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-rw-r--r--src/live_effects/spiro.cpp1122
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diff --git a/src/live_effects/spiro.cpp b/src/live_effects/spiro.cpp
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+++ b/src/live_effects/spiro.cpp
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+// SPDX-License-Identifier: GPL-2.0-or-later
+/** @file
+ * C implementation of third-order polynomial spirals.
+ *//*
+ * Authors: see git history
+ * Raph Levien
+ * Johan Engelen
+ *
+ * Copyright (C) 2018 Authors
+ * Released under GNU GPL v2+, read the file 'COPYING' for more information.
+ */
+
+#include "spiro.h"
+
+#include <cmath>
+#include <cstdlib>
+#include <cstring>
+
+#include "display/curve.h"
+
+#define SPIRO_SHOW_INFINITE_COORDINATE_CALLS
+
+namespace Spiro {
+
+void spiro_run(const spiro_cp *src, int src_len, SPCurve &curve)
+{
+ spiro_seg *s = Spiro::run_spiro(src, src_len);
+ Spiro::ConverterSPCurve bc(curve);
+ Spiro::spiro_to_otherpath(s, src_len, bc);
+ free(s);
+}
+
+void spiro_run(const spiro_cp *src, int src_len, Geom::Path &path)
+{
+ spiro_seg *s = Spiro::run_spiro(src, src_len);
+ Spiro::ConverterPath bc(path);
+ Spiro::spiro_to_otherpath(s, src_len, bc);
+ free(s);
+}
+
+
+/************************************
+ * Spiro math
+ */
+
+struct spiro_seg_s {
+ double x;
+ double y;
+ char ty;
+ double bend_th;
+ double ks[4];
+ double seg_ch;
+ double seg_th;
+ double l;
+};
+
+struct bandmat {
+ double a[11]; /* band-diagonal matrix */
+ double al[5]; /* lower part of band-diagonal decomposition */
+};
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846 /* pi */
+#endif
+
+int n = 4;
+
+#ifndef ORDER
+#define ORDER 12
+#endif
+
+/* Integrate polynomial spiral curve over range -.5 .. .5. */
+static void
+integrate_spiro(const double ks[4], double xy[2])
+{
+#if 0
+ int n = 1024;
+#endif
+ double th1 = ks[0];
+ double th2 = .5 * ks[1];
+ double th3 = (1./6) * ks[2];
+ double th4 = (1./24) * ks[3];
+ double x, y;
+ double ds = 1. / n;
+ double ds2 = ds * ds;
+ double ds3 = ds2 * ds;
+ double k0 = ks[0] * ds;
+ double k1 = ks[1] * ds;
+ double k2 = ks[2] * ds;
+ double k3 = ks[3] * ds;
+ int i;
+ double s = .5 * ds - .5;
+
+ x = 0;
+ y = 0;
+
+ for (i = 0; i < n; i++) {
+
+#if ORDER > 2
+ double u, v;
+ double km0, km1, km2, km3;
+
+ if (n == 1) {
+ km0 = k0;
+ km1 = k1 * ds;
+ km2 = k2 * ds2;
+ } else {
+ km0 = (((1./6) * k3 * s + .5 * k2) * s + k1) * s + k0;
+ km1 = ((.5 * k3 * s + k2) * s + k1) * ds;
+ km2 = (k3 * s + k2) * ds2;
+ }
+ km3 = k3 * ds3;
+#endif
+
+ {
+
+#if ORDER == 4
+ double km0_2 = km0 * km0;
+ u = 24 - km0_2;
+ v = km1;
+#endif
+
+#if ORDER == 6
+ double km0_2 = km0 * km0;
+ double km0_4 = km0_2 * km0_2;
+ u = 24 - km0_2 + (km0_4 - 4 * km0 * km2 - 3 * km1 * km1) * (1./80);
+ v = km1 + (km3 - 6 * km0_2 * km1) * (1./80);
+#endif
+
+#if ORDER == 8
+ double t1_1 = km0;
+ double t1_2 = .5 * km1;
+ double t1_3 = (1./6) * km2;
+ double t1_4 = (1./24) * km3;
+ double t2_2 = t1_1 * t1_1;
+ double t2_3 = 2 * (t1_1 * t1_2);
+ double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
+ double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
+ double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
+ double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
+ double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
+ double t4_4 = t2_2 * t2_2;
+ double t4_5 = 2 * (t2_2 * t2_3);
+ double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
+ double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
+ double t6_6 = t4_4 * t2_2;
+ u = 1;
+ v = 0;
+ v += (1./12) * t1_2 + (1./80) * t1_4;
+ u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6;
+ v -= (1./480) * t3_4 + (1./2688) * t3_6;
+ u += (1./1920) * t4_4 + (1./10752) * t4_6;
+ v += (1./53760) * t5_6;
+ u -= (1./322560) * t6_6;
+#endif
+
+#if ORDER == 10
+ double t1_1 = km0;
+ double t1_2 = .5 * km1;
+ double t1_3 = (1./6) * km2;
+ double t1_4 = (1./24) * km3;
+ double t2_2 = t1_1 * t1_1;
+ double t2_3 = 2 * (t1_1 * t1_2);
+ double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
+ double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
