#ifndef lint static char *RCSid = "$Id: interpol.c,v 1.6.2.2 2002/02/01 18:41:05 broeker 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 "plot.h" #include "setshow.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 */ extern double min_array[AXIS_ARRAY_SIZE]; extern double max_array[AXIS_ARRAY_SIZE]; extern int auto_array[AXIS_ARRAY_SIZE]; extern TBOOLEAN log_array[AXIS_ARRAY_SIZE]; extern double base_array[AXIS_ARRAY_SIZE]; extern double log_base_array[AXIS_ARRAY_SIZE]; #define Inc_c_token if (++c_token >= num_tokens) \ int_error ("Syntax error", c_token); /* * 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)); GP_INLINE static double s_pow __PROTO((double base, unsigned int exponent)); 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)); int compare_points __PROTO((SORTFUNC_ARGS p1, SORTFUNC_ARGS 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) */ /* * well, this routine runs faster with the 68040 striptease FPU * and it handles zeroes correctly - there had been some trouble with TC */ GP_INLINE static double s_pow(base, exponent) double base; unsigned int exponent; { double y; if (exponent == 0) return (1.0); if (base == 0.0) return (0.0); /* consider i in binary = abcd * x^i = x^(8a+4b+2c+d) = x^8a * x^4b * x^2b * x^d * = a?x^2^2^2:1 * b?x^2^2:1 + ... * so for each bit in exponent, square x, multiplying it into accumulator * */ y = 1; while (exponent) { if (exponent & 1) y *= base; base *= base; /* if exponent was signed, this could be trouble ! */ exponent >>= 1; } return (y); } 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 <= n; i++) { double u = exp(c[i] + log_dsr_to_the_n + i * log_sr_over_dsr); lx += this_points[i].x * u; ly += this_points[i].y * u; } *px = lx; *py = ly; } } /* * generate a new set of coordinates representing the bezier curve and * set it to the plot */ static void do_bezier(cp, bc, first_point, num_points, dest) struct curve_points *cp; double *bc; int first_point; /* where to start in plot->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 <= n - 1; i++) { hv[i][3] = m[i][1] - m[i][0] * hv[i - 2][1]; hv[i][0] = m[i][2] - m[i][0] * hv[i - 2][2] - hv[i][3] * hv[i - 1][1]; if (hv[i][0] == 0) { free(hv); return FALSE; } hv[i][1] = (m[i][3] - hv[i][3] * hv[i - 1][2]) / hv[i][0]; hv[i][2] = m[i][4] / hv[i][0]; } hv[0][4] = 0; hv[1][4] = r[0] / hv[0][0]; for (i = 1; i <= n - 1; i++) { hv[i + 1][4] = (r[i] - m[i][0] * hv[i - 1][4] - hv[i][3] * hv[i][4]) / hv[i][0]; } x[n - 1] = hv[n][4]; x[n - 2] = hv[n - 1][4] - hv[n - 2][1] * x[n - 1]; for (i = n - 3; i >= 0; i--) x[i] = hv[i + 1][4] - hv[i][1] * x[i + 1] - hv[i][2] * x[i + 2]; free(hv); return TRUE; } /* * Calculation of approximation cubic splines * Input: x[i], y[i], weights z[i] * * Returns matrix of spline coefficients */ static spline_coeff *cp_approx_spline(plot, first_point, num_points) struct curve_points *plot; int first_point; /* where to start in plot->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("Can't calculate approximation splines, need at least 4 points", NO_CARET); this_points = (plot->points) + first_point; for (i = 0; i <= num_points - 1; i++) if (this_points[i].z <= 0) int_error("Can't calculate approximation splines, all weights have to be > 0", NO_CARET); m = (five_diag *) gp_alloc((num_points - 2) * sizeof(five_diag), "spline help matrix"); r = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline right side"); x = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline solution vector"); h = (double *) gp_alloc((num_points - 1) * sizeof(double), "spline help vector"); xp = (double *) gp_alloc((num_points) * sizeof(double), "x pos"); yp = (double *) gp_alloc((num_points) * sizeof(double), "y pos"); /* KB 981107: With logarithmic axis first convert back to linear scale */ if (log_array[xaxis]) { for (i = 0; i <= num_points - 1; i++) xp[i] = exp(this_points[i].x * log_base_array[xaxis]); } else { for (i = 0; i <= num_points - 1; i++) xp[i] = this_points[i].x; } if (log_array[yaxis]) { for (i = 0; i <= num_points - 1; i++) yp[i] = exp(this_points[i].y * log_base_array[yaxis]); } else { for (i = 0; i <= num_points - 1; i++) yp[i] = this_points[i].y; } for (i = 0; i <= num_points - 2; i++) h[i] = xp[i + 1] - xp[i]; /* set up the matrix and the vector */ for (i = 0; i <= num_points - 3; i++) { r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1] - (yp[i + 1] - yp[i]) / h[i]); if (i < 2) m[i][0] = 0; else m[i][0] = 6 / this_points[i].z / h[i - 1] / h[i]; if (i < 1) m[i][1] = 0; else m[i][1] = h[i] - 6 / this_points[i].z / h[i] * (1 / h[i - 1] + 1 / h[i]) - 6 / this_points[i + 1].z / h[i] * (1 / h[i] + 1 / h[i + 1]); m[i][2] = 2 * (h[i] + h[i + 1]) + 6 / this_points[i].z / h[i] / h[i] + 6 / this_points[i + 1].z * (1 / h[i] + 1 / h[i + 1]) * (1 / h[i] + 1 / h[i + 1]) + 6 / this_points[i + 2].z / h[i + 1] / h[i + 1]; if (i > num_points - 4) m[i][3] = 0; else m[i][3] = h[i + 1] - 6 / this_points[i + 1].z / h[i + 1] * (1 / h[i] + 1 / h[i + 1]) - 6 / this_points[i + 2].z / h[i + 1] * (1 / h[i + 1] + 1 / h[i + 2]); if (i > num_points - 5) m[i][4] = 0; else m[i][4] = 6 / this_points[i + 2].z / h[i + 1] / h[i + 2]; } /* solve the matrix */ if (!solve_five_diag(m, r, x, num_points - 2)) { free(h); free(x); free(r); free(m); free(xp); free(yp); int_error("Can't calculate approximation splines", NO_CARET); } sc[0][2] = 0; for (i = 1; i <= num_points - 2; i++) sc[i][2] = x[i - 1]; sc[num_points - 1][2] = 0; sc[0][0] = yp[0] + 2 / this_points[0].z / h[0] * (sc[0][2] - sc[1][2]); for (i = 1; i <= num_points - 2; i++) sc[i][0] = yp[i] - 2 / this_points[i].z * (sc[i - 1][2] / h[i - 1] - sc[i][2] * (1 / h[i - 1] + 1 / h[i]) + sc[i + 1][2] / h[i]); sc[num_points - 1][0] = yp[num_points - 1] - 2 / this_points[num_points - 1].z / h[num_points - 2] * (sc[num_points - 2][2] - sc[num_points - 1][2]); for (i = 0; i <= num_points - 2; i++) { sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i] - h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]); sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i]; } free(h); free(x); free(r); free(m); free(xp); free(yp); return (sc); } /* * Calculation of cubic splines * * This can be treated as a special case of approximation cubic splines, with * all weights -> infinity. * * Returns matrix of spline coefficients */ static spline_coeff *cp_tridiag(plot, first_point, num_points) struct curve_points *plot; int first_point, num_points; { spline_coeff *sc; tri_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; if (num_points < 3) int_error("Can't calculate splines, need at least 3 points", NO_CARET); this_points = (plot->points) + first_point; sc = (spline_coeff *) gp_alloc((num_points) * sizeof(spline_coeff), "spline matrix"); m = (tri_diag *) gp_alloc((num_points - 2) * sizeof(tri_diag), "spline help matrix"); r = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline right side"); x = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline solution vector"); h = (double *) gp_alloc((num_points - 