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-rw-r--r--src/toys/curve-curve-nearest-time.cpp609
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diff --git a/src/toys/curve-curve-nearest-time.cpp b/src/toys/curve-curve-nearest-time.cpp
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+++ b/src/toys/curve-curve-nearest-time.cpp
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+/*
+ * Nearest Points Toy 3
+ *
+ * Authors:
+ * Nathan Hurst <njh at njhurst.com>
+ * 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/bezier-to-sbasis.h>
+#include <2geom/sbasis-geometric.h>
+#include <2geom/piecewise.h>
+#include <2geom/path-intersection.h>
+
+#include <toys/path-cairo.h>
+#include <toys/toy-framework-2.h>
+
+#include <algorithm>
+
+
+using namespace Geom;
+
+
+class np_finder
+{
+public:
+ np_finder(cairo_t* _cr, D2<SBasis> const& _c1, D2<SBasis> const& _c2)
+ : cr(_cr), cc1(_c1), cc2(_c2), c1(_c1), c2(_c2)
+ {
+
+ dc1 = derivative(_c1);
+ dc2 = derivative(_c2);
+ cd1 = dot(_c1,dc1);
+ cd2 = dot(_c2,dc2);
+ dsq = 10e30;
+
+ Piecewise< D2<SBasis> > uv1 = unitVector(dc1, EPSILON);
+ Piecewise< D2<SBasis> > uv2 = unitVector(dc2, EPSILON);
+
+ dcn1 = dot(Piecewise< D2<SBasis> >(dc1), uv1);
+ dcn2 = dot(Piecewise< D2<SBasis> >(dc2), uv2);
+
+ r_dcn1 = cross(derivative(uv1), uv1);
+ r_dcn2 = cross(derivative(uv2), uv2);
+
+ k1 = Geom::divide(r_dcn1, dcn1, EPSILON, 3);
+ k2 = Geom::divide(r_dcn2, dcn2, EPSILON, 3);
+
+
+ n1 = divide(rot90(uv1), k1, EPSILON, 3);
+ n2 = divide(rot90(uv2), k2, EPSILON, 3);
+
+ std::vector<double> cuts1, cuts2;
+
+ // add cuts at points where the curvature is discontinuos
+ for ( unsigned int i = 1; i < k1.size(); ++i )
+ {
+ if( !are_near(k1[i-1].at1(), k1[i].at0()) )
+ {
+ cuts1.push_back(k1.cuts[i]);
+ }
+ }
+ for ( unsigned int i = 1; i < k2.size(); ++i )
+ {
+ if( !are_near(k2[i-1].at1(), k2[i].at0()) )
+ {
+ cuts2.push_back(k2.cuts[i]);
+ }
+ }
+
+ c1 = partition(c1, cuts1);
+ c2 = partition(c2, cuts2);
+
+// std::cerr << "# k1 discontinuitis" << std::endl;
+// for( unsigned int i = 0; i < cuts1.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << cuts1[i] << std::endl;
+// }
+// std::cerr << "# k2 discontinuitis" << std::endl;
+// for( unsigned int i = 0; i < cuts2.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << cuts2[i] << std::endl;
+// }
+
+ // add cuts at points were the curvature is zero
+ std::vector<double> k1_roots = roots(k1);
+ std::vector<double> k2_roots = roots(k2);
+ std::sort(k1_roots.begin(), k1_roots.end());
+ std::sort(k2_roots.begin(), k2_roots.end());
+ c1 = partition(c1, k1_roots);
+ c2 = partition(c2, k2_roots);
+
+// std::cerr << "# k1 zeros" << std::endl;
+// for( unsigned int i = 0; i < k1_roots.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << k1_roots[i] << std::endl;
+// }
+// std::cerr << "# k2 zeros" << std::endl;
