#ifndef lint
static char *RCSid() { return RCSid("$Id: interpol.c,v 1.13.2.1 2000/05/03 21:26:11 joze Exp $"); }
#endif
/* GNUPLOT - interpol.c */
/*[
* Copyright 1986 - 1993, 1998 Thomas Williams, Colin Kelley
*
* Permission to use, copy, and distribute this software and its
* documentation for any purpose with or without fee is hereby granted,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation.
*
* Permission to modify the software is granted, but not the right to
* distribute the complete modified source code. Modifications are to
* be distributed as patches to the released version. Permission to
* distribute binaries produced by compiling modified sources is granted,
* provided you
* 1. distribute the corresponding source modifications from the
* released version in the form of a patch file along with the binaries,
* 2. add special version identification to distinguish your version
* in addition to the base release version number,
* 3. provide your name and address as the primary contact for the
* support of your modified version, and
* 4. retain our contact information in regard to use of the base
* software.
* Permission to distribute the released version of the source code along
* with corresponding source modifications in the form of a patch file is
* granted with same provisions 2 through 4 for binary distributions.
*
* This software is provided "as is" without express or implied warranty
* to the extent permitted by applicable law.
]*/
/*
* C-Source file identification Header
*
* This file belongs to a project which is:
*
* done 1993 by MGR-Software, Asgard (Lars Hanke)
* written by Lars Hanke
*
* Contact me via:
*
* InterNet: mgr@asgard.bo.open.de
* FIDO: Lars Hanke @ 2:243/4802.22 (as long as they keep addresses)
*
**************************************************************************
*
* Project: gnuplot
* Module:
* File: interpol.c
*
* Revisor: Lars Hanke
* Revised: 26/09/93
* Revision: 1.0
*
**************************************************************************
*
* LEGAL
* This module is part of gnuplot and distributed under whatever terms
* gnuplot is or will be published, unless exclusive rights are claimed.
*
* DESCRIPTION
* Supplies 2-D data interpolation and approximation routines
*
* IMPORTS
* plot.h
* - cp_extend()
* - structs: curve_points, coordval, coordinate
*
* setshow.h
* - samples, is_log_x, base_log_x, xmin, xmax, autoscale_lx
* - plottypes
*
* proto.h
* - solve_tri_diag()
* - typedef tri_diag
*
* EXPORTS
* gen_interp()
* sort_points()
* cp_implode()
*
* BUGS and TODO
* I would really have liked to use Gershon Elbers contouring code for
* all the stuff done here, but I failed. So I used my own code.
* If somebody is able to consolidate Gershon's code for this purpose
* a lot of gnuplot users would be very happy - due to memory problems.
*
**************************************************************************
*
* HISTORY
* Changes:
* Nov 24, 1995 Markus Schuh (M.Schuh@meteo.uni-koeln.de):
* changed the algorithm for csplines
* added algorithm for approximation csplines
* copied point storage and range fix from plot2d.c
*
* Dec 12, 1995 David Denholm
* oops - at the time this is called, stored co-ords are
* internal (ie maybe log of data) but min/max are in
* user co-ordinates.
* Work with min and max of internal co-ords, and
* check at the end whether external min and max need to
* be increased. (since samples is typically 100 ; we
* dont want to take more logs than necessary)
* Also, need to take into account which axes are active
*
* Jun 30, 1996 Jens Emmerich
* implemented handling of UNDEFINED points
*/
#include "interpol.h"
#include "alloc.h"
#include "contour.h"
#include "graphics.h"
#include "misc.h"
#include "setshow.h"
#include "util.h"
/* in order to support multiple axes, and to simplify ranging in
* parametric plots, we use arrays to store some things. For 2d plots,
* elements are z=0,y1=1,x1=2,z2=4,y2=5,x2=6 these are given symbolic
* names in plot.h
*/
/*
* IMHO, code is getting too cluttered with repeated chunks of
* code. Some macros to simplify, I hope.