+ double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
+ double t2_7 = 2 * (t1_3 * t1_4);
+ double t2_8 = t1_4 * t1_4;
+ double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
+ double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
+ double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
+ double t4_4 = t2_2 * t2_2;
+ double t4_5 = 2 * (t2_2 * t2_3);
+ double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
+ double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
+ double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
+ double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
+ double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
+ double t6_6 = t4_4 * t2_2;
+ double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
+ double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
+ double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
+ double t8_8 = t6_6 * t2_2;
+ u = 1;
+ v = 0;
+ v += (1./12) * t1_2 + (1./80) * t1_4;
+ u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
+ v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8;
+ u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8;
+ v += (1./53760) * t5_6 + (1./276480) * t5_8;
+ u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8;
+ v -= (1./1.16122e+07) * t7_8;
+ u += (1./9.28973e+07) * t8_8;
+#endif
+
+#if ORDER == 12
+ double t1_1 = km0;
+ double t1_2 = .5 * km1;
+ double t1_3 = (1./6) * km2;
+ double t1_4 = (1./24) * km3;
+ double t2_2 = t1_1 * t1_1;
+ double t2_3 = 2 * (t1_1 * t1_2);
+ double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
+ double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
+ double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
+ double t2_7 = 2 * (t1_3 * t1_4);
+ double t2_8 = t1_4 * t1_4;
+ double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
+ double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
+ double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
+ double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
+ double t4_4 = t2_2 * t2_2;
+ double t4_5 = 2 * (t2_2 * t2_3);
+ double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
+ double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
+ double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
+ double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
+ double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
+ double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
+ double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
+ double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
+ double t6_6 = t4_4 * t2_2;
+ double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
+ double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
+ double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
+ double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
+ double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
+ double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
+ double t8_8 = t6_6 * t2_2;
+ double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
+ double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
+ double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
+ double t10_10 = t8_8 * t2_2;
+ u = 1;
+ v = 0;
+ v += (1./12) * t1_2 + (1./80) * t1_4;
+ u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
+ v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8 + (1./67584) * t3_10;
+ u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8 + (1./270336) * t4_10;
+ v += (1./53760) * t5_6 + (1./276480) * t5_8 + (1./1.35168e+06) * t5_10;
+ u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8 + (1./8.11008e+06) * t6_10;
+ v -= (1./1.16122e+07) * t7_8 + (1./5.67706e+07) * t7_10;
+ u += (1./9.28973e+07) * t8_8 + (1./4.54164e+08) * t8_10;
+ v += (1./4.08748e+09) * t9_10;
+ u -= (1./4.08748e+10) * t10_10;
+#endif
+
+#if ORDER == 14
+ double t1_1 = km0;
+ double t1_2 = .5 * km1;
+ double t1_3 = (1./6) * km2;
+ double t1_4 = (1./24) * km3;
+ double t2_2 = t1_1 * t1_1;
+ double t2_3 = 2 * (t1_1 * t1_2);
+ double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
