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authorLars-Dominik Braun <lars@6xq.net>2015-05-02 21:36:31 +0200
committerLars-Dominik Braun <lars@6xq.net>2015-05-02 21:36:31 +0200
commitb2dfbdf4d9644c684c938cb2730deab66aa06d9b (patch)
tree2710c26a94f8c85887389619682892363303f9db /interpolation.c
parentfb1c90e18b0d77a8b4035461722b89c7db46db51 (diff)
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+/*
+ FLAM3 - cosmic recursive fractal flames
+ Copyright (C) 1992-2009 Spotworks LLC
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+
+#include "interpolation.h"
+#include "palettes.h"
+
+double adjust_percentage(double in) {
+
+ if (in==0.0)
+ return(0.0);
+ else
+ return(pow(10.0, -log(1.0/in)/log(2)));
+
+}
+
+double motion_funcs(int funcnum, double timeval) {
+
+ /* motion funcs should be cyclic, and equal to 0 at integral time values */
+ /* abs peak values should be not be greater than 1 */
+ if (funcnum==MOTION_SIN) {
+ return (sin(2.0*M_PI*timeval));
+ } else if (funcnum==MOTION_TRIANGLE) {
+ double fr = fmod(timeval,1.0);
+
+ if (fr<0) fr+= 1.0;
+
+ if (fr<=.25)
+ fr = 4.0 * fr;
+ else if (fr<=.75)
+ fr = -4.0 * fr + 2.0;
+ else
+ fr = 4.0 * fr - 4.0;
+
+ return(fr);
+ } else { //if (funcnum==MOTION_HILL) {
+ return( (1.0-cos(2.0*M_PI*timeval)) * 0.5);
+ }
+
+}
+
+double det_matrix(double s[2][2]) {
+ return s[0][0] * s[1][1] - s[0][1] * s[1][0];
+}
+
+int id_matrix(double s[3][2]) {
+ return
+ (s[0][0] == 1.0) &&
+ (s[0][1] == 0.0) &&
+ (s[1][0] == 0.0) &&
+ (s[1][1] == 1.0) &&
+ (s[2][0] == 0.0) &&
+ (s[2][1] == 0.0);
+}
+
+int zero_matrix(double s[3][2]) {
+ return
+ (s[0][0] == 0.0) &&
+ (s[0][1] == 0.0) &&
+ (s[1][0] == 0.0) &&
+ (s[1][1] == 0.0) &&
+ (s[2][0] == 0.0) &&
+ (s[2][1] == 0.0);
+}
+
+void copy_matrix(double to[3][2], double from[3][2]) {
+
+ to[0][0] = from[0][0];
+ to[0][1] = from[0][1];
+ to[1][0] = from[1][0];
+ to[1][1] = from[1][1];
+ to[2][0] = from[2][0];
+ to[2][1] = from[2][1];
+}
+
+
+void clear_matrix(double m[3][2]) {
+ m[0][0] = 0.0;
+ m[0][1] = 0.0;
+ m[1][0] = 0.0;
+ m[1][1] = 0.0;
+ m[2][0] = 0.0;
+ m[2][1] = 0.0;
+}
+
+void sum_matrix(double s, double m1[3][2], double m2[3][2]) {
+
+ m2[0][0] += s * m1[0][0];
+ m2[0][1] += s * m1[0][1];
+ m2[1][0] += s * m1[1][0];
+ m2[1][1] += s * m1[1][1];
+ m2[2][0] += s * m1[2][0];
+ m2[2][1] += s * m1[2][1];
+}
+
+void mult_matrix(double s1[2][2], double s2[2][2], double d[2][2]) {
+ d[0][0] = s1[0][0] * s2[0][0] + s1[1][0] * s2[0][1];
+ d[1][0] = s1[0][0] * s2[1][0] + s1[1][0] * s2[1][1];
+ d[0][1] = s1[0][1] * s2[0][0] + s1[1][1] * s2[0][1];
+ d[1][1] = s1[0][1] * s2[1][0] + s1[1][1] * s2[1][1];
+}
+
+int compare_xforms(const void *av, const void *bv) {
+ flam3_xform *a = (flam3_xform *) av;
+ flam3_xform *b = (flam3_xform *) bv;
+ double aa[2][2];
+ double bb[2][2];
+ double ad, bd;
+
+ aa[0][0] = a->c[0][0];
+ aa[0][1] = a->c[0][1];
+ aa[1][0] = a->c[1][0];
+ aa[1][1] = a->c[1][1];
+ bb[0][0] = b->c[0][0];
+ bb[0][1] = b->c[0][1];
+ bb[1][0] = b->c[1][0];
+ bb[1][1] = b->c[1][1];
+ ad = det_matrix(aa);
+ bd = det_matrix(bb);
+
+ if (a->color_speed > b->color_speed) return 1;
+ if (a->color_speed < b->color_speed) return -1;
+ if (a->color_speed) {