*
* do { } while(0) is comp.lang.c recommendation for complex macros
* also means that break can be specified as an action, and it will
*
*/
/* store VALUE or log(VALUE) in STORE, set TYPE as appropriate
* Do OUT_ACTION or UNDEF_ACTION as appropriate
* adjust range provided type is INRANGE (ie dont adjust y if x is outrange
* VALUE must not be same as STORE
*/
#define STORE_AND_FIXUP_RANGE(STORE, VALUE, TYPE, MIN, MAX, AUTO, OUT_ACTION, UNDEF_ACTION)\
do { STORE=VALUE; \
if (TYPE != INRANGE) break; /* dont set y range if x is outrange, for example */ \
if ( VALUEMAX ) {\
if (AUTO & 2) MAX=VALUE; else { TYPE=OUTRANGE; OUT_ACTION; } \
} \
} while(0)
#define UPDATE_RANGE(TEST,OLD,NEW,AXIS) \
do { if (TEST) { \
if (log_array[AXIS]) OLD = pow(base_array[AXIS], NEW); else OLD = NEW; \
} \
} while(0)
/* use this instead empty macro arguments to work around NeXT cpp bug */
/* if this fails on any system, we might use ((void)0) */
#define NOOP /* */
#define spline_coeff_size 4
typedef double spline_coeff[spline_coeff_size];
typedef double five_diag[5];
static int next_curve __PROTO((struct curve_points * plot, int *curve_start));
static int num_curves __PROTO((struct curve_points * plot));
static double *cp_binomial __PROTO((int points));
static void eval_bezier __PROTO((struct curve_points * cp, int first_point,
int num_points, double sr, coordval * px,
coordval *py, double *c));
static void do_bezier __PROTO((struct curve_points * cp, double *bc, int first_point, int num_points, struct coordinate * dest));
static int solve_five_diag __PROTO((five_diag m[], double r[], double x[], int n));
static spline_coeff *cp_approx_spline __PROTO((struct curve_points * plot, int first_point, int num_points));
static spline_coeff *cp_tridiag __PROTO((struct curve_points * plot, int first_point, int num_points));
static void do_cubic __PROTO((struct curve_points * plot, spline_coeff * sc, int first_point, int num_points, struct coordinate * dest));
static int compare_points __PROTO((struct coordinate * p1, struct coordinate * p2));
/*
* position curve_start to index the next non-UNDEFINDED point,
* start search at initial curve_start,
* return number of non-UNDEFINDED points from there on,
* if no more valid points are found, curve_start is set
* to plot->p_count and 0 is returned
*/
static int
next_curve(plot, curve_start)
struct curve_points *plot;
int *curve_start;
{
int curve_length;
/* Skip undefined points */
while (*curve_start < plot->p_count
&& plot->points[*curve_start].type == UNDEFINED) {
(*curve_start)++;
};
curve_length = 0;
/* curve_length is first used as an offset, then the correkt # points */
while ((*curve_start) + curve_length < plot->p_count
&& plot->points[(*curve_start) + curve_length].type != UNDEFINED) {
curve_length++;
};
return (curve_length);
}
/*
* determine the number of curves in plot->points, separated by
* UNDEFINED points
*/
static int
num_curves(plot)
struct curve_points *plot;
{
int curves;
int first_point;
int num_points;
first_point = 0;
curves = 0;
while ((num_points = next_curve(plot, &first_point)) > 0) {
curves++;
first_point += num_points;
}
return (curves);
}
/*
* build up a cntr_struct list from curve_points
* this funtion is only used for the alternate entry point to
* Gershon's code and thus commented out
***deleted***
*/
/* HBB 990205: rewrote the 'bezier' interpolation routine,
* to prevent numerical overflow and other undesirable things happening
* for large data files (num_data about 1000 or so), where binomial
* coefficients would explode, and powers of 'sr' (0 < sr < 1) become
* extremely small. Method used: compute logarithms of these
* extremely large and small numbers, and only go back to the
* real numbers once they've cancelled out each other, leaving
* a reasonable-sized one. */
/*
* cp_binomial() computes the binomial coefficients needed for BEZIER stuff
* and stores them into an array which is hooked to sdat.
* (MGR 1992)
*/
static double *
cp_binomial(points)
int points;
{
register double *coeff;
register int n, k;
int e;
e = points; /* well we're going from k=0 to k=p_count-1 */
coeff = (double *) gp_alloc(e * sizeof(double), "bezier coefficients");
n = points - 1;
e = n / 2;
/* HBB 990205: calculate these in 'logarithmic space',
* as they become _very_ large, with growing n (4^n) */
coeff[0] = 0.0;
for (k = 0; k < e; k++) {
coeff[k + 1] = coeff[k] + log(((double) (n - k)) / ((double) (k + 1)));
}
for (k = n; k >= e; k--)
coeff[k] = coeff[n - k];
return (coeff);
}
/* This is a subfunction of do_bezier() for BEZIER style computations.
