interp2d.c

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/*!
 * \file interp2d.c
 *
 * \author
 * Lubos Mitas (original program and various modifications)
 *
 * \author
 * H. Mitasova,
 * I. Kosinovsky, D. Gerdes,
 * D. McCauley
 * (GRASS4.1 version of the program and GRASS4.2 modifications)
 *
 * \author
 * L. Mitas,
 * H. Mitasova,
 * I. Kosinovsky,
 * D.Gerdes,
 * D. McCauley
 * (1993, 1995)
 *
 * \author modified by McCauley in August 1995
 * \author modified by Mitasova in August 1995, Nov. 1996
 * \author
 * bug fixes(mask) and modification for variable smoothing
 * Mitasova (Jan 1997)
 *
 * \copyright
 * (C) 1993-1999 by Lubos Mitas and the GRASS Development Team
 *
 * \copyright
 * This program is free software under the
 * GNU General Public License (>=v2).
 * Read the file COPYING that comes with GRASS
 * for details.
 */


#include <stdio.h>
#include <math.h>
#include <unistd.h>

#include <grass/gis.h>
#include <grass/raster.h>
#include <grass/glocale.h>
#include <grass/bitmap.h>

#include <grass/interpf.h>


#define CEULER .57721566


/*!
 * Calculates grid values for a given segment
 *
 * Calculates grid for the given segment represented by data (contains
 * n_rows, n_cols, ew_res,ns_res, and all points inside + overlap) using
 * solutions of system of linear equations and interpolating functions
 * interp() and interpder(). Also calls secpar() to compute slope, aspect
 * and curvatures if required.
 * 
 * *ertot* can be also called *RMS deviation of the interpolated surface*
 */
int IL_grid_calc_2d(struct interp_params *params,
                    struct quaddata *data,  /*!< given segment */
                    struct BM *bitmask,  /*!< bitmask */
                    double zmin, double zmax,  /*!< min and max input z-values */
                    double *zminac, double *zmaxac,  /*!< min and max interp. z-values */
                    double *gmin, double *gmax,  /*!< min and max interp. slope val. */
                    double *c1min, double *c1max,  /*!< min and max interp. curv. val. */
                    double *c2min, double *c2max,  /*!< min and max interp. curv. val. */
                    double *ertot,  /*!< total interpolating func. error */
                    double *b,  /*!< solutions of linear equations */
                    off_t offset1,  /*!< offset for temp file writing */
                    double dnorm)
{

    /*
     * C C       INTERPOLATION BY FUNCTIONAL METHOD : TPS + complete regul.
     * c
     */
    double x_or = data->x_orig;
    double y_or = data->y_orig;
    int n_rows = data->n_rows;
    int n_cols = data->n_cols;
    int n_points = data->n_points;
    struct triple *points;
    static double *w2 = NULL;
    static double *w = NULL;
    int cond1, cond2;
    double r;
    double stepix, stepiy, xx, xg, yg, xx2;
    double rfsta2, /* cons, cons1, */ wm, dx, dy, dxx, dyy, dxy, h, bmgd1,
        bmgd2;
    double r2, gd1, gd2;        /* for interpder() */
    int n1, k, l, m;
    int ngstc, nszc, ngstr, nszr;
    double zz;
    int bmask = 1;
    static int first_time_z = 1;
    off_t offset, offset2;
    double fstar2 = params->fi * params->fi / 4.;
    double tfsta2, tfstad;
    double ns_res, ew_res;
    double rsin = 0, rcos = 0, teta, scale = 0; /*anisotropy parameters - added by JH 2002 */
    double xxr, yyr;

    if (params->theta) {
        teta = params->theta / M_R2D;   /* deg to rad */
        rsin = sin(teta);
        rcos = cos(teta);
    }
    if (params->scalex)
        scale = params->scalex;

    ns_res = (((struct quaddata *)(data))->ymax -
              ((struct quaddata *)(data))->y_orig) / data->n_rows;
    ew_res = (((struct quaddata *)(data))->xmax -
              ((struct quaddata *)(data))->x_orig) / data->n_cols;

    /*  tfsta2 = fstar2 * 2.; modified after removing normalization of z */
    tfsta2 = (fstar2 * 2.) / dnorm;
    tfstad = tfsta2 / dnorm;
    points = data->points;

    /*
     * normalization
     */
    stepix = ew_res / dnorm;
    stepiy = ns_res / dnorm;

    cond2 = ((params->adxx != NULL) || (params->adyy != NULL) ||
             (params->adxy != NULL));
    cond1 = ((params->adx != NULL) || (params->ady != NULL) || cond2);

    if (!w) {
        if (!(w = (double *)G_malloc(sizeof(double) * (params->KMAX2 + 9)))) {
            G_warning(_("Out of memory"));
            return -1;
        }
    }
    if (!w2) {
        if (!(w2 = (double *)G_malloc(sizeof(double) * (params->KMAX2 + 9)))) {
            G_warning(_("Out of memory"));
            return -1;
        }
    }
    n1 = n_points + 1;
    /*
     * C C         INTERPOLATION   *  MOST INNER LOOPS ! C
     */
    ngstc = (int)(x_or / ew_res + 0.5) + 1;
    nszc = ngstc + n_cols - 1;
    ngstr = (int)(y_or / ns_res + 0.5) + 1;
    nszr = ngstr + n_rows - 1;


