Adding upstream version 1.3.upstream/1.3upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1000 insertions, 0 deletions

diff --git a/src/toys/curve-curve-distance.cpp b/src/toys/curve-curve-distance.cpp
new file mode 100644
index 0000000..bca0f27
--- /dev/null
+++ b/src/toys/curve-curve-distance.cpp
@@ -0,0 +1,1000 @@
+/*
+ * curve-curve distance
+ *
+ * Authors:
+ * 		Marco Cecchetti <mrcekets at gmail.com>
+ *
+ * Copyright 2008  authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+#include <2geom/d2.h>
+#include <2geom/sbasis.h>
+#include <2geom/path.h>
+#include <2geom/angle.h>
+#include <2geom/bezier-to-sbasis.h>
+#include <2geom/sbasis-geometric.h>
+#include <2geom/piecewise.h>
+
+#include <toys/path-cairo.h>
+#include <toys/toy-framework-2.h>
+
+#include <2geom/nearest-time.h>
+#include <2geom/numeric/linear_system.h>
+
+#include <algorithm>
+
+
+
+namespace Geom
+{
+
+namespace detail
+{
+
+// this wrapper class is an helper to make up a curve portion and access it
+// in an homogeneous way 
+template< typename Curve01T >
+class CurvePortion
+{
+  public:
+    CurvePortion(const Curve & curve, double from, double to)
+        : m_curve_ptr(curve.portion(from, to))
+    {
+    }
+
+    Curve01T & get_curve()
+    {
+        return *( static_cast<Curve01T*>(m_curve_ptr) );
+    }
+
+    ~CurvePortion()
+    {
+        if (m_curve_ptr != NULL)
+            delete m_curve_ptr;
+    }
+
+  private:
+    Curve* m_curve_ptr;
+};
+
+template<>
+class CurvePortion< D2<SBasis> >
+{
+  public:
+    CurvePortion< D2<SBasis> >(const D2<SBasis> & curve, double from, double to)
+        : m_curve(portion(curve, from, to))
+    {
+    }
+
+    D2<SBasis> & get_curve()
+    {
+        return m_curve;
+    }
+
+  private:
+    D2<SBasis> m_curve;
+};
+
+
+template< typename Curve01T, typename CurveT >
+class distance_impl
+{
+    typedef Curve01T curveA_type;
+    typedef CurveT curveB_type;
+    // determine how near a distance sample and the value computed through
+    // the interpolated function have to be
+    double accuracy;
+    // determine the recursion limit
+    double adaptive_limit;
+    // pieces of the initial subdivision
+    unsigned int piecees;
+    // degree of the polynomial used to interpolate a piece
+    unsigned int piece_degree;
+    // number of coefficients = piece_degree + 1
+    unsigned int piece_size;
+    unsigned int samples_per_piece;
+    // total initial samples
+    unsigned int N;
+    // a junction is a part of the previous or of the next piece
+    unsigned int samples_per_junction;
+    unsigned int samples_per_2junctions;
+    // number of distance samples used in the interpolation (in the general case)
+    unsigned int samples_per_interpolation;
+
+    // distance between two consecutive parameters at which samples are evaluated
+    double step;
+    double half_step;
+    // length of the initial domain interval of a piece
+    double piece_step;
+    // length of the interval related to a junction
+    double junction_step;
+    // index of the first sample related to a piece
+    unsigned int interval_si;
+    // index of the last sample related to a piece
+    unsigned int interval_ei;
+    // index of the first sample to be evaluated for the current piece
+    unsigned int evaluation_si;
+    // index of the last sample to be evaluated for the current piece
+    unsigned int evaluation_ei;
+    // index of the first sample to be used for interpolating the current piece
+    unsigned int interpolation_si;
+    // index of the last sample to be used for interpolating the current piece
+    unsigned int interpolation_ei;
+    // number of total samples to be used for interpolating the current piece
+    // this is equal to samples_per_interpolation except for the first and last
+    // piece
+    unsigned int interpolation_samples;
+    // parameter value for the first sample related to the current piece
+    double interval_st;
+    // interval_st + piece_step
+    double interval_et;
+    // curve piece start t
+    double portion_st;
+    // curve piece end t
+    double portion_et;
+
+    unsigned int rec_pieces;
+    unsigned int rec_N;