+// for( unsigned int i = 0; i < k2_roots.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << k2_roots[i] << std::endl;
+// }
+
+
+ cairo_set_line_width(cr, 0.2);
+// cairo_set_source_rgba(cr, 0.0, 0.5, 0.0, 1.0);
+// for( unsigned int i = 1; i < c1.size(); ++i )
+// {
+// draw_circ(cr, c1[i].at0() );
+// }
+// for( unsigned int i = 1; i < c2.size(); ++i )
+// {
+// draw_circ(cr, c2[i].at0() );
+// }
+
+
+ // add cuts at nearest points to the other curve cuts points
+ cuts1.clear();
+ cuts1.reserve(c1.size()+1);
+ for ( unsigned int i = 0; i < c1.size(); ++i )
+ {
+ cuts1.push_back( nearest_time(c1[i].at0(), _c2, dc2, cd2) );
+ }
+ cuts1.push_back( nearest_time(c1[c1.size()-1].at1(), _c2, dc2, cd2) );
+
+// for ( unsigned int i = 0; i < c1.size(); ++i )
+// {
+// cairo_move_to( cr, c1[i].at0() );
+// cairo_line_to(cr, c2(cuts1[i]) );
+// }
+// cairo_move_to( cr, c1[c1.size()-1].at1() );
+// cairo_line_to(cr, c2(cuts1[c1.size()]));
+
+ std::sort(cuts1.begin(), cuts1.end());
+
+ cuts2.clear();
+ cuts2.reserve(c2.size()+1);
+ for ( unsigned int i = 0; i < c2.size(); ++i )
+ {
+ cuts2.push_back( nearest_time(c2[i].at0(), _c1, dc1, cd1) );
+ }
+ cuts2.push_back( nearest_time(c2[c2.size()-1].at1(), _c1, dc1, cd1) );
+
+// for ( unsigned int i = 0; i < c2.size(); ++i )
+// {
+// cairo_move_to( cr, c2[i].at0() );
+// cairo_line_to(cr, c1(cuts2[i]) );
+// }
+// cairo_move_to( cr, c2[c2.size()-1].at1() );
+// cairo_line_to(cr, c1(cuts2[c2.size()]));
+// cairo_stroke(cr);
+
+ std::sort(cuts2.begin(), cuts2.end());
+
+ c1 = partition(c1, cuts2);
+ c2 = partition(c2, cuts1);
+
+
+ // copy curve to preserve cuts status
+ Piecewise< D2<SBasis> > pwc1 = c1;
+ n1 = partition(n1, pwc1.cuts);
+ pwc1 = partition(pwc1, n1.cuts);
+ r_dcn1 = partition(r_dcn1, n1.cuts);
+ Piecewise< D2<SBasis> > pwc2 = c2;
+ n2 = partition(n2, pwc2.cuts);
+ pwc2 = partition(pwc2, n2.cuts);
+
+ assert( pwc1.size() == n1.size() );
+ assert( pwc2.size() == n2.size() );
+ assert( r_dcn1.size() == n1.size() );
+
+ // add cuts at curvature max and min points
+ Piecewise<SBasis> dk1 = derivative(k1);
+ Piecewise<SBasis> dk2 = derivative(k2);
+ std::vector<double> dk1_roots = roots(dk1);
+ std::vector<double> dk2_roots = roots(dk2);
+ std::sort(dk1_roots.begin(), dk1_roots.end());
+ std::sort(dk2_roots.begin(), dk2_roots.end());
+
+ c1 = partition(c1, dk1_roots);
+ c2 = partition(c2, dk2_roots);
+
+// std::cerr << "# k1 min/max" << std::endl;
+// for( unsigned int i = 0; i < dk1_roots.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << dk1_roots[i] << std::endl;
+// }
+// std::cerr << "# k2 min/max" << std::endl;
+// for( unsigned int i = 0; i < dk2_roots.size(); ++i )
+// {
+// std::cerr << "[" << i << "]= " << dk2_roots[i] << std::endl;
+// }
+
+// cairo_set_source_rgba(cr, 0.0, 0.0, 0.6, 1.0);
+// for( unsigned int i = 0; i < dk1_roots.size(); ++i )
+// {
+// draw_handle(cr, c1(dk1_roots[i]));
+// }
