text: /*
  ** libproj -- library of cartographic projections
  **
  ** Copyright (c) 2003, 2006   Gerald I. Evenden
  */
  static const char
  LIBPROJ_ID[] = "$Id$";
  /*
  ** Permission is hereby granted, free of charge, to any person obtaining
  ** a copy of this software and associated documentation files (the
  ** "Software"), to deal in the Software without restriction, including
  ** without limitation the rights to use, copy, modify, merge, publish,
  ** distribute, sublicense, and/or sell copies of the Software, and to
  ** permit persons to whom the Software is furnished to do so, subject to
  ** the following conditions:
  **
  ** The above copyright notice and this permission notice shall be
  ** included in all copies or substantial portions of the Software.
  **
  ** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  ** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  ** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
  ** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
  ** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  ** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
  ** SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  */
  #define N_TOL 1e-6
  #define PROJ_LIB__
  #ifdef PROJ_HAVE_GSL
  #include <gsl/gsl_integration.h>
  #define GSL_WORK 1000
  #define PROJ_PARMS__ \
    double n[2]; \
    gsl_function func; \
    gsl_integration_workspace *work; \
    int mode;
  #include  <lib_proj.h>
    double
  mayr_kernel(double x, void * n) {
    return (pow(cos(x), *(double*)n));
  }
  #else
  #define PROJ_PARMS__ \
    int mode;
  #include  <lib_proj.h>
  #endif
  PROJ_HEAD(mayr, "Mayr (Tobler Meridian  Geometric Mean)") "\n\tPCyl., Sph., NoInv.";
  /* definition of segment bounds for <1e-7 error (unit sphere)  */
  #define SEG1 1.4
  #define SEG2 1.55
  #define SEG3 1.57
  #define BASE1 1.151132004484049
  #define BASE2 1.196140916241303
  #define BASE3 1.19812525384759
  #define HALFN 4
  /* Gauss Legendre weights/abscissa */
  double X[] = {
      0.96028985649753618,
      0.79666647741362673,
      0.52553240991632899,
      0.18343464249564981 };
  double W[] = {
      0.10122853629037638,
      0.22238103445337443,
      0.31370664587788744,
      0.36268378337836199 };
  /* Mayr kernel */
  #define func(v) sqrt(cos(v))
    static
  double gauss_legendre(double x0, double x1) {
    int i = 0;
    double s = 0., *x = X,  *w = W, xsize, xmean, arg;
  
    xmean = 0.5 * (x1 + x0);
    xsize = 0.5 * (x1 - x0);
    while ( i++ < HALFN ) {
      arg = xsize * *x++;
      s += *w++ * (func(xmean - arg) + func(xmean + arg));
    };
    return xsize * s;
  }
    static
  double integrate(double val) {
    double out;
  
    if (val <= SEG1)
      out = gauss_legendre(0., val);
    else if (val <= SEG2)
      out = BASE1 + gauss_legendre(SEG1, val);
    else if (val <= SEG3)
      out = BASE2 + gauss_legendre(SEG2, val);
    else
      out = BASE3 + gauss_legendre(SEG3, val);
    return out;
  }
  FORWARD(s_forward); /* spheroid */
    (void) P; /* avoid warning */
  
    xy.x = lp.lam * func(lp.phi);
    xy.y = integrate(fabs(lp.phi));
    if (lp.phi < 0.)
      xy.y = -xy.y;
    return (xy);
  }
  #ifdef PROJ_HAVE_GSL
  FORWARD(s_forwardg); /* numerical integration n <> 0.5 */
    double error;
    
    gsl_integration_qags(&P->func, 0., fabs(lp.phi), 1e-7, 1e-8, GSL_WORK,
      P->work, &xy.y, &error);
    xy.x = lp.lam * pow(cos(lp.phi), P->n[1]);
    if (lp.phi < 0.)
      xy.y = -xy.y;
    return (xy);
  }
  #endif
  FREEUP;
    if (P) {
  #if PROJ_HAVE_GSL
      if (P->mode) 
        gsl_integration_workspace_free(P->work);
  #endif
      free(P);
    }
  }
  ENTRY0(mayr)
    P->es = 0;
    if (proj_param(P->params, "tn").i) {
  #if PROJ_HAVE_GSL
      P->n[0] = proj_param(P->params, "dn").f;
      if ((P->n[0] < N_TOL) || (P->n[0] > 1.-N_TOL))
        E_ERROR(-40)
      P->fwd = s_forwardg;
      P->n[1] = 1. - P->n[0];
      P->func.function = &mayr_kernel;
      P->func.params = P->n;
      P->work = gsl_integration_workspace_alloc (GSL_WORK);
      P->mode = 1;
  #else
      E_ERROR(-47)
  #endif
    } else {
      P->mode = 0;
      P->fwd = s_forward;
    }
  ENDENTRY(P)
  /*
  ** $Log: proj_mayr.c,v $
  ** Revision 3.2  2006/01/19 01:52:59  gie
  ** correct some casting ^)*^&^
  **
  ** Revision 3.1  2006/01/11 01:38:18  gie
  ** Initial
  **
  */
  