
           {
              Point normal = get_normal();
              p.rotate(center, normal, angle);

           }  /* |if (angle != ZERO_REAL)|  */

        return p;

     }   /* |else| (|start >= half_size|)  */

@q **** (4) @>   

} /* End of |Reg_Cl_Plane_Curve::half()| definition.  */

@q ** (2) Quarter.@>
@*1 Quarter.
@^\cfunc{Reg\_Cl\_Plane\_Curve}{quarter}@>

|quarter()| creates a curve using a quarter of the points in
|points| starting from point 0.  If the argument |angle| is not zero, the
resulting |Path| is rotated by that amount about a line from |center|
in the direction of the normal to the |Reg_Cl_Plane_Curve|.
If the argument |closed| is |true|, then the segment is closed and can
be filled using |fill()| or |filldraw()|.
\initials{LDF Undated.} 

\LOG
\initials{LDF 2004.11.26.}
Changed the call to |Reg_Cl_Plane_Curve::segment()| to reflect
its new calling convention.

\initials{LDF 2004.11.26.}
Rewrote this function and made it virtual and non-inline.
Added the optional arguments |vector<Point*>::size_type start| 
and |Scanner_Node scanner_node|, both with default 0.

\initials{LDF 2007.07.09.}
Changed call to |Path::get_size| to a call to |Path::size|.  
Removed the former function, since it simply duplicated the latter one.
\ENDLOG 

@q *** (3) Declaration.@> 

@<Declare |Reg_Cl_Plane_Curve| functions@>=

virtual
Path
quarter(vector<Point*>::size_type start = 0,
        real angle = 0, 
        bool closed = true,
        Scanner_Node scanner_node = 0) const; 



@q *** (3) Definition.@> 

@
@<Define |Reg_Cl_Plane_Curve| functions@>=
Path
Reg_Cl_Plane_Curve::quarter(vector<Point*>::size_type start,
                            real angle, 
                            bool closed,
                            Scanner_Node scanner_node) const 
{

    vector<Point*>::size_type path_size = size();
    vector<Point*>::size_type quarter_size = path_size / 4;
    vector<Point*>::size_type end = start + quarter_size;
    
@q **** (4) @>   

    if (start < quarter_size)
      {
         return segment(start, end, angle, closed, scanner_node);
      }

@q **** (4) @>   

    else /* |start >= quarter_size|  */
     {
        Path p;

        vector<Point*>::size_type i = start;
        vector<Point*>::size_type j = i;

@q ***** (5) @>   

        for (; i <= end; ++i, ++j)
           {
              if (j == path_size)
                 j = 0;
                                
              p += get_point(j);
              if (i != end)
                 p += get_connector(j);

           } /* |for|  */

@q ***** (5) @>   
@
\LOG
\initials{LDF 2009.09.15.}
Changed ``\.{&}'' to ``\.{..}''.
\ENDLOG 

@<Define |Reg_Cl_Plane_Curve| functions@>=

        if (closed)
           {
              p += "..";
              p += p.get_last_point();
              p += "--";
              p += p.get_point(0);
              p += "..";
              p.set_cycle(true);

           } /* |if (closed)|  */
       

@q ***** (5) @>   
@
@<Define |Reg_Cl_Plane_Curve| functions@>=

        if (angle != ZERO_REAL)
           {
              Point normal = get_normal();
              p.rotate(center, normal, angle);

           }  /* |if (angle != ZERO_REAL)|  */

        return p;

     }   /* |else| (|start >= quarter_size|)  */

@q **** (4) @>   

} /* End of |Reg_Cl_Plane_Curve::quarter()| definition.  */

@q * Putting Reg_Cl_Plane_Curve together.@>
@ Putting {\bf Reg\_Cl\_Plane\_Curve} together.

This is what's compiled.
@c
@<Include files@>@;
@<Define |class Reg_Cl_Plane_Curve|@>@;
@<Define |Reg_Cl_Plane_Curve| functions@>@;

@ This is what's written to \filename{curves.h}.
@(curves.h@>=
@<Define |class Reg_Cl_Plane_Curve|@>@;


@q Local Variables:          @>
@q mode:CWEB                 @>
@q eval:(display-time)       @>
@q abbrev-mode:t             @>
@q eval:(read-abbrev-file)   @>
@q indent-tabs-mode:nil      @>
@q eval:(outline-minor-mode) @>
@q End:                      @>