/* * Nearest Points Toy * * 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 <toys/path-cairo.h> #include <toys/toy-framework.h> using namespace Geom; class np_finder { public: np_finder(cairo_t* _cr, D2<SBasis> const& _c1, D2<SBasis> const& _c2) : cr(_cr), c1(_c1), c2(_c2) { dc1 = derivative(c1); dc2 = derivative(c2); cd1 = dot(c1,dc1); cd2 = dot(c2,dc2); dsq = 10e30; } void operator() () { nearest_times_impl(0.5, 0, 1); 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, double from = 0, double to = 1 ) { //std::cerr << "[" << from << "," << to << "] t: " << t << std::endl; double st = t, et = t; std::pair<double, double> npc = loc_nearest_times(t, from, to); //std::cerr << "(" << npc.first << "," << npc.second << ")" << std::endl; 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); } if (npc.first < t) st = npc.first; else et = npc.first; //std::cerr << "[" << st << "," << et << "]" << std::endl; double d1 = std::fabs(st - from); double d2 = std::fabs(to - et); if ( d1 > EPSILON ) nearest_times_impl(from + d1/2, from, st); if ( d2 > EPSILON ) nearest_times_impl(et + d2/2, et, to); } std::pair<double, double> loc_nearest_times( double t, double from = 0, double to = 1 ) { unsigned int i = 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; //cairo_set_source_rgba(cr, 1/(t+1), t*t, t, 1.0); //cairo_move_to(cr, c1(t)); while( !are_near(ct, pt) ) { ++i; pt = ct; s = nearest_time(c1(ct), c2, dc2, cd2); //std::cerr << "s: " << s << std::endl; //cairo_line_to(cr, c2(s)); ct = nearest_time(c2(s), c1, dc1, cd1, from, to); //std::cerr << "t: " << t1 << std::endl; //cairo_line_to(cr, c1(ct)); if ( ct < from ) return npf; if ( ct > to ) return npt; } //std::cerr << "\n \n"; //std::cerr << "iterations: " << i << std::endl; 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 ( unsigned int i = 0; i < zeros.size(); ++i ) { if ( distsq > L2sq(sbc(zeros[i])) ) { closest = zeros[i]; 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; } private: static const Coord EPSILON = 10e-3; cairo_t* cr; D2<SBasis> const& c1, c2; D2<SBasis> dc1, dc2; SBasis cd1, cd2; double t1, t2, d, dsq; Point p1, p2; }; class NearestPoints : public Toy { private: void draw( cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) { cairo_set_line_width (cr, 0.2); D2<SBasis> A = handles_to_sbasis(handles.begin(), A_bez_ord-1); cairo_d2_sb(cr, A); D2<SBasis> B = handles_to_sbasis(handles.begin()+A_bez_ord, B_bez_ord-1); cairo_d2_sb(cr, B); np_finder np(cr, A, B); np(); 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) { unsigned int total_handles = A_bez_ord + B_bez_ord; for ( unsigned int i = 0; i < total_handles; ++i ) handles.push_back(Geom::Point(uniform()*400, uniform()*400)); } private: 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 :