int VizGeorefSpline2D::get_point( const double Px, const double Py, double *vars )
{
int v, r;
double tmp, Pu;
double fact;
int leftP=0, rightP=0, found = 0;
switch ( type )
{
case VIZ_GEOREF_SPLINE_ZERO_POINTS :
for ( v = 0; v < _nof_vars; v++ )
vars[v] = 0.0;
break;
case VIZ_GEOREF_SPLINE_ONE_POINT :
for ( v = 0; v < _nof_vars; v++ )
vars[v] = rhs[v][3];
break;
case VIZ_GEOREF_SPLINE_TWO_POINTS :
fact = _dx * ( Px - x[0] ) + _dy * ( Py - y[0] );
for ( v = 0; v < _nof_vars; v++ )
vars[v] = ( 1 - fact ) * rhs[v][3] + fact * rhs[v][4];
break;
case VIZ_GEOREF_SPLINE_ONE_DIMENSIONAL :
Pu = _dx * ( Px - x[0] ) + _dy * ( Py - y[0] );
if ( Pu <= u[index[0]] )
{
leftP = index[0];
rightP = index[1];
}
else if ( Pu >= u[index[_nof_points-1]] )
{
leftP = index[_nof_points-2];
rightP = index[_nof_points-1];
}
else
{
for ( r = 1; !found && r < _nof_points; r++ )
{
leftP = index[r-1];
rightP = index[r];
if ( Pu >= u[leftP] && Pu <= u[rightP] )
found = 1;
}
}
fact = ( Pu - u[leftP] ) / ( u[rightP] - u[leftP] );
for ( v = 0; v < _nof_vars; v++ )
vars[v] = ( 1.0 - fact ) * rhs[v][leftP+3] +
fact * rhs[v][rightP+3];
break;
case VIZ_GEOREF_SPLINE_FULL :
for ( v = 0; v < _nof_vars; v++ )
vars[v] = coef[v][0] + coef[v][1] * Px + coef[v][2] * Py;
for ( r = 0; r < _nof_points; r++ )
{
tmp = base_func( Px, Py, x[r], y[r] );
for ( v= 0; v < _nof_vars; v++ )
vars[v] += coef[v][r+3] * tmp;
}
break;
case VIZ_GEOREF_SPLINE_POINT_WAS_ADDED :
fprintf(stderr, " A point was added after the last solve\n");
fprintf(stderr, " NO interpolation - return values are zero\n");
for ( v = 0; v < _nof_vars; v++ )
vars[v] = 0.0;
return(0);
break;
case VIZ_GEOREF_SPLINE_POINT_WAS_DELETED :
fprintf(stderr, " A point was deleted after the last solve\n");
fprintf(stderr, " NO interpolation - return values are zero\n");
for ( v = 0; v < _nof_vars; v++ )
vars[v] = 0.0;
return(0);
break;
default :
return(0);
break;
}
return(1);
}
const base_type* base() const { return &base_func(); }
int VizGeorefSpline2D::solve(void)
{
int r, c, v;
int p;
// No points at all
if ( _nof_points < 1 )
{
type = VIZ_GEOREF_SPLINE_ZERO_POINTS;
return(0);
}
// Only one point
if ( _nof_points == 1 )
{
type = VIZ_GEOREF_SPLINE_ONE_POINT;
return(1);
}
// Just 2 points - it is necessarily 1D case
if ( _nof_points == 2 )
{
_dx = x[1] - x[0];
_dy = y[1] - y[0];
double fact = 1.0 / ( _dx * _dx + _dy * _dy );
_dx *= fact;
_dy *= fact;
type = VIZ_GEOREF_SPLINE_TWO_POINTS;
return(2);
}
// More than 2 points - first we have to check if it is 1D or 2D case