+ double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
+ double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
+ double t2_7 = 2 * (t1_3 * t1_4);
+ double t2_8 = t1_4 * t1_4;
+ double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
+ double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
+ double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
+ double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
+ double t3_12 = t2_8 * t1_4;
+ double t4_4 = t2_2 * t2_2;
+ double t4_5 = 2 * (t2_2 * t2_3);
+ double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
+ double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
+ double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
+ double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
+ double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
+ double t4_11 = 2 * (t2_3 * t2_8 + t2_4 * t2_7 + t2_5 * t2_6);
+ double t4_12 = 2 * (t2_4 * t2_8 + t2_5 * t2_7) + t2_6 * t2_6;
+ double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
+ double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
+ double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
+ double t5_12 = t4_8 * t1_4 + t4_9 * t1_3 + t4_10 * t1_2 + t4_11 * t1_1;
+ double t6_6 = t4_4 * t2_2;
+ double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
+ double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
+ double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
+ double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
+ double t6_11 = t4_4 * t2_7 + t4_5 * t2_6 + t4_6 * t2_5 + t4_7 * t2_4 + t4_8 * t2_3 + t4_9 * t2_2;
+ double t6_12 = t4_4 * t2_8 + t4_5 * t2_7 + t4_6 * t2_6 + t4_7 * t2_5 + t4_8 * t2_4 + t4_9 * t2_3 + t4_10 * t2_2;
+ double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
+ double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
+ double t7_12 = t6_8 * t1_4 + t6_9 * t1_3 + t6_10 * t1_2 + t6_11 * t1_1;
+ double t8_8 = t6_6 * t2_2;
+ double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
+ double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
+ double t8_11 = t6_6 * t2_5 + t6_7 * t2_4 + t6_8 * t2_3 + t6_9 * t2_2;
+ double t8_12 = t6_6 * t2_6 + t6_7 * t2_5 + t6_8 * t2_4 + t6_9 * t2_3 + t6_10 * t2_2;
+ double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
+ double t9_12 = t8_8 * t1_4 + t8_9 * t1_3 + t8_10 * t1_2 + t8_11 * t1_1;
+ double t10_10 = t8_8 * t2_2;
+ double t10_11 = t8_8 * t2_3 + t8_9 * t2_2;
+ double t10_12 = t8_8 * t2_4 + t8_9 * t2_3 + t8_10 * t2_2;
+ double t11_12 = t10_10 * t1_2 + t10_11 * t1_1;
+ double t12_12 = t10_10 * t2_2;
+ u = 1;
+ v = 0;
+ v += (1./12) * t1_2 + (1./80) * t1_4;
+ u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
+ v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8 + (1./67584) * t3_10 + (1./319488) * t3_12;
+ u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8 + (1./270336) * t4_10 + (1./1.27795e+06) * t4_12;
+ v += (1./53760) * t5_6 + (1./276480) * t5_8 + (1./1.35168e+06) * t5_10 + (1./6.38976e+06) * t5_12;
+ u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8 + (1./8.11008e+06) * t6_10 + (1./3.83386e+07) * t6_12;
+ v -= (1./1.16122e+07) * t7_8 + (1./5.67706e+07) * t7_10 + (1./2.6837e+08) * t7_12;
+ u += (1./9.28973e+07) * t8_8 + (1./4.54164e+08) * t8_10 + (1./2.14696e+09) * t8_12;
+ v += (1./4.08748e+09) * t9_10 + (1./1.93226e+10) * t9_12;
+ u -= (1./4.08748e+10) * t10_10 + (1./1.93226e+11) * t10_12;
+ v -= (1./2.12549e+12) * t11_12;
+ u += (1./2.55059e+13) * t12_12;
+#endif
+
+#if ORDER == 16
+ double t1_1 = km0;
+ double t1_2 = .5 * km1;
+ double t1_3 = (1./6) * km2;
+ double t1_4 = (1./24) * km3;
+ double t2_2 = t1_1 * t1_1;
+ double t2_3 = 2 * (t1_1 * t1_2);
+ double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
+ double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
+ double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
+ double t2_7 = 2 * (t1_3 * t1_4);
+ double t2_8 = t1_4 * t1_4;
+ double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
+ double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
+ double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
+ double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