+// for( unsigned int i = 0; i < dk2_roots.size(); ++i )
+// {
+// draw_handle(cr, c2(dk2_roots[i]));
+// }
+
+
+ // add cuts at nearest points to max and min curvature points
+ // of the other curve
+ cuts1.clear();
+ cuts1.reserve(dk2_roots.size());
+ for (double dk2_root : dk2_roots)
+ {
+ cuts1.push_back(nearest_time(_c2(dk2_root), _c1, dc1, cd1));
+ }
+
+// for( unsigned int i = 0; i < dk2_roots.size(); ++i )
+// {
+// cairo_move_to(cr, c2(dk2_roots[i]));
+// cairo_line_to(cr, c1(cuts1[i]));
+// }
+// cairo_stroke(cr);
+
+ std::sort(cuts1.begin(), cuts1.end());
+ c1 = partition(c1, cuts1);
+
+
+ // swap normal vector direction and fill the skip list
+ skip_list.clear();
+ skip_list.resize(c1.size(), false);
+ double npt;
+ Point p, nv;
+ unsigned int si;
+ for ( unsigned int i = 0; i < pwc1.size(); ++i )
+ {
+ p = pwc1[i](0.5);
+ nv = n1[i](0.5);
+ npt = nearest_time(p, _c2, dc2, cd2);
+ if( dot( _c2(npt) - p, nv ) > 0 )
+ {
+ if ( dot( nv, n2(npt) ) > 0 )
+ {
+ n1[i] = -n1[i];
+ r_dcn1[i] = -r_dcn1[i];
+ }
+ else
+ {
+ si = c1.segN( n1.mapToDomain(0.5, i) );
+ skip_list[si] = true;
+ }
+ }
+ }
+
+
+ for ( unsigned int i = 0; i < pwc2.size(); ++i )
+ {
+ p = pwc2[i](0.5);
+ nv = n2[i](0.5);
+ npt = nearest_time(p, _c1, dc1, cd1);
+ if( dot( _c1(npt) - p, nv ) > 0 )
+ {
+ if ( dot( nv, n1(npt) ) > 0 )
+ {
+ n2[i] = -n2[i];
+ }
+ }
+ }
+
+
+ evl1 = c1 + n1;
+ evl2 = c2 + n2;
+
+// cairo_set_source_rgba(cr, 0.3, 0.3, 0.3, 1.0);
+// for ( unsigned int i = 0; i < c1.size(); ++i )
+// {
+// double t = c1.mapToDomain(0.5, i);
+// cairo_move_to(cr, c1(t));
+// cairo_line_to(cr, c1(t) + 30*unit_vector(n1(t)));
+// }
+//
+// for ( unsigned int i = 0; i < c2.size(); ++i )
+// {
+// double t = c2.mapToDomain(0.5, i);
+// cairo_move_to(cr, c2(t));
+// cairo_line_to(cr, c2(t) + 30*unit_vector(n2(t)));
+// }
+// cairo_stroke(cr);
+
+ std::cerr << "# skip list: ";
+ for( unsigned int i = 0; i < c1.cuts.size(); ++i )
+ {
+ if ( skip_list[i] )
+ std::cerr << i << " ";
+ }
+ std::cerr << std::endl;
+
+ cairo_set_line_width(cr, 0.4);
+ cairo_set_source_rgba(cr, 0.6, 0.0, 0.0, 1.0);
+ for( unsigned int i = 0; i < c1.size(); ++i )
+ {
+ if ( skip_list[i] )
+ {
+ cairo_move_to(cr, c1[i].at0());
+ cairo_line_to(cr, c1[i].at1());
+ }
+ }
+ cairo_stroke(cr);
+
+ cairo_set_source_rgba(cr, 0.2, 0.2, 0.2, 1.0);
+ for( unsigned int i = 1; i < c1.size(); ++i )
+ {
+ draw_circ(cr, c1[i].at0() );
+ }
+ cairo_stroke(cr);
+
+ std::cerr << "# c1 cuts: " << std::endl;
+ for( unsigned int i = 0; i < c1.cuts.size(); ++i )
+ {
+ std::cerr << "c1.cuts[" << i << "]= " << c1.cuts[i] << std::endl;
+ }
+
+ }
+
+ void operator() ()
+ {
+ nearest_times_impl();
+ d = sqrt(dsq);
+ }
+
+ Point firstPoint() const
+ {
+ return p1;
+ }
+
+ Point secondPoint() const
+ {
+ return p2;
+ }
+
+ double firstValue() const
+ {
+ return t1;
+ }
+
+ double secondValue() const
+ {
+ return t2;
+ }
+
+ double distance() const