1) * sizeof(double), "spline help vector"); xp = (double *) gp_alloc((num_points) * sizeof(double), "x pos"); yp = (double *) gp_alloc((num_points) * sizeof(double), "y pos"); /* KB 981107: With logarithmic axis first convert back to linear scale */ if (log_array[xaxis]) { for (i = 0; i <= num_points - 1; i++) xp[i] = exp(this_points[i].x * log_base_array[xaxis]); } else { for (i = 0; i <= num_points - 1; i++) xp[i] = this_points[i].x; } if (log_array[yaxis]) { for (i = 0; i <= num_points - 1; i++) yp[i] = exp(this_points[i].y * log_base_array[yaxis]); } else { for (i = 0; i <= num_points - 1; i++) yp[i] = this_points[i].y; } for (i = 0; i <= num_points - 2; i++) h[i] = xp[i + 1] - xp[i]; /* set up the matrix and the vector */ for (i = 0; i <= num_points - 3; i++) { r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1] - (yp[i + 1] - yp[i]) / h[i]); if (i < 1) m[i][0] = 0; else m[i][0] = h[i]; m[i][1] = 2 * (h[i] + h[i + 1]); if (i > num_points - 4) m[i][2] = 0; else m[i][2] = h[i + 1]; } /* solve the matrix */ if (!solve_tri_diag(m, r, x, num_points - 2)) { free(h); free(x); free(r); free(m); free(xp); free(yp); int_error("Can't calculate cubic splines", NO_CARET); } sc[0][2] = 0; for (i = 1; i <= num_points - 2; i++) sc[i][2] = x[i - 1]; sc[num_points - 1][2] = 0; for (i = 0; i <= num_points - 1; i++) sc[i][0] = yp[i]; for (i = 0; i <= num_points - 2; i++) { sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i] - h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]); sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i]; } free(h); free(x); free(r); free(m); free(xp); free(yp); return (sc); } static void do_cubic(plot, sc, first_point, num_points, dest) struct curve_points *plot; /* still containes old plot->points */ spline_coeff *sc; /* generated by cp_tridiag */ int first_point; /* where to start in plot->points */ int num_points; /* to determine end in plot->points */ struct coordinate *dest; /* where to put the interpolated data */ { double xdiff, temp, x, y; int i, l; int xaxis = plot->x_axis; int yaxis = plot->y_axis; /* HBB 980308: added 'GPHUGE' tag */ struct coordinate GPHUGE *this_points; /* 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]; } this_points = (plot->points) + first_point; l = 0; xdiff = (this_points[num_points - 1].x - this_points[0].x) / (samples - 1); for (i = 0; i < samples; i++) { x = this_points[0].x + i * xdiff; while ((x >= this_points[l + 1].x) && (l < num_points - 2)) l++; /* KB 981107: With logarithmic x axis the values were converted back to linear */ /* scale before calculating the coefficients. Use exponential for log x values. */ if (log_array[xaxis]) { temp = exp(x * log_base_array[xaxis]) - exp(this_points[l].x * log_base_array[xaxis]); y = ((sc[l][3] * temp + sc[l][2]) * temp + sc[l][1]) * temp + sc[l][0]; } else { temp = x - this_points[l].x; y = ((sc[l][3] * temp + sc[l][2]) * temp + sc[l][1]) * temp + sc[l][0]; } /* With logarithmic y axis, we need to convert from linear to log scale now. */ if (log_array[yaxis]) { if (y > 0.) y = log(y) / log_base_array[yaxis]; else y = symin - (symax - symin); } 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); } /* * This is the main entry point used. As stated in the header, it is fine, * but I'm not too happy with it. */ void gen_interp(plot) struct curve_points *plot; { spline_coeff *sc; double *bc; struct coordinate *new_points; int i, curves; int first_point, num_points; curves = num_curves(plot); new_points = (struct coordinate *) gp_alloc((samples + 1) * curves * sizeof(struct coordinate), "interpolation table"); first_point = 0; for (i = 0; i < curves; i++) { num_points = next_curve(plot, &first_point); switch (plot->plot_smooth) { case CSPLINES: sc = cp_tridiag(plot, first_point, num_points); do_cubic(plot, sc, first_point, num_points, new_points + i * (samples + 1)); free(sc); break; case ACSPLINES: sc = cp_approx_spline(plot, first_point, num_points); do_cubic(plot, sc, first_point, num_points, new_points + i * (samples + 1)); free(sc); break; case BEZIER: case SBEZIER: bc = cp_binomial(num_points); do_bezier(plot, bc, first_point, num_points, new_points + i * (samples + 1)); free((char *) bc); break; default: /* keep gcc -Wall quiet */ ; } new_points[(i + 1) * (samples + 1) - 1].type = UNDEFINED; first_point += num_points; } free(plot->points); plot->points = new_points; plot->p_max = curves * (samples + 1); plot->p_count = plot->p_max - 1; return; } /* * sort_points * * sort data succession for further evaluation by plot_splines, etc. * This routine is mainly introduced for compilers *NOT* supporting the * UNIX qsort() routine. You can then easily replace it by more convenient * stuff for your compiler. * (MGR 1992) */ int compare_points(argp1, argp2) SORTFUNC_ARGS argp1; SORTFUNC_ARGS argp2; { const struct coordinate *p1 = argp1; const struct coordinate *p2 = argp2; if (p1->x > p2->x) return (1); if (p1->x < p2->x) return (-1); return (0); } void sort_points(plot) struct curve_points *plot; { int first_point, num_points; first_point = 0; while ((num_points = next_curve(plot, &first_point)) > 0) { /* Sort this set of points, does qsort handle 1 point correctly? */ qsort((char *) (plot->points + first_point), num_points, sizeof(struct coordinate), compare_points); first_point += num_points; } return; } /* * cp_implode() if averaging is selected this function computes the new * entries and shortens the whole thing to the necessary * size * MGR Addendum */ void cp_implode(cp) struct curve_points *cp; { int first_point, num_points; int i, j, k; double x, y, sux, slx, suy, sly; enum coord_type dot; j = 0; first_point = 0; while ((num_points = next_curve(cp, &first_point)) > 0) { k = 0; for (i = first_point; i < first_point + num_points; i++) { if (!k) { x = cp->points[i].x; y = cp->points[i].y; sux = cp->points[i].xhigh; slx = cp->points[i].xlow; suy = cp->points[i].yhigh; sly = cp->points[i].ylow; dot = INRANGE; if (cp->points[i].type != INRANGE) dot = UNDEFINED; /* This means somthing other than usual *//* just signal to check if INRANGE */ k = 1; } else if (cp->points[i].x == x) { y += cp->points[i].y; sux += cp->points[i].xhigh; slx += cp->points[i].xlow; suy += cp->points[i].yhigh; sly += cp->points[i].ylow; if (cp->points[i].type != INRANGE) dot = UNDEFINED; k++; } else { 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 (dot != INRANGE) { if ((cp->points[j].x > xmax) || (cp->points[j].x < xmin)) cp->points[j].type = OUTRANGE; else if (!autoscale_ly) { if ((cp->points[j].y > ymax) || (cp->points[j].y < ymin)) cp->points[j].type = OUTRANGE; } else cp->points[j].type = INRANGE; } 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 (dot != INRANGE) { if ((cp->points[j].x > xmax) || (cp->points[j].x < xmin)) cp->points[j].type = OUTRANGE; else if (!autoscale_ly) { if ((cp->points[j].y > ymax) || (cp->points[j].y < ymin)) cp->points[j].type = OUTRANGE; } else cp->points[j].type = INRANGE; } 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); }