+ double t3_12 = t2_8 * t1_4;
+ double t4_4 = t2_2 * t2_2;
+ double t4_5 = 2 * (t2_2 * t2_3);
+ double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
+ double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
+ double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
+ double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
+ double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
+ double t4_11 = 2 * (t2_3 * t2_8 + t2_4 * t2_7 + t2_5 * t2_6);
+ double t4_12 = 2 * (t2_4 * t2_8 + t2_5 * t2_7) + t2_6 * t2_6;
+ double t4_13 = 2 * (t2_5 * t2_8 + t2_6 * t2_7);
+ double t4_14 = 2 * (t2_6 * t2_8) + t2_7 * t2_7;
+ double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
+ double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
+ double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
+ double t5_12 = t4_8 * t1_4 + t4_9 * t1_3 + t4_10 * t1_2 + t4_11 * t1_1;
+ double t5_14 = t4_10 * t1_4 + t4_11 * t1_3 + t4_12 * t1_2 + t4_13 * t1_1;
+ double t6_6 = t4_4 * t2_2;
+ double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
+ double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
+ double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
+ double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
+ double t6_11 = t4_4 * t2_7 + t4_5 * t2_6 + t4_6 * t2_5 + t4_7 * t2_4 + t4_8 * t2_3 + t4_9 * t2_2;
+ double t6_12 = t4_4 * t2_8 + t4_5 * t2_7 + t4_6 * t2_6 + t4_7 * t2_5 + t4_8 * t2_4 + t4_9 * t2_3 + t4_10 * t2_2;
+ double t6_13 = t4_5 * t2_8 + t4_6 * t2_7 + t4_7 * t2_6 + t4_8 * t2_5 + t4_9 * t2_4 + t4_10 * t2_3 + t4_11 * t2_2;
+ double t6_14 = t4_6 * t2_8 + t4_7 * t2_7 + t4_8 * t2_6 + t4_9 * t2_5 + t4_10 * t2_4 + t4_11 * t2_3 + t4_12 * t2_2;
+ double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
+ double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
+ double t7_12 = t6_8 * t1_4 + t6_9 * t1_3 + t6_10 * t1_2 + t6_11 * t1_1;
+ double t7_14 = t6_10 * t1_4 + t6_11 * t1_3 + t6_12 * t1_2 + t6_13 * t1_1;
+ double t8_8 = t6_6 * t2_2;
+ double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
+ double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
+ double t8_11 = t6_6 * t2_5 + t6_7 * t2_4 + t6_8 * t2_3 + t6_9 * t2_2;
+ double t8_12 = t6_6 * t2_6 + t6_7 * t2_5 + t6_8 * t2_4 + t6_9 * t2_3 + t6_10 * t2_2;
+ double t8_13 = t6_6 * t2_7 + t6_7 * t2_6 + t6_8 * t2_5 + t6_9 * t2_4 + t6_10 * t2_3 + t6_11 * t2_2;
+ double t8_14 = t6_6 * t2_8 + t6_7 * t2_7 + t6_8 * t2_6 + t6_9 * t2_5 + t6_10 * t2_4 + t6_11 * t2_3 + t6_12 * t2_2;
+ double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
+ double t9_12 = t8_8 * t1_4 + t8_9 * t1_3 + t8_10 * t1_2 + t8_11 * t1_1;
+ double t9_14 = t8_10 * t1_4 + t8_11 * t1_3 + t8_12 * t1_2 + t8_13 * t1_1;
+ double t10_10 = t8_8 * t2_2;
+ double t10_11 = t8_8 * t2_3 + t8_9 * t2_2;
+ double t10_12 = t8_8 * t2_4 + t8_9 * t2_3 + t8_10 * t2_2;
+ double t10_13 = t8_8 * t2_5 + t8_9 * t2_4 + t8_10 * t2_3 + t8_11 * t2_2;
+ double t10_14 = t8_8 * t2_6 + t8_9 * t2_5 + t8_10 * t2_4 + t8_11 * t2_3 + t8_12 * t2_2;
+ double t11_12 = t10_10 * t1_2 + t10_11 * t1_1;
+ double t11_14 = t10_10 * t1_4 + t10_11 * t1_3 + t10_12 * t1_2 + t10_13 * t1_1;
+ double t12_12 = t10_10 * t2_2;
+ double t12_13 = t10_10 * t2_3 + t10_11 * t2_2;
+ double t12_14 = t10_10 * t2_4 + t10_11 * t2_3 + t10_12 * t2_2;
+ double t13_14 = t12_12 * t1_2 + t12_13 * t1_1;
+ double t14_14 = t12_12 * t2_2;
+ u = 1;
+ u -= 1./24 * t2_2 + 1./160 * t2_4 + 1./896 * t2_6 + 1./4608 * t2_8;
+ u += 1./1920 * t4_4 + 1./10752 * t4_6 + 1./55296 * t4_8 + 1./270336 * t4_10 + 1./1277952 * t4_12 + 1./5898240 * t4_14;
+ u -= 1./322560 * t6_6 + 1./1658880 * t6_8 + 1./8110080 * t6_10 + 1./38338560 * t6_12 + 1./176947200 * t6_14;
+ u += 1./92897280 * t8_8 + 1./454164480 * t8_10 + 4.6577500191e-10 * t8_12 + 1.0091791708e-10 * t8_14;
+ u -= 2.4464949595e-11 * t10_10 + 5.1752777990e-12 * t10_12 + 1.1213101898e-12 * t10_14;
+ u += 3.9206649992e-14 * t12_12 + 8.4947741650e-15 * t12_14;
+ u -= 4.6674583324e-17 * t14_14;
+ v = 0;
+ v += 1./12 * t1_2 + 1./80 * t1_4;
+ v -= 1./480 * t3_4 + 1./2688 * t3_6 + 1./13824 * t3_8 + 1./67584 * t3_10 + 1./319488 * t3_12;
