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//--------------------------------------------------------------------------
//
// File: linear.c
//
// Created: 04/08/2000
//
// Author: Pavel Sakov
// CSIRO Marine Research
//
// Purpose: 2D linear interpolation
//
// Description: `lpi' -- "Linear Point Interpolator" -- is
// a structure for conducting linear interpolation on a given
// data on a "point-to-point" basis. It interpolates linearly
// within each triangle resulted from the Delaunay
// triangluation of input data. `lpi' is much
// faster than all Natural Neighbours interpolators in `nn'
// library.
//
// Revisions: None
//
//--------------------------------------------------------------------------
#include <stdlib.h>
#include <stdio.h>
#include "nan.h"
#include "delaunay.h"
typedef struct
{
double w[3];
} lweights;
struct lpi
{
delaunay* d;
lweights* weights;
};
int delaunay_xytoi( delaunay* d, point* p, int seed );
// Builds linear interpolator.
//
// @param d Delaunay triangulation
// @return Linear interpolator
//
lpi* lpi_build( delaunay* d )
{
int i;
lpi * l = malloc( sizeof ( lpi ) );
l->d = d;
l->weights = malloc( (size_t) d->ntriangles * sizeof ( lweights ) );
for ( i = 0; i < d->ntriangles; ++i )
{
triangle* t = &d->triangles[i];
lweights* lw = &l->weights[i];
double x0 = d->points[t->vids[0]].x;
double y0 = d->points[t->vids[0]].y;
double z0 = d->points[t->vids[0]].z;
double x1 = d->points[t->vids[1]].x;
double y1 = d->points[t->vids[1]].y;
double z1 = d->points[t->vids[1]].z;
double x2 = d->points[t->vids[2]].x;
double y2 = d->points[t->vids[2]].y;
double z2 = d->points[t->vids[2]].z;
double x02 = x0 - x2;
double y02 = y0 - y2;
double z02 = z0 - z2;
double x12 = x1 - x2;
double y12 = y1 - y2;
double z12 = z1 - z2;
if ( y12 != 0.0 )
{
double y0212 = y02 / y12;
lw->w[0] = ( z02 - z12 * y0212 ) / ( x02 - x12 * y0212 );
lw->w[1] = ( z12 - lw->w[0] * x12 ) / y12;
lw->w[2] = ( z2 - lw->w[0] * x2 - lw->w[1] * y2 );
}
else
{
double x0212 = x02 / x12;
lw->w[1] = ( z02 - z12 * x0212 ) / ( y02 - y12 * x0212 );
lw->w[0] = ( z12 - lw->w[1] * y12 ) / x12;
lw->w[2] = ( z2 - lw->w[0] * x2 - lw->w[1] * y2 );
}
}
return l;
}
// Destroys linear interpolator.
//
// @param l Structure to be destroyed
//
void lpi_destroy( lpi* l )
{
free( l->weights );
free( l );
}
// Finds linearly interpolated value in a point.
//
// @param l Linear interpolation
// @param p Point to be interpolated (p->x, p->y -- input; p->z -- output)
//
void lpi_interpolate_point( lpi* l, point* p )
{
delaunay* d = l->d;
int tid = delaunay_xytoi( d, p, d->first_id );
if ( tid >= 0 )
{
lweights* lw = &l->weights[tid];
d->first_id = tid;
p->z = p->x * lw->w[0] + p->y * lw->w[1] + lw->w[2];
}
else
p->z = NaN;
}
// Linearly interpolates data from one array of points for another array of
// points.
//
// @param nin Number of input points
// @param pin Array of input points [pin]
// @param nout Number of ouput points
// @param pout Array of output points [nout]
//
void lpi_interpolate_points( int nin, point pin[], int nout, point pout[] )
{
delaunay* d = delaunay_build( nin, pin, 0, NULL, 0, NULL );
lpi * l = lpi_build( d );
int seed = 0;
int i;
if ( nn_verbose )
{
fprintf( stderr, "xytoi:\n" );
for ( i = 0; i < nout; ++i )
{
point* p = &pout[i];
fprintf( stderr, "(%.7g,%.7g) -> %d\n", p->x, p->y, delaunay_xytoi( d, p, seed ) );
}
}
for ( i = 0; i < nout; ++i )
lpi_interpolate_point( l, &pout[i] );
if ( nn_verbose )
{
fprintf( stderr, "output:\n" );
for ( i = 0; i < nout; ++i )
{
point* p = &pout[i];;
fprintf( stderr, " %d:%15.7g %15.7g %15.7g\n", i, p->x, p->y, p->z );
}
}
lpi_destroy( l );
delaunay_destroy( d );
}
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