+ if (ad < 0) return -1;
+ if (bd < 0) return 1;
+ ad = atan2(a->c[0][0], a->c[0][1]);
+ bd = atan2(b->c[0][0], b->c[0][1]);
+ }
+
+ if (ad < bd) return -1;
+ if (ad > bd) return 1;
+ return 0;
+}
+
+void interpolate_cmap(flam3_palette cmap, double blend,
+ int index0, double hue0, int index1, double hue1) {
+
+ flam3_palette p0,p1;
+ int i, j, rcode;
+
+ rcode = flam3_get_palette(index0, p0, hue0);
+ if (rcode<0)
+ fprintf(stderr,"unable to retrieve palette %d, setting to white\n", index0);
+ rcode = flam3_get_palette(index1, p1, hue1);
+ if (rcode<0)
+ fprintf(stderr,"unable to retrieve palette %d, setting to white\n", index1);
+
+ for (i = 0; i < 256; i++) {
+ double t[5], s[5];
+
+ rgb2hsv(p0[i].color, s);
+ rgb2hsv(p1[i].color, t);
+
+ s[3] = p0[i].color[3];
+ t[3] = p1[i].color[3];
+
+ s[4] = p0[i].index;
+ t[4] = p1[i].index;
+
+ for (j = 0; j < 5; j++)
+ t[j] = ((1.0-blend) * s[j]) + (blend * t[j]);
+
+ hsv2rgb(t, cmap[i].color);
+ cmap[i].color[3] = t[3];
+ cmap[i].index = t[4];
+ }
+}
+
+void interp_and_convert_back(double *c, int ncps, int xfi, double cxang[4][2],
+ double cxmag[4][2], double cxtrn[4][2],double store_array[3][2]) {
+
+ int i,col;
+
+ double accang[2],accmag[2];
+ double expmag;
+ int accmode[2];
+
+ accang[0] = 0.0;
+ accang[1] = 0.0;
+ accmag[0] = 0.0;
+ accmag[1] = 0.0;
+
+ accmode[0]=accmode[1]=0;
+
+ /* accumulation mode defaults to logarithmic, but in special */
+ /* cases we want to switch to linear accumulation */
+ for (col=0; col<2; col++) {
+ for (i=0; i<ncps; i++) {
+ if (log(cxmag[i][col])<-10)
+ accmode[col]=1; // Mode set to linear interp
+ }
+ }
+
+ for (i=0; i<ncps; i++) {
+ for (col=0; col<2; col++) {
+
+ accang[col] += c[i] * cxang[i][col];
+
+ if (accmode[col]==0)
+ accmag[col] += c[i] * log(cxmag[i][col]);
+ else
+ accmag[col] += c[i] * (cxmag[i][col]);
+
+ /* translation is ready to go */
+ store_array[2][col] += c[i] * cxtrn[i][col];
+ }
+ }
+
+ /* Convert the angle back to rectangular */
+ for (col=0;col<2;col++) {
+ if (accmode[col]==0)
+ expmag = exp(accmag[col]);
+ else
+ expmag = accmag[col];
+
+ store_array[col][0] = expmag * cos(accang[col]);
+ store_array[col][1] = expmag * sin(accang[col]);
+ }
+
+}
+
+void convert_linear_to_polar(flam3_genome *cp, int ncps, int xfi, int cflag,
+ double cxang[4][2], double cxmag[4][2], double cxtrn[4][2]) {
+
+ double c1[2],d,t,refang;
+ int col,k;
+ int zlm[2];
+
+ for (k=0; k<ncps;k++) {
+
+ /* Establish the angles and magnitudes for each component */
+ /* Keep translation linear */
+ zlm[0]=zlm[1]=0;
+ for (col=0;col<2;col++) {
+
+ if (cflag==0) {
+ c1[0] = cp[k].xform[xfi].c[col][0];
+ c1[1] = cp[k].xform[xfi].c[col][1];
+ t = cp[k].xform[xfi].c[2][col];
+ } else {
+ c1[0] = cp[k].xform[xfi].post[col][0];
+ c1[1] = cp[k].xform[xfi].post[col][1];
+ t = cp[k].xform[xfi].post[2][col];
+ }
+
+ cxang[k][col] = atan2(c1[1],c1[0]);
+ cxmag[k][col] = sqrt(c1[0]*c1[0] + c1[1]*c1[1]);
+
+ if (cxmag[k][col]== 0.0)
+ zlm[col]=1;
+
+ cxtrn[k][col] = t;
+ }
+
+ if (zlm[0]==1 && zlm[1]==0)
+ cxang[k][0] = cxang[k][1];
+ else if (zlm[0]==0 && zlm[1]==1)
+ cxang[k][1] = cxang[k][0];
+
+ }
+
+ /* Make sure the rotation is the shorter direction around the circle */