+    unsigned int shared_si;
+    unsigned int shared_ei;
+    double rec_step;
+    double rec_half_step;
+    double rec_piece_step;
+    double rec_piece_2steps;
+    unsigned int rec_total_samples;
+
+
+    void init()
+    {
+        piece_degree = 3;
+        piece_size = piece_degree + 1;
+        samples_per_piece = 4;
+        N = piecees * samples_per_piece;
+        samples_per_junction = 2;
+        samples_per_2junctions = 2*samples_per_junction;
+        samples_per_interpolation
+            =  samples_per_piece + samples_per_2junctions;
+        step = 1.0 / N;
+        half_step = step / 2;
+        piece_step = samples_per_piece * step;
+        junction_step = samples_per_junction * step;
+        interval_si = samples_per_junction;
+        interval_ei = interval_si + samples_per_piece;
+        portion_st = (double)(samples_per_junction) / samples_per_interpolation;
+        portion_et = portion_st
+                     + (double)(samples_per_piece) / samples_per_interpolation;
+
+        // recursive routine parameters
+        rec_pieces = 2;
+        rec_N = rec_pieces * samples_per_piece;
+        rec_total_samples = 2 * samples_per_piece + 1;
+        shared_si = samples_per_piece - samples_per_junction;
+        shared_ei = samples_per_piece + samples_per_junction;
+        rec_step = 1.0 / rec_N;
+        rec_half_step = rec_step / 2;
+        rec_piece_step = samples_per_piece * rec_step;
+        rec_piece_2steps = 2 * rec_piece_step;
+    }
+
+    bool check_accuracy( SBasis const& piece,
+                         NL::Vector const& sample_distances,
+                         double step )
+    {
+        double t = 0;
+        for (unsigned int i = 0; i < sample_distances.size(); ++i)
+        {
+            if ( !are_near(piece(t), sample_distances[i], accuracy) )
+            {
+                return false;
+            }
+            t += step;
+        }
+        return true;
+    }
+
+
+    void append( Piecewise<SBasis> & pwc,
+                 Piecewise<SBasis> const& spwc,
+                 double interval_st,
+                 double interval_length )
+    {
+        double cut;
+        for (unsigned int i = 0; i < spwc.size(); ++i)
+        {
+            cut = interval_st + spwc.cuts[i+1] * interval_length;
+            pwc.push(spwc.segs[i], cut);
+        }
+    }
+
+    void init_power_matrix(NL::Matrix & power_matrix)
+    {
+        double t = 0;
+        double u0, u1, s;
+        unsigned int half_rows = power_matrix.rows() / 2;
+        unsigned int n = power_matrix.rows() - 1;
+        for (unsigned int i0 = 0, i1 = n; i0 < half_rows; ++i0, --i1)
+        {
+            u0 = 1-t;
+            u1 = t;
+            s = u0 * u1;
+            for (unsigned int j = 0; j < piece_size; j+=2)
+            {
+                power_matrix(i0, j) = u0;
+                power_matrix(i0, j+1) = u1;
+                power_matrix(i1, j) = u1;
+                power_matrix(i1, j+1) = u0;
+                u0 *= s;
+                u1 *= s;
+            }
+            t += rec_step;
+        }
+        // t = 1/2
+        assert( are_near(t, 0.5) );
+        u1 = 1/2.0;
+        s = 1/4.0;
+        for (unsigned int j = 0; j < piece_size; j+=2)
+        {
+            power_matrix(half_rows, j) = u1;
+            power_matrix(half_rows, j+1) = u1;
+            u1 *= s;
+        }
+    }
+
+    void interpolate( SBasis & piece,
+                      NL::Matrix & psdinv_matrix,
+                      NL::Vector & sample_distances,
+                      double interpolation_si, double interpolation_samples,
+                      double _portion_st, double _portion_et )
+    {
+        piece.resize(2);
+
+        NL::VectorView v( sample_distances,
+                          interpolation_samples,
+                          interpolation_si );
+        NL::Vector coeff = psdinv_matrix * v;
+        for (unsigned int i = 0, k = 0; i < piece_size; i+=2, ++k)
+        {
+            piece[k][0] = coeff[i];
+            piece[k][1] = coeff[i+1];
+        }
+        piece = portion(piece, _portion_st, _portion_et);
+    }
+
+    void evaluate_samples( curveA_type const& A,