* It is passed the stepration (STEP/MAXSTEPS) and the addresses of
* the double values holding the next x and y coordinates.
* (MGR 1992)
*/
static void
eval_bezier(cp, first_point, num_points, sr, px, py, c)
struct curve_points *cp;
int first_point; /* where to start in plot->points (to find x-range) */
int num_points; /* to determine end in plot->points */
double sr;
coordval *px;
coordval *py;
double *c;
{
unsigned int n = num_points - 1;
/* HBB 980308: added 'GPHUGE' tag for DOS */
struct coordinate GPHUGE *this_points;
this_points = (cp->points) + first_point;
if (sr == 0.0) {
*px = this_points[0].x;
*py = this_points[0].y;
} else if (sr == 1.0) {
*px = this_points[n].x;
*py = this_points[n].y;
} else {
/* HBB 990205: do calculation in 'logarithmic space',
* to avoid over/underflow errors, which would exactly cancel
* out each other, anyway, in an exact calculation
*/
unsigned int i;
double lx = 0.0, ly = 0.0;
double log_dsr_to_the_n = n * log(1 - sr);
double log_sr_over_dsr = log(sr) - log(1 - sr);
for (i = 0; i points */
int num_points; /* to determine end in plot->points */
struct coordinate *dest; /* where to put the interpolated data */
{
int i;
coordval x, y;
int xaxis = cp->x_axis;
int yaxis = cp->y_axis;
/* min and max in internal (eg logged) co-ordinates. We update
* these, then update the external extrema in user co-ordinates
* at the end.
*/
double ixmin, ixmax, iymin, iymax;
double sxmin, sxmax, symin, symax; /* starting values of above */
if (log_array[xaxis]) {
ixmin = sxmin = log(min_array[xaxis]) / log_base_array[xaxis];
ixmax = sxmax = log(max_array[xaxis]) / log_base_array[xaxis];
} else {
ixmin = sxmin = min_array[xaxis];
ixmax = sxmax = max_array[xaxis];
}
if (log_array[yaxis]) {
iymin = symin = log(min_array[yaxis]) / log_base_array[yaxis];
iymax = symax = log(max_array[yaxis]) / log_base_array[yaxis];
} else {
iymin = symin = min_array[yaxis];
iymax = symax = max_array[yaxis];
}
for (i = 0; i < samples; i++) {
eval_bezier(cp, first_point, num_points, (double) i / (double) (samples - 1), &x, &y, bc);
/* now we have to store the points and adjust the ranges */
dest[i].type = INRANGE;
STORE_AND_FIXUP_RANGE(dest[i].x, x, dest[i].type, ixmin, ixmax, auto_array[xaxis], NOOP, continue);
STORE_AND_FIXUP_RANGE(dest[i].y, y, dest[i].type, iymin, iymax, auto_array[yaxis], NOOP, NOOP);
dest[i].xlow = dest[i].xhigh = dest[i].x;
dest[i].ylow = dest[i].yhigh = dest[i].y;
dest[i].z = -1;
}
UPDATE_RANGE(ixmax > sxmax, max_array[xaxis], ixmax, xaxis);
UPDATE_RANGE(ixmin < sxmin, min_array[xaxis], ixmin, xaxis);
UPDATE_RANGE(iymax > symax, max_array[yaxis], iymax, yaxis);
UPDATE_RANGE(iymin < symin, min_array[yaxis], iymin, yaxis);
}
/*
* call contouring routines -- main entry
*/
/*
* it should be like this, but it doesn't run. If you find out why,
* contact me: mgr@asgard.bo.open.de or Lars Hanke 2:243/4802.22@fidonet
*
* Well, all this had originally been inside contour.c, so maybe links
* to functions and of contour.c are broken.
* ***deleted***
* end of unused entry point to Gershon's code
*
*/
/*
* Solve five diagonal linear system equation. The five diagonal matrix is
* defined via matrix M, right side is r, and solution X i.e. M * X = R.