+ /* by adjusting each angle in succession, and rotate clockwise if 180 degrees */
+ for (col=0; col<2; col++) {
+ for (k=1;k<ncps;k++) {
+
+ /* Adjust angles differently if we have an asymmetric case */
+ if (cp[k].xform[xfi].wind[col]>0 && cflag==0) {
+
+ /* Adjust the angles to make sure that it's within wind:wind+2pi */
+ refang = cp[k].xform[xfi].wind[col] - 2*M_PI;
+
+ /* Make sure both angles are within [refang refang+2*pi] */
+ while(cxang[k-1][col] < refang)
+ cxang[k-1][col] += 2*M_PI;
+
+ while(cxang[k-1][col] > refang + 2*M_PI)
+ cxang[k-1][col] -= 2*M_PI;
+
+ while(cxang[k][col] < refang)
+ cxang[k][col] += 2*M_PI;
+
+ while(cxang[k][col] > refang + 2*M_PI)
+ cxang[k][col] -= 2*M_PI;
+
+ } else {
+
+ /* Normal way of adjusting angles */
+ d = cxang[k][col]-cxang[k-1][col];
+
+ /* Adjust to avoid the -pi/pi discontinuity */
+ if (d > M_PI+EPS)
+ cxang[k][col] -= 2*M_PI;
+ else if (d < -(M_PI-EPS) ) /* Forces clockwise rotation at 180 */
+ cxang[k][col] += 2*M_PI;
+ }
+ }
+ }
+}
+
+void interpolate_catmull_rom(flam3_genome cps[], double t, flam3_genome *result) {
+ double t2 = t * t;
+ double t3 = t2 * t;
+ double cmc[4];
+
+ cmc[0] = (2*t2 - t - t3) / 2;
+ cmc[1] = (3*t3 - 5*t2 + 2) / 2;
+ cmc[2] = (4*t2 - 3*t3 + t) / 2;
+ cmc[3] = (t3 - t2) / 2;
+
+ flam3_interpolate_n(result, 4, cps, cmc, 0);
+}
+
+double smoother(double t) {
+ return 3*t*t - 2*t*t*t;
+}
+
+double get_stagger_coef(double t, double stagger_prc, int num_xforms, int this_xform) {
+
+ /* max_stag is the spacing between xform start times if stagger_prc = 1.0 */
+ double max_stag = (double)(num_xforms-1)/num_xforms;
+
+ /* scale the spacing by stagger_prc */
+ double stag_scaled = stagger_prc * max_stag;
+
+ /* t ranges from 1 to 0 (the contribution of cp[0] to the blend) */
+ /* the first line below makes the first xform interpolate first */
+ /* the second line makes the last xform interpolate first */
+ double st = stag_scaled * (num_xforms - 1 - this_xform) / (num_xforms-1);
+// double st = stag_scaled * (this_xform) / (num_xforms-1);
+ double et = st + (1-stag_scaled);
+
+// printf("t=%f xf:%d st=%f et=%f : : %f\n",t,this_xform,st,et,smoother((t-st)/(1-stag_scaled)));
+
+ if (t <= st)
+ return (0);
+ else if (t >= et)
+ return (1);
+ else
+ return ( smoother((t-st)/(1-stag_scaled)) );
+
+}
+
+
+
+/* all cpi and result must be aligned (have the same number of xforms,
+ and have final xform in the same slot) */
+void flam3_interpolate_n(flam3_genome *result, int ncp,
+ flam3_genome *cpi, double *c, double stagger) {
+ int i, j, k, numstd;
+
+ if (flam3_palette_interpolation_hsv == cpi[0].palette_interpolation) {
+
+ for (i = 0; i < 256; i++) {
+ double t[3], s[5];
+ int alpha1 = 1;
+
+ s[0] = s[1] = s[2] = s[3] = s[4] = 0.0;
+
+ for (k = 0; k < ncp; k++) {
+ rgb2hsv(cpi[k].palette[i].color, t);
+ for (j = 0; j < 3; j++)
+ s[j] += c[k] * t[j];
+
+ s[3] += c[k] * cpi[k].palette[i].color[3];
+ if (cpi[k].palette[i].color[3] != 1.0)
+ alpha1 = 0;
+ s[4] += c[k] * cpi[k].palette[i].index;
+
+ }
+
+ if (alpha1 == 1)
+ s[3] = 1.0;
+
+ hsv2rgb(s, result->palette[i].color);
+ result->palette[i].color[3] = s[3];
+ result->palette[i].index = s[4];
+
+ for (j = 0; j < 4; j++) {