+                           curveB_type const& B,
+                           NL::Vector & sample_distances,
+                           double& t )
+    {
+        Point At;
+        double nptime;
+        for (unsigned int i = evaluation_si; i < evaluation_ei; ++i)
+        {
+            At = A(t);
+            nptime = nearest_time(At, B);
+            sample_distances[i] = distance(At, B(nptime));
+            t += step;
+        }
+    }
+
+    void evaluate_piece_rec( Piecewise<SBasis> & pwc,
+                             curveA_type const& A,
+                             curveB_type const& B,
+                             NL::Matrix & psdinv_matrix,
+                             NL::Matrix & fpi_matrix,
+                             NL::Matrix & lpi_matrix,
+                             NL::Vector & curr_vector,
+                             NL::Vector & sample_distances,
+                             bool adaptive,
+                             double _interpolation_si,
+                             double _interpolation_ei,
+                             double _interval_st,
+                             double _interval_et,
+                             double half_real_step )
+    {
+        SBasis piece;
+        double _interpolation_samples = _interpolation_ei - _interpolation_si;
+        interpolate( piece, psdinv_matrix, curr_vector,
+                     _interpolation_si, _interpolation_samples,
+                     _interval_st, _interval_et );
+        if (adaptive)
+        {
+            bool good
+                = check_accuracy( piece, sample_distances, rec_step );
+            if (!good)
+            {
+                Piecewise<SBasis> spwc;
+                CurvePortion<curveA_type> cp(A, _interval_st, _interval_et);
+                evaluate_rec( spwc,
+                              cp.get_curve(),
+                              B,
+                              fpi_matrix,
+                              lpi_matrix,
+                              sample_distances,
+                              half_real_step );
+                append(pwc, spwc, _interval_st, rec_piece_step);
+            }
+            else
+            {
+                pwc.push(piece, _interval_et);
+            }
+        }
+        else
+        {
+            pwc.push(piece, _interval_et);
+        }
+    }
+
+
+    // recursive routine: if the interpolated piece is accurate enough
+    // it's returned in the out-parameter pwc, otherwise the computation of
+    // two new piecees is performed using half of the current step so the
+    // number of samples per piece is always the same, while the interpolation
+    // of one piece is split into the computation of two new piecees when
+    // needed.
+    void evaluate_rec( Piecewise<SBasis> & pwc,
+                       curveA_type const& A,
+                       curveB_type const& B,
+                       NL::Matrix & fpi_matrix,
+                       NL::Matrix & lpi_matrix,
+                       NL::Vector & sample_distances,
+                       double real_step )
+    {
+        const double half_real_step = real_step / 2;
+        const bool adaptive = !(real_step < adaptive_limit);
+        static const unsigned int middle_sample_index = samples_per_piece + 1;
+
+        pwc.clear();
+        pwc.push_cut(0);
+        // sample_distances used to check accuracy and for the interpolation
+        // of the two sub-pieces when needed
+        NL::Vector sample_distances_1(rec_total_samples);
+        NL::Vector sample_distances_2(rec_total_samples);
+
+        // view of even indexes of sample_distances_1
+        NL::VectorView
+        sd1_view_0(sample_distances_1, middle_sample_index, 0, 2);
+        // view of even indexes of sample_distances_2
+        NL::VectorView
+        sd2_view_0(sample_distances_2, middle_sample_index, 0, 2);
+        // view of first half (+ 1) of sample_distances
+        NL::VectorView
+        sd_view_1(sample_distances, middle_sample_index, 0);
+        // view of second half of sample_distances
+        NL::VectorView
+        sd_view_2(sample_distances, middle_sample_index, samples_per_piece);