    for (k = ngstr; k <= nszr; k++) {
        offset = offset1 * (k - 1);     /* rows offset */
        yg = (k - ngstr) * stepiy + stepiy / 2.;        /* fixed by J.H. in July 01 */
        for (m = 1; m <= n_points; m++) {
            wm = yg - points[m - 1].y;
            w[m] = wm;
            w2[m] = wm * wm;
        }
        for (l = ngstc; l <= nszc; l++) {
            if (bitmask != NULL)
                /*      if(params->maskmap != NULL)  PK Apr 03 MASK support */
                bmask = BM_get(bitmask, l - 1, k - 1);  /*fixed by helena jan 97 */
            /*    if(bmask==0 || bmask==-1) fprintf(stderr, "bmask=%d, at (%d,%d)\n", bmask, l, k); */
            xg = (l - ngstc) * stepix + stepix / 2.;    /*fixed by J.H. in July 01 */
            dx = 0.;
            dy = 0.;
            dxx = 0.;
            dyy = 0.;
            dxy = 0.;
            zz = 0.;
            if (bmask == 1) {   /* compute everything for area which is
                                 * not masked out */
                h = b[0];
                for (m = 1; m <= n_points; m++) {
                    xx = xg - points[m - 1].x;
                    if ((params->theta) && (params->scalex)) {
                        /* we run anisotropy */
                        xxr = xx * rcos + w[m] * rsin;
                        yyr = w[m] * rcos - xx * rsin;
                        xx2 = xxr * xxr;
                        w2[m] = yyr * yyr;
                        r2 = scale * xx2 + w2[m];
                        r = r2;
                        rfsta2 = scale * xx2 + w2[m];
                    }
                    else {
                        xx2 = xx * xx;
                        r2 = xx2 + w2[m];
                        r = r2;
                        rfsta2 = xx2 + w2[m];
                    }

                    h = h + b[m] * params->interp(r, params->fi);
                    if (cond1) {
                        if (!params->interpder(r, params->fi, &gd1, &gd2))
                            return -1;
                        bmgd1 = b[m] * gd1;
                        dx = dx + bmgd1 * xx;
                        dy = dy + bmgd1 * w[m];
                        if (cond2) {
                            bmgd2 = b[m] * gd2;
                            dxx = dxx + bmgd2 * xx2 + bmgd1;
                            dyy = dyy + bmgd2 * w2[m] + bmgd1;
                            dxy = dxy + bmgd2 * xx * w[m];
                        }
                    }
                }

                /*      zz = (h * dnorm) + zmin; replaced by helena jan. 97 due to removing norma
                   lization of z and zm in segmen2d.c */
                zz = h + zmin;
                if (first_time_z) {
                    first_time_z = 0;
                    *zmaxac = *zminac = zz;
                }
                *zmaxac = amax1(zz, *zmaxac);
                *zminac = amin1(zz, *zminac);
                if ((zz > zmax + 0.1 * (zmax - zmin))
                    || (zz < zmin - 0.1 * (zmax - zmin))) {
                    static int once = 0;

                    if (!once) {
                        once = 1;
                        G_warning(_("Overshoot - increase in tension suggested. "
                                    "Overshoot occurs at (%d,%d) cell. "
                                    "Z-value %f, zmin %f, zmax %f."),
                                  l, k, zz, zmin, zmax);
                    }
                }
                
                params->az[l] = (FCELL) zz;
                
                if (cond1) {
                    params->adx[l] = (FCELL) (-dx * tfsta2);
                    params->ady[l] = (FCELL) (-dy * tfsta2);
                    if (cond2) {
                        params->adxx[l] = (FCELL) (-dxx * tfstad);
                        params->adyy[l] = (FCELL) (-dyy * tfstad);
                        params->adxy[l] = (FCELL) (-dxy * tfstad);
                    }
                }

            }
            else {
                Rast_set_d_null_value(params->az + l, 1);
                /*          fprintf (stderr, "zz=%f, az[l]=%f, c=%d\n", zz, params->az[l], l); */

                if (cond1) {
                    Rast_set_d_null_value(params->adx + l, 1);
                    Rast_set_d_null_value(params->ady + l, 1);
                    if (cond2) {
                        Rast_set_d_null_value(params->adxx + l, 1);
                        Rast_set_d_null_value(params->adyy + l, 1);
                        Rast_set_d_null_value(params->adxy + l, 1);
                    }
                }
            }

        }
        if (cond1 && (params->deriv != 1)) {
            if (params->secpar(params, ngstc, nszc, k, bitmask,
                               gmin, gmax, c1min, c1max, c2min, c2max, cond1,
                               cond2) < 0)
                return -1;
        }

        offset2 = (offset + ngstc - 1) * sizeof(FCELL);
        if (params->wr_temp(params, ngstc, nszc, offset2) < 0)
            return -1;
    }
    return 1;
}