+ if (result->palette[i].color[j] < 0.0)
+ result->palette[i].color[j] = 0.0;
+ if (result->palette[i].color[j] > 1.0)
+ result->palette[i].color[j] = 1.0;
+ }
+
+ if (result->palette[i].index < 0.0)
+ result->palette[i].index = 0.0;
+ if (result->palette[i].index > 255.0)
+ result->palette[i].index = 255.0;
+ }
+ } else {
+ /* Sweep - not the best option for float indices */
+ for (i = 0; i < 256; i++) {
+ j = (i < (256 * c[0])) ? 0 : 1;
+ result->palette[i] = cpi[j].palette[i];
+ }
+ }
+
+ result->palette_index = flam3_palette_random;
+ result->symmetry = 0;
+ result->spatial_filter_select = cpi[0].spatial_filter_select;
+ result->temporal_filter_type = cpi[0].temporal_filter_type;
+ result->palette_mode = cpi[0].palette_mode;
+
+ result->interpolation_type = cpi[0].interpolation_type;
+ INTERP(brightness);
+ INTERP(contrast);
+ INTERP(highlight_power);
+ INTERP(gamma);
+ INTERP(vibrancy);
+ INTERP(hue_rotation);
+ INTERI(width);
+ INTERI(height);
+ INTERI(spatial_oversample);
+ INTERP(center[0]);
+ INTERP(center[1]);
+ INTERP(rot_center[0]);
+ INTERP(rot_center[1]);
+ INTERP(background[0]);
+ INTERP(background[1]);
+ INTERP(background[2]);
+ INTERP(pixels_per_unit);
+ INTERP(spatial_filter_radius);
+ INTERP(temporal_filter_exp);
+ INTERP(temporal_filter_width);
+ INTERP(sample_density);
+ INTERP(zoom);
+ INTERP(rotate);
+ INTERI(nbatches);
+ INTERI(ntemporal_samples);
+ INTERP(estimator);
+ INTERP(estimator_minimum);
+ INTERP(estimator_curve);
+ INTERP(gam_lin_thresh);
+
+ /* Interpolate the chaos array */
+ numstd = cpi[0].num_xforms - (cpi[0].final_xform_index >= 0);
+ for (i=0;i<numstd;i++) {
+ for (j=0;j<numstd;j++) {
+ INTERP(chaos[i][j]);
+ if (result->chaos[i][j]<0) result->chaos[i][j]=0;
+ //chaos can be > 1
+ //if (result->chaos[i][j]>1) result->chaos[i][j]=1.0;
+ }
+ }
+
+ /* Interpolate each xform */
+ for (i = 0; i < cpi[0].num_xforms; i++) {
+
+ double csave[2];
+ double td;
+ int all_id;
+ int nx = cpi[0].num_xforms-(cpi[0].final_xform_index>=0);
+
+ if (ncp==2 && stagger>0 && i!=cpi[0].final_xform_index) {
+ csave[0] = c[0];
+ csave[1] = c[1];
+ c[0] = get_stagger_coef(csave[0],stagger,nx,i);
+ c[1] = 1.0-c[0];
+ }
+
+
+ INTERP(xform[i].density);
+ td = result->xform[i].density;
+ result->xform[i].density = (td < 0.0) ? 0.0 : td;
+ INTERP(xform[i].color);
+ if (result->xform[i].color<0) result->xform[i].color=0;
+ if (result->xform[i].color>1) result->xform[i].color=1;
+
+ INTERP(xform[i].color_speed);
+ if (result->xform[i].color_speed<0) result->xform[i].color_speed=0;
+ if (result->xform[i].color_speed>1) result->xform[i].color_speed=1;
+
+ INTERP(xform[i].opacity);
+ INTERP(xform[i].animate);
+ INTERP(xform[i].blob_low);
+ INTERP(xform[i].blob_high);
+ INTERP(xform[i].blob_waves);
+ INTERP(xform[i].pdj_a);
+ INTERP(xform[i].pdj_b);
+ INTERP(xform[i].pdj_c);
+ INTERP(xform[i].pdj_d);
+ INTERP(xform[i].fan2_x);
+ INTERP(xform[i].fan2_y);
+ INTERP(xform[i].rings2_val);
+ INTERP(xform[i].perspective_angle);
+ INTERP(xform[i].perspective_dist);
+ INTERP(xform[i].julian_power);
+ INTERP(xform[i].julian_dist);
+ INTERP(xform[i].juliascope_power);
+ INTERP(xform[i].juliascope_dist);
+ INTERP(xform[i].radial_blur_angle);