+
+        sd1_view_0 = sd_view_1;
+        sd2_view_0 = sd_view_2;
+
+        // if we have to check accuracy and go on with recursion
+        // we need to compute the distance samples of middle points
+        // of all current samples, because the new step is half of
+        // the current one
+        if (adaptive)
+        {
+            Point At;
+            double nptime;
+            double t = rec_half_step;
+            for (unsigned int i = 1; i < sample_distances.size(); i+=2)
+            {
+                At = A(t);
+                nptime = nearest_time(At, B);
+                sample_distances_1[i] = distance(At, B(nptime));
+                At = A(t + rec_piece_step);
+                nptime = nearest_time(At, B);
+                sample_distances_2[i] = distance(At, B(nptime));
+                t += rec_step;
+            }
+        }
+
+        // first piece
+        evaluate_piece_rec( pwc, A, B,
+                            fpi_matrix,
+                            fpi_matrix,
+                            lpi_matrix,
+                            sample_distances,
+                            sample_distances_1,
+                            adaptive,
+                            0,                  // interpolation_si
+                            shared_ei,          // interpolation_ei
+                            0,                  // portion_st
+                            rec_piece_step,     // portion_et
+                            half_real_step );
+
+        // copy back junction parts because
+        // the interpolate routine modifies them
+        for ( unsigned int i = 0, j = samples_per_piece - 1;
+              i < samples_per_junction;
+              ++i, --j )
+        {
+            sd_view_1[j] = sd1_view_0[j];
+            sd_view_2[i] = sd2_view_0[i];
+        }
+
+
+        // last piece
+        evaluate_piece_rec( pwc, A, B,
+                            lpi_matrix,
+                            fpi_matrix,
+                            lpi_matrix,
+                            sample_distances,
+                            sample_distances_2,
+                            adaptive,
+                            shared_si,          // interpolation_si
+                            rec_total_samples,  // interpolation_ei
+                            rec_piece_step,     // portion_st
+                            rec_piece_2steps,   // portion_et
+                            half_real_step );
+    }
+
+
+    void evaluate_piece( Piecewise<SBasis> & pwc,
+                         curveA_type const& A,
+                         curveB_type const& B,
+                         NL::Matrix & psdinv_matrix,
+                         NL::Matrix & fpi_matrix,
+                         NL::Matrix & lpi_matrix,
+                         NL::Vector & curr_vector,
+                         NL::Vector & sample_distances,
+                         NL::Vector & end_junction,
+                         NL::VectorView & start_junction_view,
+                         NL::VectorView & end_junction_view,
+                         double & t )
+    {
+        //static size_t index = 0;
+        //std::cerr << "index = " << index++ << std::endl;
+        bool good;
+        SBasis piece;
+        Piecewise<SBasis> spwc;
+        interval_et += piece_step;
+        //std::cerr << "interval: " << interval_st << ", " << interval_et << std::endl;
+        //std::cerr << "interpolation range: " << interpolation_si << ", " << interpolation_ei << std::endl;
+        //std::cerr << "interpolation samples = " <<  interpolation_samples << std::endl;
+        evaluate_samples( A, B, curr_vector, t );
+        //std::cerr << "current vector: " << curr_vector << std::endl;
+        for ( unsigned int i = 0, k = interval_si;
+              i < sample_distances.size();
+              i+=2, ++k )
+        {
+            sample_distances[i] = curr_vector[k];
+        }
+        Point At;
+        double nptime;
+        double tt = interval_st + half_step;
+        for (unsigned int i = 1; i < sample_distances.size(); i+=2)
+        {
+            At = A(tt);