+ {
+ return d;
+ }
+
+private:
+ void nearest_times_impl()
+ {
+ double t;
+ for ( unsigned int i = 0; i < c1.size(); ++i )
+ {
+ if ( skip_list[i] ) continue;
+ std::cerr << i << " ";
+ t = c1.mapToDomain(0.5, i);
+ std::pair<double, double> npc = loc_nearest_times(t, c1.cuts[i], c1.cuts[i+1]);
+ if ( npc.second != -1 && dsq > L2sq(c1(npc.first) - c2(npc.second)) )
+ {
+ t1 = npc.first;
+ t2 = npc.second;
+ p1 = c1(t1);
+ p2 = c2(t2);
+ dsq = L2sq(p1 - p2);
+ }
+ }
+ }
+
+ std::pair<double, double>
+ loc_nearest_times( double t, double from = 0, double to = 1 )
+ {
+ std::cerr << "[" << from << "," << to << "] t: " << t << std::endl;
+ unsigned int iter = 0, iter1 = 0, iter2 = 0;
+ std::pair<double, double> np(-1,-1);
+ std::pair<double, double> npf(from, -1);
+ std::pair<double, double> npt(to, -1);
+ double ct = t;
+ double pt = -1;
+ double s = nearest_time(c1(t), cc2, dc2, cd2);
+ cairo_set_source_rgba(cr, 1/(t+1), t*t, t, 1.0);
+ cairo_move_to(cr, c1(t));
+ while( !are_near(ct, pt) && iter < 1000 )
+ {
+ pt = ct;
+ double angle = angle_between( n1(ct), evl2(s) - evl1(ct) );
+ assert( !std::isnan(angle) );
+ angle = (angle > 0) ? angle - M_PI : angle + M_PI;
+ if ( std::fabs(angle) < M_PI/12 )
+ {
+ ++iter2;
+// cairo_move_to(cr, c1(ct));
+// cairo_line_to(cr, evl1(ct));
+// cairo_line_to(cr, evl2(s));
+ //std::cerr << "s: " << s << std::endl;
+ //std::cerr << "t: " << ct << std::endl;
+
+ ct = ct + angle / r_dcn1(ct);
+ s = nearest_time(c1(ct), cc2, dc2, cd2);
+// angle = angle_between( n2(s), evl1(ct) - evl2(s) );
+// assert( !std::isnan(angle) );
+// angle = (angle > 0) ? angle - M_PI : angle + M_PI;
+// s = s + angle / (dcn2(s) * k2(s));
+ }
+ else
+ {
+ ++iter1;
+ ct = nearest_time(c2(s), cc1, dc1, cd1, from, to);
+ s = nearest_time(c1(ct), cc2, dc2, cd2);
+ }
+ iter = iter1 + iter2;
+ //std::cerr << "s: " << s << std::endl;
+ //std::cerr << "t: " << ct << std::endl;
+ //cairo_line_to(cr, c2(s));
+ //cairo_line_to(cr, c1(ct));
+ //std::cerr << "d(pt, ct) = " << std::fabs(ct - pt) << std::endl;
+ if ( ct < from )
+ {
+ std::cerr << "break left" << std::endl;
+ np = npf;
+ break;
+ }
+ if ( ct > to )
+ {
+ std::cerr << "break right" << std::endl;
+ np =npt;
+ break;
+ }
+ }
+ //std::cerr << "\n \n";
+ std::cerr << "iterations: " << iter1 << " + " << iter2 << " = "<< iter << std::endl;
+ assert(iter < 3000);
+ //cairo_move_to(cr, c1(ct));
+ //cairo_line_to(cr, c2(s));
+ cairo_stroke(cr);
+ np.first = ct;
+ np.second = s;
+ return np;
+ }
+
+ double nearest_time( Point const& p, D2<SBasis> const&c, D2<SBasis> const& dc, SBasis const& cd, double from = 0, double to = 1 )
+ {
+ D2<SBasis> sbc = c - p;
+ SBasis dd = cd - dotp(p, dc);
+ std::vector<double> zeros = roots(dd);
+ double closest = from;
+ double distsq = L2sq(sbc(from));
+ for (double zero : zeros)
+ {
+ if ( distsq > L2sq(sbc(zero)) )
+ {
+ closest = zero;