+ INTERP(xform[i].pie_slices);
+ INTERP(xform[i].pie_rotation);
+ INTERP(xform[i].pie_thickness);
+ INTERP(xform[i].ngon_sides);
+ INTERP(xform[i].ngon_power);
+ INTERP(xform[i].ngon_circle);
+ INTERP(xform[i].ngon_corners);
+ INTERP(xform[i].curl_c1);
+ INTERP(xform[i].curl_c2);
+ INTERP(xform[i].rectangles_x);
+ INTERP(xform[i].rectangles_y);
+ INTERP(xform[i].amw_amp);
+ INTERP(xform[i].disc2_rot);
+ INTERP(xform[i].disc2_twist);
+ INTERP(xform[i].super_shape_rnd);
+ INTERP(xform[i].super_shape_m);
+ INTERP(xform[i].super_shape_n1);
+ INTERP(xform[i].super_shape_n2);
+ INTERP(xform[i].super_shape_n3);
+ INTERP(xform[i].super_shape_holes);
+ INTERP(xform[i].flower_petals);
+ INTERP(xform[i].flower_holes);
+ INTERP(xform[i].conic_eccentricity);
+ INTERP(xform[i].conic_holes);
+ INTERP(xform[i].parabola_height);
+ INTERP(xform[i].parabola_width);
+ INTERP(xform[i].bent2_x);
+ INTERP(xform[i].bent2_y);
+ INTERP(xform[i].bipolar_shift);
+ INTERP(xform[i].cell_size);
+ INTERP(xform[i].cpow_r);
+ INTERP(xform[i].cpow_i);
+ INTERP(xform[i].cpow_power);
+ INTERP(xform[i].curve_xamp);
+ INTERP(xform[i].curve_yamp);
+ INTERP(xform[i].curve_xlength);
+ INTERP(xform[i].curve_ylength);
+ INTERP(xform[i].escher_beta);
+ INTERP(xform[i].lazysusan_x);
+ INTERP(xform[i].lazysusan_y);
+ INTERP(xform[i].lazysusan_twist);
+ INTERP(xform[i].lazysusan_space);
+ INTERP(xform[i].lazysusan_spin);
+ INTERP(xform[i].modulus_x);
+ INTERP(xform[i].modulus_y);
+ INTERP(xform[i].oscope_separation);
+ INTERP(xform[i].oscope_frequency);
+ INTERP(xform[i].oscope_amplitude);
+ INTERP(xform[i].oscope_damping);
+ INTERP(xform[i].popcorn2_x);
+ INTERP(xform[i].popcorn2_y);
+ INTERP(xform[i].popcorn2_c);
+ INTERP(xform[i].separation_x);
+ INTERP(xform[i].separation_xinside);
+ INTERP(xform[i].separation_y);
+ INTERP(xform[i].separation_yinside);
+ INTERP(xform[i].split_xsize);
+ INTERP(xform[i].split_ysize);
+ INTERP(xform[i].splits_x);
+ INTERP(xform[i].splits_y);
+ INTERP(xform[i].stripes_space);
+ INTERP(xform[i].stripes_warp);
+ INTERP(xform[i].wedge_angle);
+ INTERP(xform[i].wedge_hole);
+ INTERP(xform[i].wedge_count);
+ INTERP(xform[i].wedge_swirl);
+ INTERP(xform[i].wedge_julia_angle);
+ INTERP(xform[i].wedge_julia_count);
+ INTERP(xform[i].wedge_julia_power);
+ INTERP(xform[i].wedge_julia_dist);
+ INTERP(xform[i].wedge_sph_angle);
+ INTERP(xform[i].wedge_sph_hole);
+ INTERP(xform[i].wedge_sph_count);
+ INTERP(xform[i].wedge_sph_swirl);
+ INTERP(xform[i].whorl_inside);
+ INTERP(xform[i].whorl_outside);
+ INTERP(xform[i].waves2_scalex);
+ INTERP(xform[i].waves2_scaley);
+ INTERP(xform[i].waves2_freqx);
+ INTERP(xform[i].waves2_freqy);
+ INTERP(xform[i].auger_sym);
+ INTERP(xform[i].auger_weight);
+ INTERP(xform[i].auger_freq);
+ INTERP(xform[i].auger_scale);
+ INTERP(xform[i].flux_spread);
+ INTERP(xform[i].mobius_re_a);
+ INTERP(xform[i].mobius_im_a);
+ INTERP(xform[i].mobius_re_b);
+ INTERP(xform[i].mobius_im_b);
+ INTERP(xform[i].mobius_re_c);
+ INTERP(xform[i].mobius_im_c);
+ INTERP(xform[i].mobius_re_d);
+ INTERP(xform[i].mobius_im_d);
+
+ for (j = 0; j < flam3_nvariations; j++)
+ INTERP(xform[i].var[j]);
+
+ if (flam3_inttype_log == cpi[0].interpolation_type) {