+            nptime = nearest_time(At, B);
+            sample_distances[i] = distance(At, B(nptime));
+            tt += step;
+        }
+        //std::cerr << "sample_distances: " << sample_distances << std::endl;
+        end_junction = end_junction_view;
+        interpolate( piece, psdinv_matrix, curr_vector,
+                     interpolation_si, interpolation_samples,
+                     portion_st, portion_et );
+        good = check_accuracy( piece, sample_distances, rec_step );
+        //std::cerr << "good: " << good << std::endl;
+        //good = true;
+        if (!good)
+        {
+            CurvePortion<curveA_type> cp(A, interval_st, interval_et);
+            evaluate_rec( spwc,
+                          cp.get_curve(),
+                          B,
+                          fpi_matrix,
+                          lpi_matrix,
+                          sample_distances,
+                          half_step );
+            append(pwc, spwc, interval_st, piece_step);
+        }
+        else
+        {
+            pwc.push(piece, interval_et);
+        }
+        interval_st = interval_et;
+        for (unsigned int i = 0; i < samples_per_junction; ++i)
+        {
+            curr_vector[i] = start_junction_view[i];
+            curr_vector[samples_per_junction + i] =  end_junction[i];
+        }
+    }
+
+  public:
+    void evaluate( Piecewise<SBasis> & pwc,
+                   curveA_type const& A,
+                   curveB_type const& B,
+                   unsigned int _piecees )
+    {
+        piecees = _piecees;
+        init();
+        assert( !(piecees & 1) );
+        assert( !(piece_size & 1) );
+        assert( rec_total_samples & 1);
+        pwc.clear();
+        pwc.push_cut(0);
+        NL::Matrix power_matrix(rec_total_samples, piece_size);
+        init_power_matrix(power_matrix);
+
+        NL::MatrixView rec_fmv( power_matrix,
+                                0, 0,
+                                shared_ei, piece_size );
+        NL::Matrix rec_fpim = NL::pseudo_inverse(rec_fmv);
+        NL::MatrixView rec_lmv( power_matrix,
+                                shared_si, 0,
+                                rec_total_samples - shared_si, piece_size );
+        NL::Matrix rec_lpim = NL::pseudo_inverse(rec_lmv);
+
+
+
+        NL::Vector curr_vector(samples_per_interpolation);
+        NL::Vector sample_distances(rec_total_samples);
+        NL::Vector end_junction(samples_per_junction);
+        NL::VectorView start_junction_view(
+                           sample_distances,
+                           samples_per_junction,
+                           rec_total_samples - 1 - samples_per_2junctions,
+                           2 );
+        NL::VectorView end_junction_view(
+                           curr_vector,
+                           samples_per_junction,
+                           samples_per_junction + samples_per_piece );
+
+        double t = 0;
+
+        // first piece
+        evaluation_si = interval_si;
+        evaluation_ei = samples_per_interpolation;
+        interpolation_si = evaluation_si;
+        interpolation_ei = evaluation_ei;
+        interpolation_samples = interpolation_ei - interpolation_si;
+        interval_st = 0;
+        interval_et = 0;
+        NL::MatrixView fmv( power_matrix,
+                            interpolation_si, 0,
+                            interpolation_samples, piece_size );
+        NL::Matrix fpim = NL::pseudo_inverse(fmv);
+
+        evaluate_piece( pwc, A, B, fpim,
+                        rec_fpim, rec_lpim,
+                        curr_vector, sample_distances, end_junction,
+                        start_junction_view, end_junction_view,
+                        t );
+
+        // general case
+        evaluation_si = interval_si + samples_per_junction;
+        evaluation_ei = samples_per_interpolation;
+        interpolation_si = 0;
+        interpolation_ei = evaluation_ei;
+        interpolation_samples = interpolation_ei - interpolation_si;
+        NL::MatrixView gmv( power_matrix,
+                            interpolation_si, 0,
+                            interpolation_samples, piece_size );