+ v += 1./53760 * t5_6 + 1./276480 * t5_8 + 1./1351680 * t5_10 + 1./6389760 * t5_12 + 1./29491200 * t5_14;
+ v -= 1./11612160 * t7_8 + 1./56770560 * t7_10 + 1./268369920 * t7_12 + 8.0734333664e-10 * t7_14;
+ v += 2.4464949595e-10 * t9_10 + 5.1752777990e-11 * t9_12 + 1.1213101898e-11 * t9_14;
+ v -= 4.7047979991e-13 * t11_12 + 1.0193728998e-13 * t11_14;
+ v += 6.5344416654e-16 * t13_14;
+#endif
+
+ }
+
+ if (n == 1) {
+#if ORDER == 2
+ x = 1;
+ y = 0;
+#else
+ x = u;
+ y = v;
+#endif
+ } else {
+ double th = (((th4 * s + th3) * s + th2) * s + th1) * s;
+ double cth = cos(th);
+ double sth = sin(th);
+
+#if ORDER == 2
+ x += cth;
+ y += sth;
+#else
+ x += cth * u - sth * v;
+ y += cth * v + sth * u;
+#endif
+ s += ds;
+ }
+ }
+
+#if ORDER == 4 || ORDER == 6
+ xy[0] = x * (1./24 * ds);
+ xy[1] = y * (1./24 * ds);
+#else
+ xy[0] = x * ds;
+ xy[1] = y * ds;
+#endif
+}
+
+static double
+compute_ends(const double ks[4], double ends[2][4], double seg_ch)
+{
+ double xy[2];
+ double ch, th;
+ double l, l2, l3;
+ double th_even, th_odd;
+ double k0_even, k0_odd;
+ double k1_even, k1_odd;
+ double k2_even, k2_odd;
+
+ integrate_spiro(ks, xy);
+ ch = hypot(xy[0], xy[1]);
+ th = atan2(xy[1], xy[0]);
+ l = ch / seg_ch;
+
+ th_even = .5 * ks[0] + (1./48) * ks[2];
+ th_odd = .125 * ks[1] + (1./384) * ks[3] - th;
+ ends[0][0] = th_even - th_odd;
+ ends[1][0] = th_even + th_odd;
+ k0_even = l * (ks[0] + .125 * ks[2]);
+ k0_odd = l * (.5 * ks[1] + (1./48) * ks[3]);
+ ends[0][1] = k0_even - k0_odd;
+ ends[1][1] = k0_even + k0_odd;
+ l2 = l * l;
+ k1_even = l2 * (ks[1] + .125 * ks[3]);
+ k1_odd = l2 * .5 * ks[2];
+ ends[0][2] = k1_even - k1_odd;
+ ends[1][2] = k1_even + k1_odd;
+ l3 = l2 * l;
+ k2_even = l3 * ks[2];
+ k2_odd = l3 * .5 * ks[3];
+ ends[0][3] = k2_even - k2_odd;
+ ends[1][3] = k2_even + k2_odd;
+
+ return l;
+}
+
+static void
+compute_pderivs(const spiro_seg *s, double ends[2][4], double derivs[4][2][4],
+ int jinc)
+{
+ double recip_d = 2e6;
+ double delta = 1./ recip_d;
+ double try_ks[4];
+ double try_ends[2][4];
+ int i, j, k;
+
+ compute_ends(s->ks, ends, s->seg_ch);
+ for (i = 0; i < jinc; i++) {
+ for (j = 0; j < 4; j++)
+ try_ks[j] = s->ks[j];
+ try_ks[i] += delta;
+ compute_ends(try_ks, try_ends, s->seg_ch);
+ for (k = 0; k < 2; k++)
+ for (j = 0; j < 4; j++)
+ derivs[j][k][i] = recip_d * (try_ends[k][j] - ends[k][j]);
+ }
+}
+
+static double
+mod_2pi(double th)
+{
+ double u = th / (2 * M_PI);
+ return 2 * M_PI * (u - floor(u + 0.5));
+}
+
+static spiro_seg *
+setup_path(const spiro_cp *src, int n)
+{
+ int n_seg = src[0].ty == '{' ? n - 1 : n;
+ spiro_seg *r = (spiro_seg *)malloc((n_seg + 1) * sizeof(spiro_seg));
+ int i;
+ int ilast;
+
+ for (i = 0; i < n_seg; i++) {
+ r[i].x = src[i].x;
+ r[i].y = src[i].y;
+ r[i].ty = src[i].ty;
+ r[i].ks[0] = 0.;
+ r[i].ks[1] = 0.;
+ r[i].ks[2] = 0.;
+ r[i].ks[3] = 0.;
+ }
+ r[n_seg].x = src[n_seg % n].x;
+ r[n_seg].y = src[n_seg % n].y;
+ r[n_seg].ty = src[n_seg % n].ty;
+
+ for (i = 0; i < n_seg; i++) {
+ double dx = r[i + 1].x - r[i].x;
+ double dy = r[i + 1].y - r[i].y;
+ r[i].seg_ch = hypot(dx, dy);
+ r[i].seg_th = atan2(dy, dx);
+ }
+
+ ilast = n_seg - 1;
+ for (i = 0; i < n_seg; i++) {
+ if (r[i].ty == '{' || r[i].ty == '}' || r[i].ty == 'v')
+ r[i].bend_th = 0.;
+ else
+ r[i].bend_th = mod_2pi(r[i].seg_th - r[ilast].seg_th);
+ ilast = i;
+ }
+ return r;
+}
+
+static void
+bandec11(bandmat *m, int *perm, int n)
+{
+ int i, j, k;
+ int l;
+
+ /* pack top triangle to the left. */
+ for (i = 0; i < 5; i++) {
+ for (j = 0; j < i + 6; j++)
+ m[i].a[j] = m[i].a[j + 5 - i];
+ for (; j < 11; j++)
+ m[i].a[j] = 0.;
+ }
+ l = 5;
+ for (k = 0; k < n; k++) {
+ int pivot = k;
+ double pivot_val = m[k].a[0];
+ double pivot_scale;
+
+ l = l < n ? l + 1 : n;
+
+ for (j = k + 1; j < l; j++)
+ if (fabs(m[j].a[0]) > fabs(pivot_val)) {
+ pivot_val = m[j].a[0];
+ pivot = j;
+ }
+
+ perm[k] = pivot;
+ if (pivot != k) {
+ for (j = 0; j < 11; j++) {
+ double tmp = m[k].a[j];
+ m[k].a[j] = m[pivot].a[j];
+ m[pivot].a[j] = tmp;
+ }
+ }
+
+ if (fabs(pivot_val) < 1e-12) pivot_val = 1e-12;
+ pivot_scale = 1. / pivot_val;
+ for (i = k + 1; i < l; i++) {
+ double x = m[i].a[0] * pivot_scale;