+ double cxmag[4][2]; // XXX why only 4? should be ncp
+ double cxang[4][2];
+ double cxtrn[4][2];
+
+ /* affine part */
+ clear_matrix(result->xform[i].c);
+ convert_linear_to_polar(cpi,ncp,i,0,cxang,cxmag,cxtrn);
+ interp_and_convert_back(c, ncp, i, cxang, cxmag, cxtrn,result->xform[i].c);
+
+ /* post part */
+ all_id = 1;
+ for (k=0; k<ncp; k++)
+ all_id &= id_matrix(cpi[k].xform[i].post);
+
+ clear_matrix(result->xform[i].post);
+ if (all_id) {
+ result->xform[i].post[0][0] = 1.0;
+ result->xform[i].post[1][1] = 1.0;
+ } else {
+ convert_linear_to_polar(cpi,ncp,i,1,cxang,cxmag,cxtrn);
+ interp_and_convert_back(c, ncp, i, cxang, cxmag, cxtrn,result->xform[i].post);
+ }
+
+ } else {
+
+ /* Interpolate c matrix & post */
+ clear_matrix(result->xform[i].c);
+ clear_matrix(result->xform[i].post);
+ all_id = 1;
+ for (k = 0; k < ncp; k++) {
+ sum_matrix(c[k], cpi[k].xform[i].c, result->xform[i].c);
+ sum_matrix(c[k], cpi[k].xform[i].post, result->xform[i].post);
+
+ all_id &= id_matrix(cpi[k].xform[i].post);
+
+ }
+ if (all_id) {
+ clear_matrix(result->xform[i].post);
+ result->xform[i].post[0][0] = 1.0;
+ result->xform[i].post[1][1] = 1.0;
+ }
+ }
+
+ if (ncp==2 && stagger>0 && i!=cpi[0].final_xform_index) {
+ c[0] = csave[0];
+ c[1] = csave[1];
+ }
+
+ }
+
+}
+
+void establish_asymmetric_refangles(flam3_genome *cp, int ncps) {
+
+ int k, xfi, col;
+
+ double cxang[4][2],d,c1[2];
+
+ for (xfi=0; xfi<cp[0].num_xforms; xfi++) {
+
+ /* Final xforms don't rotate regardless of their symmetry */
+ if (cp[0].final_xform_enable==1 && xfi==cp[0].final_xform_index)
+ continue;
+
+ for (k=0; k<ncps;k++) {
+
+ /* Establish the angle for each component */
+ /* Should potentially functionalize */
+ for (col=0;col<2;col++) {
+
+ c1[0] = cp[k].xform[xfi].c[col][0];
+ c1[1] = cp[k].xform[xfi].c[col][1];
+
+ cxang[k][col] = atan2(c1[1],c1[0]);
+ }
+ }
+
+ for (k=1; k<ncps; k++) {
+
+ for (col=0;col<2;col++) {
+
+ int sym0,sym1;
+ int padsymflag;
+
+ d = cxang[k][col]-cxang[k-1][col];
+
+ /* Adjust to avoid the -pi/pi discontinuity */
+ if (d > M_PI+EPS)
+ cxang[k][col] -= 2*M_PI;
+ else if (d < -(M_PI-EPS) )
+ cxang[k][col] += 2*M_PI;
+
+ /* If this is an asymmetric case, store the NON-symmetric angle */
+ /* Check them pairwise and store the reference angle in the second */
+ /* to avoid overwriting if asymmetric on both sides */
+ padsymflag = 0;
+
+ sym0 = (cp[k-1].xform[xfi].animate==0 || (cp[k-1].xform[xfi].padding==1 && padsymflag));
+ sym1 = (cp[k].xform[xfi].animate==0 || (cp[k].xform[xfi].padding==1 && padsymflag));
+
+ if ( sym1 && !sym0 )
+ cp[k].xform[xfi].wind[col] = cxang[k-1][col] + 2*M_PI;
+ else if ( sym0 && !sym1 )
+ cp[k].xform[xfi].wind[col] = cxang[k][col] + 2*M_PI;
+
+ }
+ }
+ }
+}
+
+void flam3_align(flam3_genome *dst, flam3_genome *src, int nsrc) {
+ int i, tfx, tnx, max_nx = 0, max_fx = 0;
+ int already_aligned=1;
+ int xf,j;
+ int ii,fnd;
+ double normed;
+ int usethisone;
+
+ usethisone = (nsrc/2) - 1;
+
+ max_nx = src[0].num_xforms - (src[0].final_xform_index >= 0);
+ max_fx = src[0].final_xform_enable;
+
+ for (i = 1; i < nsrc; i++) {
+ tnx = src[i].num_xforms - (src[i].final_xform_index >= 0);
+ if (max_nx != tnx) {
+ already_aligned = 0;