+ distsq = L2sq(sbc(closest));
+ }
+ }
+ if ( distsq > L2sq(sbc(to)) )
+ closest = to;
+ return closest;
+ }
+
+ SBasis dotp(Point const& p, D2<SBasis> const& c)
+ {
+ SBasis d;
+ d.resize(c[X].size());
+ for ( unsigned int i = 0; i < c[0].size(); ++i )
+ {
+ for( unsigned int j = 0; j < 2; ++j )
+ d[i][j] = p[X] * c[X][i][j] + p[Y] * c[Y][i][j];
+ }
+ return d;
+ }
+
+ Piecewise< D2<SBasis> >
+ divide( Piecewise< D2<SBasis> > const& a, Piecewise<SBasis> const& b, double tol, unsigned int k, double zero=1.e-3)
+ {
+ D2< Piecewise<SBasis> > aa = make_cuts_independent(a);
+ D2< Piecewise<SBasis> > q(Geom::divide(aa[0], b, tol, k, zero), Geom::divide(aa[1], b, tol, k, zero));
+ return sectionize(q);
+ }
+
+ struct are_near_
+ {
+ bool operator() (double x, double y, double eps = Geom::EPSILON )
+ {
+ return are_near(x, y, eps);
+ }
+ };
+
+private:
+ cairo_t* cr;
+ D2<SBasis> const& cc1, cc2;
+ Piecewise< D2<SBasis> > c1, c2;
+ D2<SBasis> dc1, dc2;
+ SBasis cd1, cd2;
+ Piecewise< D2<SBasis> > n1, n2, evl1, evl2;
+ Piecewise<SBasis> k1, k2, dcn1, dcn2, r_dcn1, r_dcn2;
+ double t1, t2, d, dsq;
+ Point p1, p2;
+ std::vector<bool> skip_list;
+};
+
+
+
+
+class NearestPoints : public Toy
+{
+ private:
+ void draw( cairo_t *cr, std::ostringstream *notify,
+ int width, int height, bool save, std::ostringstream *timer_stream) override
+ {
+ cairo_set_line_width (cr, 0.3);
+ D2<SBasis> A = pshA.asBezier();
+ cairo_d2_sb(cr, A);
+ D2<SBasis> B = pshB.asBezier();
+ cairo_d2_sb(cr, B);
+ cairo_stroke(cr);
+
+ np_finder np(cr, A, B);
+ Path AP, BP;
+ AP.append(A); BP.append(B);
+ Crossings ip_list = curve_sweep<SimpleCrosser>(AP, BP);
+ if( ip_list.empty() )
+ {
+ np();
+ cairo_set_line_width (cr, 0.4);
+ cairo_set_source_rgba(cr, 0.7, 0.0, 0.7, 1.0);
+ cairo_move_to(cr, np.firstPoint());
+ cairo_line_to(cr, np.secondPoint());
+ cairo_stroke(cr);
+ //std::cerr << "np: (" << np.firstValue() << "," << np.secondValue() << ")" << std::endl;
+ }
+ Toy::draw(cr, notify, width, height, save,timer_stream);
+ }
+
+ public:
+ NearestPoints(unsigned int _A_bez_ord, unsigned int _B_bez_ord)
+ : A_bez_ord(_A_bez_ord), B_bez_ord(_B_bez_ord)
+ {
+ handles.push_back(&pshA);
+ handles.push_back(&pshB);
+ for ( unsigned int i = 0; i < A_bez_ord; ++i )
+ pshA.push_back(Geom::Point(uniform()*400, uniform()*400));
+ for ( unsigned int i = 0; i < B_bez_ord; ++i )
+ pshB.push_back(Geom::Point(uniform()*400, uniform()*400));
+
+ }
+
+ private:
+ PointSetHandle pshA, pshB;
+ unsigned int A_bez_ord;
+ unsigned int B_bez_ord;
+};
+
+
+int main(int argc, char **argv)
+{
+ unsigned int A_bez_ord=8;
+ unsigned int B_bez_ord=5;
+ if(argc > 2)
+ sscanf(argv[2], "%d", &B_bez_ord);
+ if(argc > 1)
+ sscanf(argv[1], "%d", &A_bez_ord);
+
+ init( argc, argv, new NearestPoints(A_bez_ord, B_bez_ord));
+ 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 :
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