+ m[k].al[i - k - 1] = x;
+ for (j = 1; j < 11; j++)
+ m[i].a[j - 1] = m[i].a[j] - x * m[k].a[j];
+ m[i].a[10] = 0.;
+ }
+ }
+}
+
+static void
+banbks11(const bandmat *m, const int *perm, double *v, int n)
+{
+ int i, k, l;
+
+ /* forward substitution */
+ l = 5;
+ for (k = 0; k < n; k++) {
+ i = perm[k];
+ if (i != k) {
+ double tmp = v[k];
+ v[k] = v[i];
+ v[i] = tmp;
+ }
+ if (l < n) l++;
+ for (i = k + 1; i < l; i++)
+ v[i] -= m[k].al[i - k - 1] * v[k];
+ }
+
+ /* back substitution */
+ l = 1;
+ for (i = n - 1; i >= 0; i--) {
+ double x = v[i];
+ for (k = 1; k < l; k++)
+ x -= m[i].a[k] * v[k + i];
+ v[i] = x / m[i].a[0];
+ if (l < 11) l++;
+ }
+}
+
+static int compute_jinc(char ty0, char ty1)
+{
+ if (ty0 == 'o' || ty1 == 'o' ||
+ ty0 == ']' || ty1 == '[')
+ return 4;
+ else if (ty0 == 'c' && ty1 == 'c')
+ return 2;
+ else if (((ty0 == '{' || ty0 == 'v' || ty0 == '[') && ty1 == 'c') ||
+ (ty0 == 'c' && (ty1 == '}' || ty1 == 'v' || ty1 == ']')))
+ return 1;
+ else
+ return 0;
+}
+
+static int count_vec(const spiro_seg *s, int nseg)
+{
+ int i;
+ int n = 0;
+
+ for (i = 0; i < nseg; i++)
+ n += compute_jinc(s[i].ty, s[i + 1].ty);
+ return n;
+}
+
+static void
+add_mat_line(bandmat *m, double *v,
+ double derivs[4], double x, double y, int j, int jj, int jinc,
+ int nmat)
+{
+ if (jj >= 0) {
+ int joff = (j + 5 - jj + nmat) % nmat;
+ if (nmat < 6) {
+ joff = j + 5 - jj;
+ } else if (nmat == 6) {
+ joff = 2 + (j + 3 - jj + nmat) % nmat;
+ }
+#ifdef VERBOSE
+ printf("add_mat_line j=%d jj=%d jinc=%d nmat=%d joff=%d\n", j, jj, jinc, nmat, joff);
+#endif
+ v[jj] += x;
+ for (int k = 0; k < jinc; k++)
+ m[jj].a[joff + k] += y * derivs[k];
+ }
+}
+
+static double
+spiro_iter(spiro_seg *s, bandmat *m, int *perm, double *v, const int n)
+{
+ int cyclic = s[0].ty != '{' && s[0].ty != 'v';
+ int nmat = count_vec(s, n);
+ int n_invert;
+
+ for (int i = 0; i < nmat; i++) {
+ v[i] = 0.;
+ for (double & j : m[i].a) {
+ j = 0.;
+ }
+ for (double & j : m[i].al) {
+ j = 0.;
+ }
+ }
+
+ int j = 0;
+ int jj;
+ if (s[0].ty == 'o') {
+ jj = nmat - 2;
+ } else if (s[0].ty == 'c') {
+ jj = nmat - 1;
+ } else {
+ jj = 0;
+ }
+ for (int i = 0; i < n; i++) {
+ char ty0 = s[i].ty;
+ char ty1 = s[i + 1].ty;
+ int jinc = compute_jinc(ty0, ty1);
+ double th = s[i].bend_th;
+ double ends[2][4];
+ double derivs[4][2][4];
+ int jthl = -1, jk0l = -1, jk1l = -1, jk2l = -1;
+ int jthr = -1, jk0r = -1, jk1r = -1, jk2r = -1;
+
+ compute_pderivs(&s[i], ends, derivs, jinc);
+
+ /* constraints crossing left */
+ if (ty0 == 'o' || ty0 == 'c' || ty0 == '[' || ty0 == ']') {
+ jthl = jj++;
+ jj %= nmat;
+ jk0l = jj++;
+ }
+ if (ty0 == 'o') {
+ jj %= nmat;
+ jk1l = jj++;
+ jk2l = jj++;
+ }
+
+ /* constraints on left */
+ if ((ty0 == '[' || ty0 == 'v' || ty0 == '{' || ty0 == 'c') &&
+ jinc == 4) {
+ if (ty0 != 'c')
+ jk1l = jj++;
+ jk2l = jj++;
+ }
+
+ /* constraints on right */
+ if ((ty1 == ']' || ty1 == 'v' || ty1 == '}' || ty1 == 'c') &&
+ jinc == 4) {
+ if (ty1 != 'c')
+ jk1r = jj++;
+ jk2r = jj++;
+ }
+
+ /* constraints crossing right */
+ if (ty1 == 'o' || ty1 == 'c' || ty1 == '[' || ty1 == ']') {
+ jthr = jj;
+ jk0r = (jj + 1) % nmat;
+ }
+ if (ty1 == 'o') {
+ jk1r = (jj + 2) % nmat;
+ jk2r = (jj + 3) % nmat;
+ }
+
+ add_mat_line(m, v, derivs[0][0], th - ends[0][0], 1, j, jthl, jinc, nmat);
+ add_mat_line(m, v, derivs[1][0], ends[0][1], -1, j, jk0l, jinc, nmat);
+ add_mat_line(m, v, derivs[2][0], ends[0][2], -1, j, jk1l, jinc, nmat);
+ add_mat_line(m, v, derivs[3][0], ends[0][3], -1, j, jk2l, jinc, nmat);
+ add_mat_line(m, v, derivs[0][1], -ends[1][0], 1, j, jthr, jinc, nmat);
+ add_mat_line(m, v, derivs[1][1], -ends[1][1], 1, j, jk0r, jinc, nmat);
+ add_mat_line(m, v, derivs[2][1], -ends[1][2], 1, j, jk1r, jinc, nmat);
+ add_mat_line(m, v, derivs[3][1], -ends[1][3], 1, j, jk2r, jinc, nmat);
+ if (jthl >= 0)
+ v[jthl] = mod_2pi(v[jthl]);
+ if (jthr >= 0)
+ v[jthr] = mod_2pi(v[jthr]);
+ j += jinc;
+ }
+ if (cyclic) {
+ memcpy(m + nmat, m, sizeof(bandmat) * nmat);
+ memcpy(m + 2 * nmat, m, sizeof(bandmat) * nmat);
+ memcpy(v + nmat, v, sizeof(double) * nmat);
+ memcpy(v + 2 * nmat, v, sizeof(double) * nmat);
+ n_invert = 3 * nmat;