+ if (tnx > max_nx) max_nx = tnx;
+ }
+
+ tfx = src[i].final_xform_enable;
+ if (max_fx != tfx) {
+ already_aligned = 0;
+ max_fx |= tfx;
+ }
+ }
+
+ /* Pad the cps to equal xforms */
+ for (i = 0; i < nsrc; i++) {
+ flam3_copyx(&dst[i], &src[i], max_nx, max_fx);
+ }
+
+ /* Skip if this genome is compatibility mode */
+ if (dst[usethisone].interpolation_type == flam3_inttype_compat ||
+ dst[usethisone].interpolation_type == flam3_inttype_older)
+ return;
+
+
+ /* Check to see if there's a parametric variation present in one xform */
+ /* but not in an aligned xform. If this is the case, use the parameters */
+ /* from the xform with the variation as the defaults for the blank one. */
+
+ /* All genomes will have the same number of xforms at this point */
+ /* num = max_nx + max_fx */
+ for (i = 0; i<nsrc; i++) {
+
+
+ for (xf = 0; xf<max_nx+max_fx; xf++) {
+
+ /* Loop over the variations to see which of them are set to 0 */
+ /* Note that there are no parametric variations < 23 */
+ for (j = 23; j < flam3_nvariations; j++) {
+
+ if (dst[i].xform[xf].var[j]==0) {
+
+ if (i>0) {
+
+ /* Check to see if the prior genome's xform is populated */
+ if (dst[i-1].xform[xf].var[j] != 0) {
+
+ /* Copy the prior genome's parameters and continue */
+ flam3_copy_params(&(dst[i].xform[xf]), &(dst[i-1].xform[xf]), j);
+ continue;
+ }
+
+ } else if (i<nsrc-1) {
+
+ /* Check to see if the next genome's xform is populated */
+ if (dst[i+1].xform[xf].var[j] != 0) {
+
+ /* Copy the next genome's parameters and continue */
+ flam3_copy_params(&(dst[i].xform[xf]), &(dst[i+1].xform[xf]), j);
+ continue;
+ }
+ }
+ }
+ } /* variations */
+
+ if (dst[i].xform[xf].padding == 1 && !already_aligned) {
+
+ /* This is a new xform. Let's see if we can choose a better 'identity' xform. */
+ /* Check the neighbors to see if any of these variations are used: */
+ /* rings2, fan2, blob, perspective, julian, juliascope, ngon, curl, super_shape, split */
+ /* If so, we can use a better starting point for these */
+
+ /* Remove linear from the list */
+ dst[i].xform[xf].var[0] = 0.0;
+
+ /* Look through all of the 'companion' xforms to see if we get a match on any of these */
+ fnd=0;
+
+ /* Only do the next substitution for log interpolation */
+ if ( (i==0 && dst[i].interpolation_type == flam3_inttype_log)
+ || (i>0 && dst[i-1].interpolation_type==flam3_inttype_log) ) {
+
+ for (ii=-1; ii<=1; ii+=2) {
+
+ /* Skip if out of bounds */
+ if (i+ii<0 || i+ii>=nsrc)
+ continue;
+
+ /* Skip if this is also padding */
+ if (dst[i+ii].xform[xf].padding==1)
+ continue;
+
+ /* Spherical / Ngon (trumps all others due to holes) */
+ /* Interpolate these against a 180 degree rotated identity */
+ /* with weight -1. */
+ /* Added JULIAN/JULIASCOPE to get rid of black wedges */
+ if (dst[i+ii].xform[xf].var[VAR_SPHERICAL]>0 ||
+ dst[i+ii].xform[xf].var[VAR_NGON]>0 ||
+ dst[i+ii].xform[xf].var[VAR_JULIAN]>0 ||
+ dst[i+ii].xform[xf].var[VAR_JULIASCOPE]>0 ||
+ dst[i+ii].xform[xf].var[VAR_POLAR]>0 ||
+ dst[i+ii].xform[xf].var[VAR_WEDGE_SPH]>0 ||
+ dst[i+ii].xform[xf].var[VAR_WEDGE_JULIA]>0) {
+
+ dst[i].xform[xf].var[VAR_LINEAR] = -1.0;
+ /* Set the coefs appropriately */
+ dst[i].xform[xf].c[0][0] = -1.0;