double xmax = x[0], xmin = x[0], ymax = y[0], ymin = y[0];
double delx, dely;
double xx, yy;
double sumx = 0.0f, sumy= 0.0f, sumx2 = 0.0f, sumy2 = 0.0f, sumxy = 0.0f;
double SSxx, SSyy, SSxy;
for ( p = 0; p < _nof_points; p++ )
{
xx = x[p];
yy = y[p];
xmax = MAX( xmax, xx );
xmin = MIN( xmin, xx );
ymax = MAX( ymax, yy );
ymin = MIN( ymin, yy );
sumx += xx;
sumx2 += xx * xx;
sumy += yy;
sumy2 += yy * yy;
sumxy += xx * yy;
}
delx = xmax - xmin;
dely = ymax - ymin;
SSxx = sumx2 - sumx * sumx / _nof_points;
SSyy = sumy2 - sumy * sumy / _nof_points;
SSxy = sumxy - sumx * sumy / _nof_points;
if ( delx < 0.001 * dely || dely < 0.001 * delx ||
fabs ( SSxy * SSxy / ( SSxx * SSyy ) ) > 0.99 )
{
int p1;
type = VIZ_GEOREF_SPLINE_ONE_DIMENSIONAL;
_dx = _nof_points * sumx2 - sumx * sumx;
_dy = _nof_points * sumy2 - sumy * sumy;
double fact = 1.0 / sqrt( _dx * _dx + _dy * _dy );
_dx *= fact;
_dy *= fact;
for ( p = 0; p < _nof_points; p++ )
{
double dxp = x[p] - x[0];
double dyp = y[p] - y[0];
u[p] = _dx * dxp + _dy * dyp;
unused[p] = 1;
}
for ( p = 0; p < _nof_points; p++ )
{
int min_index = -1;
double min_u = 0;
for ( p1 = 0; p1 < _nof_points; p1++ )
{
if ( unused[p1] )
{
if ( min_index < 0 || u[p1] < min_u )
{
min_index = p1;
min_u = u[p1];
}
}
}
index[p] = min_index;
unused[min_index] = 0;
}
return(3);
}
type = VIZ_GEOREF_SPLINE_FULL;
// Make the necessary memory allocations
if ( _AA )
CPLFree(_AA);
if ( _Ainv )
CPLFree(_Ainv);
_nof_eqs = _nof_points + 3;
_AA = ( double * )CPLCalloc( _nof_eqs * _nof_eqs, sizeof( double ) );
_Ainv = ( double * )CPLCalloc( _nof_eqs * _nof_eqs, sizeof( double ) );
// Calc the values of the matrix A
for ( r = 0; r < 3; r++ )
for ( c = 0; c < 3; c++ )
A(r,c) = 0.0;
for ( c = 0; c < _nof_points; c++ )
{
A(0,c+3) = 1.0;
A(1,c+3) = x[c];
A(2,c+3) = y[c];
A(c+3,0) = 1.0;
A(c+3,1) = x[c];
A(c+3,2) = y[c];
}
for ( r = 0; r < _nof_points; r++ )
for ( c = r; c < _nof_points; c++ )
{
A(r+3,c+3) = base_func( x[r], y[r], x[c], y[c] );
if ( r != c )
A(c+3,r+3 ) = A(r+3,c+3);
}
#if VIZ_GEOREF_SPLINE_DEBUG
for ( r = 0; r < _nof_eqs; r++ )
{
for ( c = 0; c < _nof_eqs; c++ )
fprintf(stderr, "%f", A(r,c));
fprintf(stderr, "\n");
}
#endif
// Invert the matrix
int status = matrixInvert( _nof_eqs, _AA, _Ainv );
if ( !status )
{
fprintf(stderr, " There is a problem to invert the interpolation matrix\n");
return 0;
}
// calc the coefs
for ( v = 0; v < _nof_vars; v++ )
for ( r = 0; r < _nof_eqs; r++ )
{
coef[v][r] = 0.0;
for ( c = 0; c < _nof_eqs; c++ )
coef[v][r] += Ainv(r,c) * rhs[v][c];
}
return(4);
}