+ j = nmat;
+ } else {
+ n_invert = nmat;
+ j = 0;
+ }
+#ifdef VERBOSE
+ for (int i = 0; i < n; i++) {
+ for (int k = 0; k < 11; k++) {
+ printf(" %2.4f", m[i].a[k]);
+ }
+ printf(": %2.4f\n", v[i]);
+ }
+ printf("---\n");
+#endif
+ bandec11(m, perm, n_invert);
+ banbks11(m, perm, v, n_invert);
+
+ double norm = 0.;
+ for (int i = 0; i < n; i++) {
+ char ty0 = s[i].ty;
+ char ty1 = s[i + 1].ty;
+ int jinc = compute_jinc(ty0, ty1);
+ int k;
+
+ for (k = 0; k < jinc; k++) {
+ double dk = v[j++];
+
+#ifdef VERBOSE
+ printf("s[%d].ks[%d] += %f\n", i, k, dk);
+#endif
+ s[i].ks[k] += dk;
+ norm += dk * dk;
+ }
+ s[i].ks[0] = 2.0*mod_2pi(s[i].ks[0]/2.0);
+ }
+ return norm;
+}
+
+static int
+solve_spiro(spiro_seg *s, const int nseg)
+{
+ int nmat = count_vec(s, nseg);
+ int n_alloc = nmat;
+
+ if (nmat == 0) {
+ return 0;
+ }
+ if (s[0].ty != '{' && s[0].ty != 'v') {
+ n_alloc *= 3;
+ }
+ if (n_alloc < 5) {
+ n_alloc = 5;
+ }
+
+ bandmat *m = (bandmat *)malloc(sizeof(bandmat) * n_alloc);
+ double *v = (double *)malloc(sizeof(double) * n_alloc);
+ int *perm = (int *)malloc(sizeof(int) * n_alloc);
+
+ for (unsigned i = 0; i < 10; i++) {
+ double norm = spiro_iter(s, m, perm, v, nseg);
+#ifdef VERBOSE
+ printf("%% norm = %g\n", norm);
+#endif
+ if (norm < 1e-12) break;
+ }
+
+ free(m);
+ free(v);
+ free(perm);
+ return 0;
+}
+
+static void
+spiro_seg_to_otherpath(const double ks[4],
+ double x0, double y0, double x1, double y1,
+ ConverterBase &bc, int depth, bool close_last)
+{
+ double bend = fabs(ks[0]) + fabs(.5 * ks[1]) + fabs(.125 * ks[2]) +
+ fabs((1./48) * ks[3]);
+
+ if (!(bend > 1e-8)) {
+ bc.lineto(x1, y1, close_last);
+ } else {
+ double seg_ch = hypot(x1 - x0, y1 - y0);
+ double seg_th = atan2(y1 - y0, x1 - x0);
+ double xy[2];
+ double ch, th;
+ double scale, rot;
+
+ integrate_spiro(ks, xy);
+ ch = hypot(xy[0], xy[1]);
+ th = atan2(xy[1], xy[0]);
+ scale = seg_ch / ch;
+ rot = seg_th - th;
+ if (depth > 5 || bend < 1.) {
+ double ul, vl;
+ double ur, vr;
+ double th_even, th_odd;
+ th_even = (1./384) * ks[3] + (1./8) * ks[1] + rot;
+ th_odd = (1./48) * ks[2] + .5 * ks[0];
+ ul = (scale * (1./3)) * cos(th_even - th_odd);
+ vl = (scale * (1./3)) * sin(th_even - th_odd);
+ ur = (scale * (1./3)) * cos(th_even + th_odd);
+ vr = (scale * (1./3)) * sin(th_even + th_odd);
+ bc.curveto(x0 + ul, y0 + vl, x1 - ur, y1 - vr, x1, y1, close_last);
+ } else {
+ /* subdivide */
+ double ksub[4];
+ double thsub;
+ double xysub[2];
+ double xmid, ymid;
+ double cth, sth;
+
+ ksub[0] = .5 * ks[0] - .125 * ks[1] + (1./64) * ks[2] - (1./768) * ks[3];
+ ksub[1] = .25 * ks[1] - (1./16) * ks[2] + (1./128) * ks[3];
+ ksub[2] = .125 * ks[2] - (1./32) * ks[3];
+ ksub[3] = (1./16) * ks[3];
+ thsub = rot - .25 * ks[0] + (1./32) * ks[1] - (1./384) * ks[2] + (1./6144) * ks[3];
+ cth = .5 * scale * cos(thsub);
+ sth = .5 * scale * sin(thsub);
+ integrate_spiro(ksub, xysub);
+ xmid = x0 + cth * xysub[0] - sth * xysub[1];
+ ymid = y0 + cth * xysub[1] + sth * xysub[0];
+ spiro_seg_to_otherpath(ksub, x0, y0, xmid, ymid, bc, depth + 1, false);
+ ksub[0] += .25 * ks[1] + (1./384) * ks[3];
+ ksub[1] += .125 * ks[2];
+ ksub[2] += (1./16) * ks[3];
+ spiro_seg_to_otherpath(ksub, xmid, ymid, x1, y1, bc, depth + 1, close_last);
+ }
+ }
+}
+
+spiro_seg *
+run_spiro(const spiro_cp *src, int n)
+{
+ int nseg = src[0].ty == '{' ? n - 1 : n;
+ spiro_seg *s = setup_path(src, n);
+ if (nseg > 1)
+ solve_spiro(s, nseg);
+ return s;
+}
+
+void
+free_spiro(spiro_seg *s)
+{
+ free(s);
+}
+
+void
+spiro_to_otherpath(const spiro_seg *s, int n, ConverterBase &bc)
+{
+ int i;
+ int nsegs = s[n - 1].ty == '}' ? n - 1 : n;
+
+ for (i = 0; i < nsegs; i++) {
+ double x0 = s[i].x;
+ double y0 = s[i].y;
+ double x1 = s[i + 1].x;
+ double y1 = s[i + 1].y;
+
+ if (i == 0) {
+ bc.moveto(x0, y0);
+ }
+ // on the last segment, set the 'close_last' flag if path is closed
+ spiro_seg_to_otherpath(s[i].ks, x0, y0, x1, y1, bc, 0, (nsegs == n) && (i == n - 1));
+ }
+}
+
+double
+get_knot_th(const spiro_seg *s, int i)
+{
+ double ends[2][4];
+
+ if (i == 0) {
+ compute_ends(s[i].ks, ends, s[i].seg_ch);
+ return s[i].seg_th - ends[0][0];
+ } else {