+        NL::Matrix gpim = NL::pseudo_inverse(gmv);
+
+        for ( unsigned int piece_index = 1;
+              piece_index < piecees - 1;
+              ++piece_index )
+        {
+            evaluate_piece( pwc, A, B, gpim,
+                            rec_fpim, rec_lpim,
+                            curr_vector, sample_distances, end_junction,
+                            start_junction_view, end_junction_view,
+                            t );
+        }
+
+        // last piece
+        evaluation_si = interval_si + samples_per_junction;
+        evaluation_ei = interval_ei + 1;
+        interpolation_si = 0;
+        interpolation_ei = evaluation_ei;
+        interpolation_samples = interpolation_ei -interpolation_si;
+        NL::MatrixView lmv( power_matrix,
+                            interpolation_si, 0,
+                            interpolation_samples, piece_size );
+        NL::Matrix lpim = NL::pseudo_inverse(lmv);
+
+        evaluate_piece( pwc, A, B, lpim,
+                        rec_fpim, rec_lpim,
+                        curr_vector, sample_distances, end_junction,
+                        start_junction_view, end_junction_view,
+                        t );
+    }
+
+    distance_impl()
+        : accuracy(1e-3),
+          adaptive_limit(1e-5)
+    {}
+
+    void set_accuracy(double _accuracy)
+    {
+        accuracy = _accuracy;
+    }
+
+    void set_adaptive_limit(double _adaptive_limit)
+    {
+        adaptive_limit = _adaptive_limit;
+    }
+
+};  // end class distance_impl
+
+}  // end namespace detail
+
+template < typename Curve01T, typename CurveT >
+inline
+Piecewise<SBasis>
+distance( Curve01T const& A,
+          CurveT const& B,
+          unsigned int pieces = 40,
+          double adaptive_limit = 1e-5,
+          double accuracy = 1e-3 )
+{
+
+    detail::distance_impl<Curve01T, CurveT> dist;
+    dist.set_accuracy(accuracy);
+    dist.set_adaptive_limit(adaptive_limit);
+    Piecewise<SBasis> pwc;
+    dist.evaluate(pwc, A, B, pieces);
+    return pwc;
+}
+
+template < typename CurveT >
+inline
+Piecewise<SBasis>
+distance( Piecewise< D2<SBasis> > const& A,
+          CurveT const& B,
+          unsigned int pieces = 40,
+          double adaptive_limit = 1e-5,
+          double accuracy = 1e-3 )
+{
+    Piecewise<SBasis> result;
+    Piecewise<SBasis> pwc;
+    for (unsigned int i = 0; i < A.size(); ++i)
+    {
+        pwc = distance(A[i], B, pieces, adaptive_limit, accuracy);
+        pwc.scaleDomain(A.cuts[i+1] - A.cuts[i]);
+        pwc.offsetDomain(A.cuts[i]);
+        result.concat(pwc);
+    }
+    return result;
+}
+
+template < typename CurveT >
+inline
+Piecewise<SBasis>
+distance( Path const& A,
+          CurveT const& B,
+          unsigned int pieces = 40,
+          double adaptive_limit = 1e-5,
+          double accuracy = 1e-3 )
+{
+    Piecewise<SBasis> result;
+    Piecewise<SBasis> pwc;
+    unsigned int sz = A.size();
+    if (A.closed()) ++sz;
+    for (unsigned int i = 0; i < sz; ++i)
+    {
+        pwc = distance(A[i], B, pieces, adaptive_limit, accuracy);
+        pwc.offsetDomain(i);
+        result.concat(pwc);
+    }
+    return result;
+}
+
+
+template < typename Curve01T, typename CurveT >
+unsigned int dist_test( Piecewise<SBasis> const& pwc,
+                        Curve01T const& A,
+                        CurveT const& B,
+                        double step )
+{
+    std::cerr << "======= inside dist test =======" << std::endl;
+    unsigned int total_checked_values = 0;
+    unsigned int total_error = 0;
+    double nptime, sample_distance;
+    Point At;
+    for (double t = 0; t <= 1; t += step)
+    {
+        At = A(t);
+        nptime = nearest_time(At, B);
+        sample_distance = distance(At, B(nptime));
+        if ( !are_near(pwc(t), sample_distance, 0.001) )
+        {
+            ++total_error;
+            std::cerr << "error at t: " << t << std::endl;
+        }
+        ++total_checked_values;
+    }
+    std::cerr << " total checked values : " << total_checked_values << std::endl;
+    std::cerr << " total error : " << total_error << std::endl;
+    return total_error;
+}
+