+ dst[i].xform[xf].c[0][1] = 0.0;
+ dst[i].xform[xf].c[1][0] = 0.0;
+ dst[i].xform[xf].c[1][1] = -1.0;
+ dst[i].xform[xf].c[2][0] = 0.0;
+ dst[i].xform[xf].c[2][1] = 0.0;
+ fnd=-1;
+ }
+ }
+
+ }
+
+ if (fnd==0) {
+
+ for (ii=-1; ii<=1; ii+=2) {
+
+ /* Skip if out of bounds */
+ if (i+ii<0 || i+ii>=nsrc)
+ continue;
+
+ /* Skip if also padding */
+ if (dst[i+ii].xform[xf].padding==1)
+ continue;
+
+ /* Rectangles */
+ if (dst[i+ii].xform[xf].var[VAR_RECTANGLES]>0) {
+ dst[i].xform[xf].var[VAR_RECTANGLES] = 1.0;
+ dst[i].xform[xf].rectangles_x = 0.0;
+ dst[i].xform[xf].rectangles_y = 0.0;
+ fnd++;
+ }
+
+ /* Rings 2 */
+ if (dst[i+ii].xform[xf].var[VAR_RINGS2]>0) {
+ dst[i].xform[xf].var[VAR_RINGS2] = 1.0;
+ dst[i].xform[xf].rings2_val = 0.0;
+ fnd++;
+ }
+
+ /* Fan 2 */
+ if (dst[i+ii].xform[xf].var[VAR_FAN2]>0) {
+ dst[i].xform[xf].var[VAR_FAN2] = 1.0;
+ dst[i].xform[xf].fan2_x = 0.0;
+ dst[i].xform[xf].fan2_y = 0.0;
+ fnd++;
+ }
+
+ /* Blob */
+ if (dst[i+ii].xform[xf].var[VAR_BLOB]>0) {
+ dst[i].xform[xf].var[VAR_BLOB] = 1.0;
+ dst[i].xform[xf].blob_low = 1.0;
+ dst[i].xform[xf].blob_high = 1.0;
+ dst[i].xform[xf].blob_waves = 1.0;
+ fnd++;
+ }
+
+ /* Perspective */
+ if (dst[i+ii].xform[xf].var[VAR_PERSPECTIVE]>0) {
+ dst[i].xform[xf].var[VAR_PERSPECTIVE] = 1.0;
+ dst[i].xform[xf].perspective_angle = 0.0;
+ /* Keep the perspective distance as-is */
+ fnd++;
+ }
+
+ /* Curl */
+ if (dst[i+ii].xform[xf].var[VAR_CURL]>0) {
+ dst[i].xform[xf].var[VAR_CURL] = 1.0;
+ dst[i].xform[xf].curl_c1 = 0.0;
+ dst[i].xform[xf].curl_c2 = 0.0;
+ fnd++;
+ }
+
+ /* Super-Shape */
+ if (dst[i+ii].xform[xf].var[VAR_SUPER_SHAPE]>0) {
+ dst[i].xform[xf].var[VAR_SUPER_SHAPE] = 1.0;
+ /* Keep supershape_m the same */
+ dst[i].xform[xf].super_shape_n1 = 2.0;
+ dst[i].xform[xf].super_shape_n2 = 2.0;
+ dst[i].xform[xf].super_shape_n3 = 2.0;
+ dst[i].xform[xf].super_shape_rnd = 0.0;
+ dst[i].xform[xf].super_shape_holes = 0.0;
+ fnd++;
+ }
+ }
+ }
+
+ /* If we didn't have any matches with those, */
+ /* try the affine ones, fan and rings */
+ if (fnd==0) {
+
+ for (ii=-1; ii<=1; ii+=2) {
+
+ /* Skip if out of bounds */
+ if (i+ii<0 || i+ii>=nsrc)
+ continue;
+
+ /* Skip if also a padding xform */
+ if (dst[i+ii].xform[xf].padding==1)
+ continue;
+
+ /* Fan */
+ if (dst[i+ii].xform[xf].var[VAR_FAN]>0) {
+ dst[i].xform[xf].var[VAR_FAN] = 1.0;
+ fnd++;
+ }
+
+ /* Rings */
+ if (dst[i+ii].xform[xf].var[VAR_RINGS]>0) {
+ dst[i].xform[xf].var[VAR_RINGS] = 1.0;
+ fnd++;
+ }
+
+ }
+
+ if (fnd>0) {
+ /* Set the coefs appropriately */
+ dst[i].xform[xf].c[0][0] = 0.0;
+ dst[i].xform[xf].c[0][1] = 1.0;
+ dst[i].xform[xf].c[1][0] = 1.0;
+ dst[i].xform[xf].c[1][1] = 0.0;
+ dst[i].xform[xf].c[2][0] = 0.0;
+ dst[i].xform[xf].c[2][1] = 0.0;
+ }
+ }
+
+ /* If we still have no matches, switch back to linear */
+ if (fnd==0)
+
+ dst[i].xform[xf].var[VAR_LINEAR] = 1.0;
+
+ else if (fnd>0) {
+
+ /* Otherwise, go through and normalize the weights. */
+ normed = 0.0;
+ for (j = 0; j < flam3_nvariations; j++)
+ normed += dst[i].xform[xf].var[j];
+
+ for (j = 0; j < flam3_nvariations; j++)
+ dst[i].xform[xf].var[j] /= normed;
+
+ }
+ }
+ } /* xforms */
+ } /* genomes */
+
+}
+