* Size of system given in n. Return TRUE if solution exist.
* G. Engeln-Muellges/ F.Reutter:
* "Formelsammlung zur Numerischen Mathematik mit Standard-FORTRAN-Programmen"
* ISBN 3-411-01677-9
*
* / m02 m03 m04 0 0 0 0 . . . \ / x0 \ / r0 \
* I m11 m12 m13 m14 0 0 0 . . . I I x1 I I r1 I
* I m20 m21 m22 m23 m24 0 0 . . . I * I x2 I = I r2 I
* I 0 m30 m31 m32 m33 m34 0 . . . I I x3 I I r3 I
* . . . . . . . . . . . .
* \ m(n-3)0 m(n-2)1 m(n-1)2 / \x(n-1)/ \r(n-1)/
*
*/
static int
solve_five_diag(m, r, x, n)
five_diag m[];
double r[], x[];
int n;
{
int i;
five_diag *hv;
hv = (five_diag *) gp_alloc((n + 1) * sizeof(five_diag), "five_diag help vars");
hv[0][0] = m[0][2];
if (hv[0][0] == 0) {
free(hv);
return FALSE;
}
hv[0][1] = m[0][3] / hv[0][0];
hv[0][2] = m[0][4] / hv[0][0];
hv[1][3] = m[1][1];
hv[1][0] = m[1][2] - hv[1][3] * hv[0][1];
if (hv[1][0] == 0) {
free(hv);
return FALSE;
}
hv[1][1] = (m[1][3] - hv[1][3] * hv[0][2]) / hv[1][0];
hv[1][2] = m[1][4] / hv[1][0];
for (i = 2; i points */
int num_points; /* to determine end in plot->points */
{
spline_coeff *sc;
five_diag *m;
int xaxis = plot->x_axis;
int yaxis = plot->y_axis;
double *r, *x, *h, *xp, *yp;
/* HBB 980308: added 'GPHUGE' tag */
struct coordinate GPHUGE *this_points;
int i;
sc = (spline_coeff *) gp_alloc((num_points) * sizeof(spline_coeff),
"spline matrix");
if (num_points < 4)
int_error(NO_CARET, "Can't calculate approximation splines, need at least 4 points");
this_points = (plot->points) + first_point;
for (i = 0; i points[j].type = INRANGE;
if (! all_inrange) {
if (log_array[xaxis])
x = exp(x * log_base_array[xaxis]);
if (((x < min_array[xaxis]) && !(auto_array[xaxis] & 1))
|| ((x > max_array[xaxis]) && !(auto_array[xaxis] & 2)))
cp->points[j].type = OUTRANGE;
else {
if (log_array[yaxis])
y = exp(y * log_base_array[yaxis]);
if (((y < min_array[yaxis]) && !(auto_array[yaxis] & 1))
|| ((y > max_array[yaxis]) && !(auto_array[yaxis] & 2)))
cp->points[j].type = OUTRANGE;
}
}
j++; /* next valid entry */
k = 0; /* to read */
i--; /* from this (-> last after for(;;)) entry */
}
}
if (k) {
cp->points[j].x = x;
cp->points[j].y = y /= (double) k;
cp->points[j].xhigh = sux / (double) k;
cp->points[j].xlow = slx / (double) k;
cp->points[j].yhigh = suy / (double) k;
cp->points[j].ylow = sly / (double) k;
cp->points[j].type = INRANGE;
if (! all_inrange) {
if (log_array[xaxis])
x = exp(x * log_base_array[xaxis]);
if (((x < min_array[xaxis]) && !(auto_array[xaxis] & 1))
|| ((x > max_array[xaxis]) && !(auto_array[xaxis] & 2)))
cp->points[j].type = OUTRANGE;
else {
if (log_array[yaxis])
y = exp(y * log_base_array[yaxis]);
if (((y < min_array[yaxis]) && !(auto_array[yaxis] & 1))
|| ((y > max_array[yaxis]) && !(auto_array[yaxis] & 2)))
cp->points[j].type = OUTRANGE;
}
}
j++; /* next valid entry */
}
/* insert invalid point to separate curves */
if (j < cp->p_count) {
cp->points[j].type = UNDEFINED;
j++;
}
first_point += num_points;
} /* end while */
cp->p_count = j;
cp_extend(cp, j);
}