+}  // end namespace Geom
+
+
+using namespace Geom;
+
+class DCCToy : public Toy
+{
+  private:
+    void draw( cairo_t *cr, std::ostringstream *notify,
+               int width, int height, bool save, std::ostringstream *timer_stream) override
+    {
+        Point ulc(width - 300, height - 60 );
+        toggles[0].bounds = Rect(ulc, ulc + Point(160,25) );
+        toggles[1].bounds = Rect(ulc + Point(0,30), ulc + Point(160,55) );
+        sliders[0].geometry(ulc - Point(450,0), 400);
+        if (toggle0_status != toggles[0].on)
+        {
+            toggle0_status = toggles[0].on;
+            using std::swap;
+            swap(sliders[0], sliders[1]);
+        }
+
+        cairo_set_source_rgba(cr, 0.3, 0.3, 0.3, 1.0);
+        cairo_set_line_width (cr, 0.3);
+
+        if (choice == 0)
+        {
+            A = single_curve_psh.asBezier();
+            cairo_d2_sb(cr, A);
+        }
+        else if (choice == 1)
+        {
+            pA.clear();
+            for (unsigned int k = 0; k < path_curves; ++k)
+            {
+                PointSetHandle psh;
+                psh.pts.resize(path_handles_per_curve);
+                for (unsigned int h = 0; h < path_handles_per_curve; ++h)
+                {
+                    unsigned int kk = k * (path_handles_per_curve-1) + h;
+                    psh.pts[h] = path_psh.pts[kk];
+                }
+                pA.append(psh.asBezier());
+            }
+            cairo_path(cr, pA);
+        }
+        else if (choice == 2)
+        {
+            for (unsigned int i = 0; i < pwc_curves; ++i)
+            {
+                pwA.segs[i] = pwc_psh[i].asBezier();
+            }
+            cairo_pw_d2_sb(cr, pwA);
+        }
+
+        D2<SBasis> B = B_psh.asBezier();
+        cairo_d2_sb(cr, B);
+
+        double t = sliders[0].value();
+        Piecewise<SBasis> d;
+        unsigned int total_error = 0;
+        Point cursor;
+
+        if (!toggles[0].on)
+        {
+            if (choice == 0)
+            {
+                cursor = A(t);
+                d = distance(A, B, 40);
+                // uncomment following lines to view errors in computing the distance
+                //total_error = dist_test(d, A, B, 0.0004);
+            }
+            else if (choice == 1)
+            {
+                cursor = pA(t);
+                d = distance(pA, B, 40);
+                // uncomment following lines to view errors in computing the distance
+                //total_error = dist_test(d, pA, B, 0.0004);
+            }
+            else if (choice == 2)
+            {
+                cursor = pwA(t);
+                d = distance(pwA, B, 40);
+                // uncomment following lines to view errors in computing the distance
+                //total_error = dist_test(d, pwA, B, 0.0004);
+            }
+
+            double nptB = nearest_time(cursor, B);
+            draw_circ(cr, cursor);
+            cairo_move_to(cr, cursor);
+            cairo_line_to(cr, B(nptB));
+            cairo_stroke(cr);
+        }
+        else
+        {
+            Point np(0,0);
+            cursor = B(t);
+            if (choice == 0)
+            {
+                double nptA = nearest_time(cursor, A);
+                np = A(nptA);
+                d = distance(B, A, 40);
+                // uncomment following lines to view errors in computing the distance
+                //total_error = dist_test(d, B, A, 0.0004);
+            }
+            else if (choice == 1)
+            {
+                double nptA = nearest_time(cursor, pA);
+                np = pA(nptA);
+                d = distance(B, pA, 40);
+                // uncomment following lines to view errors in computing the distance
+                //total_error = dist_test(d, B, pA, 0.0004);
+            }
+            draw_circ(cr, cursor);
+            cairo_move_to(cr, cursor);
+            cairo_line_to(cr, np);
+            cairo_stroke(cr);
+        }
+
+        if (total_error != 0)
+            *notify << "total error: " << total_error << "   ";
+
+
+        // draw distance function
+        Piecewise< D2<SBasis> > pwc;
+        pwc.cuts = d.cuts;
