/***********************************************************************

   crs3d.c

   written by: Markus Metz

   based on crs.c - Center for Remote Sensing rectification routines

************************************************************************/

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>

#include <grass/gis.h>
#include <grass/imagery.h>

#include "crs.h"

/* STRUCTURE FOR USE INTERNALLY WITH THESE FUNCTIONS.  THESE FUNCTIONS EXPECT
   SQUARE MATRICES SO ONLY ONE VARIABLE IS GIVEN (N) FOR THE MATRIX SIZE */

struct MATRIX {
    int n; /* SIZE OF THIS MATRIX (N x N) */
    double *v;
};

/* CALCULATE OFFSET INTO ARRAY BASED ON R/C */

#define M(row, col) m->v[(((row)-1) * (m->n)) + (col)-1]

#define MSUCCESS    1  /* SUCCESS */
#define MNPTERR     0  /* NOT ENOUGH POINTS */
#define MUNSOLVABLE -1 /* NOT SOLVABLE */
#define MMEMERR     -2 /* NOT ENOUGH MEMORY */
#define MPARMERR    -3 /* PARAMETER ERROR */
#define MINTERR     -4 /* INTERNAL ERROR */

/***********************************************************************

  FUNCTION PROTOTYPES FOR STATIC (INTERNAL) FUNCTIONS

************************************************************************/

static int calccoef(struct Control_Points_3D *, double *, double *, double *,
                    int);
static int calcls(struct Control_Points_3D *, struct MATRIX *, double *,
                  double *, double *, double *, double *, double *);
static int exactdet(struct Control_Points_3D *, struct MATRIX *, double *,
                    double *, double *, double *, double *, double *);
static int solvemat(struct MATRIX *, double *, double *, double *, double *,
                    double *, double *);
static double term(int, double, double, double);

/***********************************************************************

  TRANSFORM A SINGLE COORDINATE PAIR.

************************************************************************/

int CRS_georef_3d(
    double e1,  /* EASTING TO BE TRANSFORMED */
    double n1,  /* NORTHING TO BE TRANSFORMED */
    double z1,  /* HEIGHT TO BE TRANSFORMED */
    double *e,  /* EASTING, TRANSFORMED */
    double *n,  /* NORTHING, TRANSFORMED */
    double *z,  /* HEIGHT, TRANSFORMED */
    double E[], /* EASTING COEFFICIENTS */
    double N[], /* NORTHING COEFFICIENTS */
    double Z[], /* HEIGHT COEFFICIENTS */
    int order   /* ORDER OF TRANSFORMATION TO BE PERFORMED, MUST MATCH THE
                   ORDER USED TO CALCULATE THE COEFFICIENTS */
)
{
    double e2, n2, z2, en, ez, nz, e3, n3, z3, e2n, e2z, en2, ez2, n2z, nz2,
        enz;

    switch (order) {
    case 1:
        *e = E[0] + E[1] * e1 + E[2] * n1 + E[3] * z1;
        *n = N[0] + N[1] * e1 + N[2] * n1 + N[3] * z1;
        *z = Z[0] + Z[1] * e1 + Z[2] * n1 + Z[3] * z1;
        break;

    case 2:
        e2 = e1 * e1;
        en = e1 * n1;
        ez = e1 * z1;
        n2 = n1 * n1;
        nz = n1 * z1;
        z2 = z1 * z1;

        *e = E[0] + E[1] * e1 + E[2] * n1 + E[3] * z1 + E[4] * e2 + E[5] * en +
             E[6] * ez + E[7] * n2 + E[8] * nz + E[9] * z2;
        *n = N[0] + N[1] * e1 + N[2] * n1 + N[3] * z1 + N[4] * e2 + N[5] * en +
             N[6] * ez + N[7] * n2 + N[8] * nz + N[9] * z2;
        *z = Z[0] + Z[1] * e1 + Z[2] * n1 + Z[3] * z1 + Z[4] * e2 + Z[5] * en +
             Z[6] * ez + Z[7] * n2 + Z[8] * nz + Z[9] * z2;
        break;

    case 3:
        e2 = e1 * e1;
        en = e1 * n1;
        ez = e1 * z1;
        n2 = n1 * n1;
        nz = n1 * z1;
        z2 = z1 * z1;

        e3 = e1 * e2;
        e2n = e2 * n1;
        e2z = e2 * z1;
        en2 = e1 * n2;
        enz = e1 * n1 * z1;
        ez2 = e1 * z2;
        n3 = n1 * n2;
        n2z = n2 * z1;
        nz2 = n1 * z2;
        z3 = z1 * z2;

        *e = E[0] + E[1] * e1 + E[2] * n1 + E[3] * z1 + E[4] * e2 + E[5] * en +
             E[6] * ez + E[7] * n2 + E[8] * nz + E[9] * z2 + E[10] * e3 +
             E[11] * e2n + E[12] * e2z + E[13] * en2 + E[14] * enz +
             E[15] * ez2 + E[16] * n3 + E[17] * n2z + E[18] * nz2 + E[19] * z3;
        *n = N[0] + N[1] * e1 + N[2] * n1 + N[3] * z1 + N[4] * e2 + N[5] * en +
             N[6] * ez + N[7] * n2 + N[8] * nz + N[9] * z2 + N[10] * e3 +
             N[11] * e2n + N[12] * e2z + N[13] * en2 + N[14] * enz +
             N[15] * ez2 + N[16] * n3 + N[17] * n2z + N[18] * nz2 + N[19] * z3;
        *z = Z[0] + Z[1] * e1 + Z[2] * n1 + Z[3] * z1 + Z[4] * e2 + Z[5] * en +
             Z[6] * ez + Z[7] * n2 + Z[8] * nz + Z[9] * z2 + Z[10] * e3 +
             Z[11] * e2n + Z[12] * e2z + Z[13] * en2 + Z[14] * enz +
             Z[15] * ez2 + Z[16] * n3 + Z[17] * n2z + Z[18] * nz2 + Z[19] * z3;
        break;

    default:
        return MPARMERR;
    }

    return MSUCCESS;
}

/***********************************************************************

  COMPUTE THE FORWARD AND BACKWARD GEOREFFERENCING COEFFICIENTS
  BASED ON A SET OF CONTROL POINTS

************************************************************************/

int CRS_compute_georef_equations_3d(struct Control_Points_3D *cp, double E12[],
                                    double N12[], double Z12[], double E21[],
                                    double N21[], double Z21[], int order)
{
    double *tempptr;
    int status;

    if (order < 1 || order > MAXORDER)
        return MPARMERR;

    /* CALCULATE THE FORWARD TRANSFORMATION COEFFICIENTS */

    status = calccoef(cp, E12, N12, Z12, order);

    if (status != MSUCCESS)
        return status;

    /* SWITCH THE 1 AND 2 EASTING, NORTHING, AND HEIGHT ARRAYS */

    tempptr = cp->e1;
    cp->e1 = cp->e2;
    cp->e2 = tempptr;
    tempptr = cp->n1;
    cp->n1 = cp->n2;
    cp->n2 = tempptr;
    tempptr = cp->z1;
    cp->z1 = cp->z2;
    cp->z2 = tempptr;

    /* CALCULATE THE BACKWARD TRANSFORMATION COEFFICIENTS */

    status = calccoef(cp, E21, N21, Z21, order);

    /* SWITCH THE 1 AND 2 EASTING, NORTHING, AND HEIGHT ARRAYS BACK */

    tempptr = cp->e1;
    cp->e1 = cp->e2;
    cp->e2 = tempptr;
    tempptr = cp->n1;
    cp->n1 = cp->n2;
    cp->n2 = tempptr;
    tempptr = cp->z1;
    cp->z1 = cp->z2;
    cp->z2 = tempptr;

    return status;
}

/***********************************************************************

  COMPUTE THE GEOREFFERENCING COEFFICIENTS
  BASED ON A SET OF CONTROL POINTS

************************************************************************/

static int calccoef(struct Control_Points_3D *cp, double E[], double N[],
                    double Z[], int order)
{
    struct MATRIX m;
    double *a;
    double *b;
    double *c;
    int numactive; /* NUMBER OF ACTIVE CONTROL POINTS */
    int status, i;

    /* CALCULATE THE NUMBER OF VALID CONTROL POINTS */

    for (i = numactive = 0; i < cp->count; i++) {
        if (cp->status[i] > 0)
            numactive++;
    }

    /* CALCULATE THE MINIMUM NUMBER OF CONTROL POINTS NEEDED TO DETERMINE
       A TRANSFORMATION OF THIS ORDER */

    /*
       2D    3D
       1st order:    3     4
       2nd order:    6    10
       3rd order:   10    20
     */

    m.n = numactive + 1;

    if (order == 1)
        m.n = 4;
    else if (order == 2)
        m.n = 10;
    else if (order == 3)
        m.n = 20;

    if (numactive < m.n)
        return MNPTERR;

    /* INITIALIZE MATRIX */

    m.v = G_calloc(m.n * m.n, sizeof(double));
    a = G_calloc(m.n, sizeof(double));
    b = G_calloc(m.n, sizeof(double));
    c = G_calloc(m.n, sizeof(double));

    if (numactive == m.n)
        status = exactdet(cp, &m, a, b, c, E, N, Z);
    else
        status = calcls(cp, &m, a, b, c, E, N, Z);

    G_free(m.v);
    G_free(a);
    G_free(b);
    G_free(c);

    return status;
}

/***********************************************************************

  CALCULATE THE TRANSFORMATION COEFFICIENTS WITH EXACTLY THE MINIMUM
  NUMBER OF CONTROL POINTS REQUIRED FOR THIS TRANSFORMATION.

************************************************************************/

static int exactdet(struct Control_Points_3D *cp, struct MATRIX *m, double a[],
                    double b[], double c[],
                    double E[], /* EASTING COEFFICIENTS */
                    double N[], /* NORTHING COEFFICIENTS */
                    double Z[]  /* HEIGHT COEFFICIENTS */
)
{
    int pntnow, currow, j;

    currow = 1;
    for (pntnow = 0; pntnow < cp->count; pntnow++) {
        if (cp->status[pntnow] > 0) {
            /* POPULATE MATRIX M */

            for (j = 1; j <= m->n; j++)
                M(currow, j) =
                    term(j, cp->e1[pntnow], cp->n1[pntnow], cp->z1[pntnow]);

            /* POPULATE MATRIX A AND B */

            a[currow - 1] = cp->e2[pntnow];
            b[currow - 1] = cp->n2[pntnow];
            c[currow - 1] = cp->z2[pntnow];

            currow++;
        }
    }

    if (currow - 1 != m->n)
        return MINTERR;

    return solvemat(m, a, b, c, E, N, Z);
}

/***********************************************************************

  CALCULATE THE TRANSFORMATION COEFFICIENTS WITH MORE THAN THE MINIMUM
  NUMBER OF CONTROL POINTS REQUIRED FOR THIS TRANSFORMATION.  THIS
  ROUTINE USES THE LEAST SQUARES METHOD TO COMPUTE THE COEFFICIENTS.

************************************************************************/

static int calcls(struct Control_Points_3D *cp, struct MATRIX *m, double a[],
                  double b[], double c[], double E[], /* EASTING COEFFICIENTS */
                  double N[], /* NORTHING COEFFICIENTS */
                  double Z[]  /* HEIGHT COEFFICIENTS */
)
{
    int i, j, n, numactive = 0;

    /* INITIALIZE THE UPPER HALF OF THE MATRIX AND THE TWO COLUMN VECTORS */

    for (i = 1; i <= m->n; i++) {
        for (j = i; j <= m->n; j++)
            M(i, j) = 0.0;
        a[i - 1] = b[i - 1] = c[i - 1] = 0.0;
    }

    /* SUM THE UPPER HALF OF THE MATRIX AND THE COLUMN VECTORS ACCORDING TO
       THE LEAST SQUARES METHOD OF SOLVING OVER DETERMINED SYSTEMS */

    for (n = 0; n < cp->count; n++) {
        if (cp->status[n] > 0) {
            numactive++;
            for (i = 1; i <= m->n; i++) {
                for (j = i; j <= m->n; j++)
                    M(i, j) += term(i, cp->e1[n], cp->n1[n], cp->z1[n]) *
                               term(j, cp->e1[n], cp->n1[n], cp->z1[n]);

                a[i - 1] +=
                    cp->e2[n] * term(i, cp->e1[n], cp->n1[n], cp->z1[n]);
                b[i - 1] +=
                    cp->n2[n] * term(i, cp->e1[n], cp->n1[n], cp->z1[n]);
                c[i - 1] +=
                    cp->z2[n] * term(i, cp->e1[n], cp->n1[n], cp->z1[n]);
            }
        }
    }

    if (numactive <= m->n)
        return MINTERR;

    /* TRANSPOSE VALUES IN UPPER HALF OF M TO OTHER HALF */

    for (i = 2; i <= m->n; i++)
        for (j = 1; j < i; j++)
            M(i, j) = M(j, i);

    return solvemat(m, a, b, c, E, N, Z);
}

/***********************************************************************

  CALCULATE THE X/Y TERM BASED ON THE TERM NUMBER

  ORDER\
  TERM   1      2      3      4      5      6      7      8      9      10
  1      e0n0z0 e1n0z0 e0n1z0 e0n0z1
  2      e0n0z0 e1n0z0 e0n1z0 e0n0z1 e2n0z0 e1n1z0 e1n0z1 e0n2z0 e0n1z1 e0n0z2
  3      e0n0z0 e1n0z0 e0n1z0 e0n0z1 e2n0z0 e1n1z0 e1n0z1 e0n2z0 e0n1z1 e0n0z2

  ORDER\
  TERM   11      12     13     14     15     16     17     18     19     20
  3      e3n0z0  e2n1z0 e2n0z1 e1n2z0 e1n1z1 e1n0z2 e0n3z0 e0n2z1 e0n1z2 e0n0z3

************************************************************************/

static double term(int term, double e, double n, double z)
{
    switch (term) {
        /* 1st order */
    case 1:
        return 1.0;
    case 2:
        return e;
    case 3:
        return n;
    case 4:
        return z;
        /* 2nd order */
    case 5:
        return e * e;
    case 6:
        return e * n;
    case 7:
        return e * z;
    case 8:
        return n * n;
    case 9:
        return n * z;
    case 10:
        return z * z;
        /* 3rd order */
    case 11:
        return e * e * e;
    case 12:
        return e * e * n;
    case 13:
        return e * e * z;
    case 14:
        return e * n * n;
    case 15:
        return e * n * z;
    case 16:
        return e * z * z;
    case 17:
        return n * n * n;
    case 18:
        return n * n * z;
    case 19:
        return n * z * z;
    case 20:
        return z * z * z;
    }

    return 0.0;
}

/***********************************************************************

  SOLVE FOR THE 'E', 'N' AND 'Z' COEFFICIENTS BY USING A
  SOMEWHAT MODIFIED GAUSSIAN ELIMINATION METHOD.

  | M11 M12 ... M1n | | E0   |   | a0   |
  | M21 M22 ... M2n | | E1   | = | a1   |
  |  .   .   .   .  | | .    |   | .    |
  | Mn1 Mn2 ... Mnn | | En-1 |   | an-1 |

  ,

  | M11 M12 ... M1n | | N0   |   | b0   |
  | M21 M22 ... M2n | | N1   | = | b1   |
  |  .   .   .   .  | | .    |   | .    |
  | Mn1 Mn2 ... Mnn | | Nn-1 |   | bn-1 |

  and

  | M11 M12 ... M1n | | Z0   |   | c0   |
  | M21 M22 ... M2n | | Z1   | = | c1   |
  |  .   .   .   .  | | .    |   | .    |
  | Mn1 Mn2 ... Mnn | | Zn-1 |   | cn-1 |

************************************************************************/

static int solvemat(struct MATRIX *m, double a[], double b[], double c[],
                    double E[], double N[], double Z[])
{
    int i, j, i2, j2, imark;
    double factor, temp;
    double pivot; /* ACTUAL VALUE OF THE LARGEST PIVOT CANDIDATE */

    for (i = 1; i <= m->n; i++) {
        j = i;

        /* find row with largest magnitude value for pivot value */

        pivot = M(i, j);
        imark = i;
        for (i2 = i + 1; i2 <= m->n; i2++) {
            temp = fabs(M(i2, j));
            if (temp > fabs(pivot)) {
                pivot = M(i2, j);
                imark = i2;
            }
        }

        /* if the pivot is very small then the points are nearly co-linear */
        /* co-linear points result in an undefined matrix, and nearly */
        /* co-linear points results in a solution with rounding error */

        if (fabs(pivot) < GRASS_EPSILON)
            return MUNSOLVABLE;

        /* if row with highest pivot is not the current row, switch them */

        if (imark != i) {
            for (j2 = 1; j2 <= m->n; j2++) {
                temp = M(imark, j2);
                M(imark, j2) = M(i, j2);
                M(i, j2) = temp;
            }

            temp = a[imark - 1];
            a[imark - 1] = a[i - 1];
            a[i - 1] = temp;

            temp = b[imark - 1];
            b[imark - 1] = b[i - 1];
            b[i - 1] = temp;

            temp = c[imark - 1];
            c[imark - 1] = c[i - 1];
            c[i - 1] = temp;
        }

        /* compute zeros above and below the pivot, and compute
           values for the rest of the row as well */

        for (i2 = 1; i2 <= m->n; i2++) {
            if (i2 != i) {
                factor = M(i2, j) / pivot;
                for (j2 = j; j2 <= m->n; j2++)
                    M(i2, j2) -= factor * M(i, j2);
                a[i2 - 1] -= factor * a[i - 1];
                b[i2 - 1] -= factor * b[i - 1];
                c[i2 - 1] -= factor * c[i - 1];
            }
        }
    }

    /* SINCE ALL OTHER VALUES IN THE MATRIX ARE ZERO NOW, CALCULATE THE
       COEFFICIENTS BY DIVIDING THE COLUMN VECTORS BY THE DIAGONAL VALUES. */

    for (i = 1; i <= m->n; i++) {
        E[i - 1] = a[i - 1] / M(i, i);
        N[i - 1] = b[i - 1] / M(i, i);
        Z[i - 1] = c[i - 1] / M(i, i);
    }

    return MSUCCESS;
}