+ compute_ends(s[i - 1].ks, ends, s[i - 1].seg_ch);
+ return s[i - 1].seg_th + ends[1][0];
+ }
+}
+
+
+} // namespace Spiro
+
+/************************************
+ * Unit_test code
+ */
+
+
+#ifdef UNIT_TEST
+#include <stdio.h>
+#include <sys/time.h> /* for gettimeofday */
+
+using namespace Spiro;
+
+static double
+get_time (void)
+{
+ struct timeval tv;
+ struct timezone tz;
+
+ gettimeofday (&tv, &tz);
+
+ return tv.tv_sec + 1e-6 * tv.tv_usec;
+}
+
+int
+test_integ(void) {
+ double ks[] = {1, 2, 3, 4};
+ double xy[2];
+ double xynom[2];
+ int i, j;
+ int nsubdiv;
+
+ n = ORDER < 6 ? 4096 : 1024;
+ integrate_spiro(ks, xynom);
+ nsubdiv = ORDER < 12 ? 8 : 7;
+ for (i = 0; i < nsubdiv; i++) {
+ double st, en;
+ double err;
+ int n_iter = (1 << (20 - i));
+
+ n = 1 << i;
+ st = get_time();
+ for (j = 0; j < n_iter; j++)
+ integrate_spiro(ks, xy);
+ en = get_time();
+ err = hypot(xy[0] - xynom[0], xy[1] - xynom[1]);
+ printf("%d %d %g %g\n", ORDER, n, (en - st) / n_iter, err);
+#if 0
+ double ch, th;
+ ch = hypot(xy[0], xy[1]);
+ th = atan2(xy[1], xy[0]);
+ printf("n = %d: integ(%g %g %g %g) = %g %g, ch = %g, th = %g\n", n,
+ ks[0], ks[1], ks[2], ks[3], xy[0], xy[1], ch, th);
+ printf("%d: %g %g\n", n, xy[0] - xynom[0], xy[1] - xynom[1]);
+#endif
+ }
+ return 0;
+}
+
+void
+print_seg(const double ks[4], double x0, double y0, double x1, double y1)
+{
+ double bend = fabs(ks[0]) + fabs(.5 * ks[1]) + fabs(.125 * ks[2]) +
+ fabs((1./48) * ks[3]);
+
+ if (bend < 1e-8) {
+ printf("%g %g lineto\n", x1, y1);
+ } else {
+ double seg_ch = hypot(x1 - x0, y1 - y0);
+ double seg_th = atan2(y1 - y0, x1 - x0);
+ double xy[2];
+ double ch, th;
+ double scale, rot;
+
+ integrate_spiro(ks, xy);
+ ch = hypot(xy[0], xy[1]);
+ th = atan2(xy[1], xy[0]);
+ scale = seg_ch / ch;
+ rot = seg_th - th;
+ if (bend < 1.) {
+ double th_even, th_odd;
+ double ul, vl;
+ double ur, vr;
+ th_even = (1./384) * ks[3] + (1./8) * ks[1] + rot;
+ th_odd = (1./48) * ks[2] + .5 * ks[0];
+ ul = (scale * (1./3)) * cos(th_even - th_odd);
+ vl = (scale * (1./3)) * sin(th_even - th_odd);
+ ur = (scale * (1./3)) * cos(th_even + th_odd);
+ vr = (scale * (1./3)) * sin(th_even + th_odd);
+ printf("%g %g %g %g %g %g curveto\n",
+ x0 + ul, y0 + vl, x1 - ur, y1 - vr, x1, y1);
+
+ } else {
+ /* subdivide */
+ double ksub[4];
+ double thsub;
+ double xysub[2];
+ double xmid, ymid;
+ double cth, sth;
+
+ ksub[0] = .5 * ks[0] - .125 * ks[1] + (1./64) * ks[2] - (1./768) * ks[3];
+ ksub[1] = .25 * ks[1] - (1./16) * ks[2] + (1./128) * ks[3];
+ ksub[2] = .125 * ks[2] - (1./32) * ks[3];
+ ksub[3] = (1./16) * ks[3];
+ thsub = rot - .25 * ks[0] + (1./32) * ks[1] - (1./384) * ks[2] + (1./6144) * ks[3];
+ cth = .5 * scale * cos(thsub);
+ sth = .5 * scale * sin(thsub);
+ integrate_spiro(ksub, xysub);
+ xmid = x0 + cth * xysub[0] - sth * xysub[1];
+ ymid = y0 + cth * xysub[1] + sth * xysub[0];
+ print_seg(ksub, x0, y0, xmid, ymid);
+ ksub[0] += .25 * ks[1] + (1./384) * ks[3];
+ ksub[1] += .125 * ks[2];
+ ksub[2] += (1./16) * ks[3];
+ print_seg(ksub, xmid, ymid, x1, y1);
+ }
+ }
+}
+
+void
+print_segs(const spiro_seg *segs, int nsegs)
+{
+ int i;
+
+ for (i = 0; i < nsegs; i++) {
+ double x0 = segs[i].x;
+ double y0 = segs[i].y;
+ double x1 = segs[i + 1].x;
+ double y1 = segs[i + 1].y;
+
+ if (i == 0)
+ printf("%g %g moveto\n", x0, y0);
+ printf("%% ks = [ %g %g %g %g ]\n",
+ segs[i].ks[0], segs[i].ks[1], segs[i].ks[2], segs[i].ks[3]);
+ print_seg(segs[i].ks, x0, y0, x1, y1);
+ }
+ printf("stroke\n");
+}
+
+int
+test_curve(void)
+{
+ spiro_cp path[] = {
+ {334, 117, 'v'},
+ {305, 176, 'v'},
+ {212, 142, 'c'},
+ {159, 171, 'c'},
+ {224, 237, 'c'},
+ {347, 335, 'c'},
+ {202, 467, 'c'},
+ {81, 429, 'v'},
+ {114, 368, 'v'},
+ {201, 402, 'c'},
+ {276, 369, 'c'},
+ {218, 308, 'c'},
+ {91, 211, 'c'},
+ {124, 111, 'c'},
+ {229, 82, 'c'}
+ };
+ spiro_seg *segs;
+ int i;
+
+ n = 1;
+ for (i = 0; i < 1000; i++) {
+ segs = setup_path(path, 15);
+ solve_spiro(segs, 15);
+ }
+ printf("100 800 translate 1 -1 scale 1 setlinewidth\n");
+ print_segs(segs, 15);
+ printf("showpage\n");
+ return 0;
+}
+
+int main(int argc, char **argv)
+{
+ return test_curve();
+}
+#endif