+        pwc.segs.resize(d.size());
+        D2<SBasis> piece;
+        double domain_length = 800 / d.domain().extent();
+        for ( unsigned int i = 0; i < d.size(); ++i )
+        {
+            piece[X] = SBasis(Linear(20,20)
+                              + domain_length * Linear(d.cuts[i], d.cuts[i+1]));
+            piece[Y] = 3 * d.segs[i];
+            pwc.segs[i] = piece;
+        }
+        cairo_set_source_rgb(cr, 0.7,0,0);
+        cairo_pw_d2_sb(cr, pwc);
+        *notify << "total cuts: " << pwc.cuts.size();
+        if (toggles[1].on)
+        {
+            for (unsigned int i = 0; i < pwc.cuts.size(); ++i)
+            {
+                draw_handle(cr, pwc(pwc.cuts[i]));
+            }
+        }
+        else
+        {
+            draw_handle(cr, pwc(0.0));
+            draw_handle(cr, pwc(0.25));
+            draw_handle(cr, pwc(0.5));
+            draw_handle(cr, pwc(0.75));
+            draw_handle(cr, pwc(1));
+        }
+        draw_circ(cr, pwc(t));
+        cairo_stroke(cr);
+        Toy::draw(cr, notify, width, height, save,timer_stream);
+    }
+
+
+  public:
+    DCCToy()
+    {
+        toggle0_status = false;
+        choice = 0;
+
+        single_curve_handles = 6;
+        path_curves = 3;
+        path_handles_per_curve = 4;
+        path_total_handles = path_curves * (path_handles_per_curve - 1) + 1;
+        pwc_curves = 3;
+        pwc_handles_per_curve = 4;
+        pwc_total_handles = pwc_curves * pwc_handles_per_curve;
+        B_handles = 4;
+
+        if (choice == 0)
+        {
+            for (unsigned int i = 0; i < single_curve_handles; ++i)
+            {
+                single_curve_psh.push_back(700*uniform(), 500*uniform());
+            }
+            handles.push_back(&single_curve_psh);
+            sliders.emplace_back(0.0, 1.0, 0.0, 0.0, "t");
+        }
+        else if (choice == 1)
+        {
+            for (unsigned int i = 0; i < path_total_handles; ++i)
+            {
+                path_psh.push_back(700*uniform(), 500*uniform());
+            }
+            handles.push_back(&path_psh);
+            sliders.emplace_back(0.0, path_curves, 0.0, 0.0, "t");
+        }
+        else if (choice == 2)
+        {
+            pwc_psh.resize(pwc_curves);
+            pwA.segs.resize(pwc_curves);
+            pwA.cuts.resize(pwc_curves+1);
+            pwA.cuts[0] = 0;
+            double length = 1.0 / pwc_curves;
+            for (unsigned int i = 0; i < pwc_curves; ++i)
+            {
+                for (unsigned int j = 0; j < pwc_handles_per_curve; ++j)
+                {
+                    pwc_psh[i].push_back(700*uniform(), 500*uniform());
+                }
+                handles.push_back(&(pwc_psh[i]));
+                pwA.cuts[i+1] = pwA.cuts[i] + length;
+            }
+            sliders.emplace_back(0.0, 1.0, 0.0, 0.0, "t");
+        }
+
+        for (unsigned int i = 0; i < B_handles; ++i)
+        {
+            B_psh.push_back(700*uniform(), 500*uniform());
+        }
+        handles.push_back(&B_psh);
+        sliders.emplace_back(0.0, 1.0, 0.0, 0.0, "t");
+
+        toggles.emplace_back("d(A,B) <-> d(B,A)", false);
+        toggles.emplace_back("Show/Hide cuts", false);
+
+        handles.push_back(&(toggles[0]));
+        handles.push_back(&(toggles[1]));
+        handles.push_back(&(sliders[0]));
+
+    }
+
+  private:
+    bool toggle0_status;
+    unsigned int choice;
+    unsigned int single_curve_handles, B_handles;
+    unsigned int path_curves, path_handles_per_curve, path_total_handles;
+    unsigned int pwc_curves, pwc_handles_per_curve, pwc_total_handles;
+    PointSetHandle single_curve_psh;
+    PointSetHandle path_psh;
+    std::vector<PointSetHandle> pwc_psh;
+    PointSetHandle B_psh;
+    std::vector<Toggle> toggles;
+    std::vector<Slider> sliders;
+    D2<SBasis> A;
+    Path pA;
+    Piecewise< D2<SBasis> > pwA;
+};
+
+
+
+
+int main(int argc, char **argv)
+{
+    init( argc, argv, new DCCToy(), 840, 600 );
+    return 0;
+}
+
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+  indent-tabs-mode:nil
+  fill-column:99
+  End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :