/***************************************************************************/
/***************************************************************************/
/*
  CRS.C - Center for Remote Sensing rectification routines

  Written By: Brian J. Buckley

  At: The Center for Remote Sensing
  Michigan State University
  302 Berkey Hall
  East Lansing, MI  48824
  (517)353-7195

  Written: 12/19/91

  Last Update: 12/26/91 Brian J. Buckley
  Last Update:  1/24/92 Brian J. Buckley
  Added printout of trnfile. Triggered by BDEBUG.
  Last Update:  1/27/92 Brian J. Buckley
  Fixed bug so that only the active control points were used.
*/
/***************************************************************************/
/***************************************************************************/

#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 *,double *,double *,int);
static int calcls(struct Control_Points *,struct MATRIX *,double *,double *,double *,double *);
static int exactdet(struct Control_Points *,struct MATRIX *,double *,double *,double *,double *);
static int solvemat(struct MATRIX *,double *,double *,double *,double *);
static double term(int,double,double);

/***************************************************************************/
/*
  TRANSFORM A SINGLE COORDINATE PAIR.
*/
/***************************************************************************/

int CRS_georef(
	double e1,  /* EASTINGS TO BE TRANSFORMED */
	double n1,  /* NORTHINGS TO BE TRANSFORMED */
	double *e,  /* EASTINGS TO BE TRANSFORMED */
	double *n,  /* NORTHINGS TO BE TRANSFORMED */
	double E[], /* EASTING COEFFICIENTS */
	double N[], /* NORTHING COEFFICIENTS */
	int order  /* ORDER OF TRANSFORMATION TO BE PERFORMED, MUST MATCH THE
		      ORDER USED TO CALCULATE THE COEFFICIENTS */
	)
{
	double e3, e2n, en2, n3, e2, en, n2;

	switch(order)
	{
	case 1:

		*e = E[0] + E[1] * e1 + E[2] * n1;
		*n = N[0] + N[1] * e1 + N[2] * n1;
		break;

	case 2:

		e2 = e1 * e1;
		n2 = n1 * n1;
		en = e1 * n1;

		*e = E[0]      + E[1] * e1 + E[2] * n1 +
			E[3] * e2 + E[4] * en + E[5] * n2;
		*n = N[0]      + N[1] * e1 + N[2] * n1 +
			N[3] * e2 + N[4] * en + N[5] * n2;
		break;

	case 3:

		e2  = e1 * e1;
		en  = e1 * n1;
		n2  = n1 * n1;
		e3  = e1 * e2;
		e2n = e2 * n1;
		en2 = e1 * n2;
		n3  = n1 * n2;

		*e = E[0]      +
			E[1] * e1 + E[2] * n1  +
			E[3] * e2 + E[4] * en  + E[5] * n2  +
			E[6] * e3 + E[7] * e2n + E[8] * en2 + E[9] * n3;
		*n = N[0]      +
			N[1] * e1 + N[2] * n1  +
			N[3] * e2 + N[4] * en  + N[5] * n2  +
			N[6] * e3 + N[7] * e2n + N[8] * en2 + N[9] * n3;
		break;

	default:
		return MPARMERR;
	}

	return MSUCCESS;
}

/***************************************************************************/
/*
  COMPUTE THE GEOREFFERENCING COEFFICIENTS BASED ON A SET OF CONTROL POINTS
*/
/***************************************************************************/

int CRS_compute_georef_equations(
	struct Control_Points *cp, double E12[], double N12[], double E21[], double N21[], int order)
{
	double *tempptr;
	int status;

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

	/* CALCULATE THE FORWARD TRANSFORMATION COEFFICIENTS */

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

	if (status != MSUCCESS)
		return status;

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

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

	/* CALCULATE THE BACKWARD TRANSFORMATION COEFFICIENTS */

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

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

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

	return status;
}

/***************************************************************************/
/*
  COMPUTE THE GEOREFFERENCING COEFFICIENTS BASED ON A SET OF CONTROL POINTS
*/
/***************************************************************************/

static int calccoef(struct Control_Points *cp, double E[], double N[], int order)
{
	struct MATRIX m;
	double *a;
	double *b;
	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 */

	m.n = ((order + 1) * (order + 2)) / 2;

	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));

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

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

	return status;
}

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

static int exactdet(
	struct Control_Points *cp,
	struct MATRIX *m,
	double a[],
	double b[],
	double E[],     /* EASTING COEFFICIENTS */
	double N[]     /* NORTHING 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]);

			/* POPULATE MATRIX A AND B */

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

			currow++;
		}
	}

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

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

/***************************************************************************/
/*
  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 *cp,
	struct MATRIX *m,
	double a[],
	double b[],
	double E[],     /* EASTING COEFFICIENTS */
	double N[]     /* NORTHING 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] = 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]) * term(j, cp->e1[n], cp->n1[n]);

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

/***************************************************************************/
/*
  CALCULATE THE X/Y TERM BASED ON THE TERM NUMBER

  ORDER\TERM   1    2    3    4    5    6    7    8    9   10
  1        e0n0 e1n0 e0n1
  2        e0n0 e1n0 e0n1 e2n0 e1n1 e0n2
  3        e0n0 e1n0 e0n1 e2n0 e1n1 e0n2 e3n0 e2n1 e1n2 e0n3
*/
/***************************************************************************/

static double term(int term, double e, double n)
{
	switch (term)
	{
	case  1: return 1.0;
	case  2: return e;
	case  3: return n;
	case  4: return e*e;
	case  5: return e*n;
	case  6: return n*n;
	case  7: return e*e*e;
	case  8: return e*e*n;
	case  9: return e*n*n;
	case 10: return n*n*n;
	}

	return 0.0;
}

/***************************************************************************/
/*
  SOLVE FOR THE 'E' AND 'N' 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 |

  and

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

static int solvemat(struct MATRIX *m, double a[], double b[], double E[], double N[])
{
	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 (pivot == 0.0)
			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;
		}

		/* 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];
			}
		}
	}

	/* 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);
	}

	return MSUCCESS;
}

