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+/** @file
+ * @brief Nearest time routines for D2<SBasis> and Piecewise<D2<SBasis>>
+ *//*
+ * Authors:
+ * Marco Cecchetti <mrcekets at gmail.com>
+ *
+ * Copyright 2007-2008 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/nearest-time.h>
+#include <algorithm>
+
+namespace Geom
+{
+
+Coord nearest_time(Point const &p, D2<Bezier> const &input, Coord from, Coord to)
+{
+ Interval domain(from, to);
+ bool partial = false;
+
+ if (domain.min() < 0 || domain.max() > 1) {
+ THROW_RANGEERROR("[from,to] interval out of bounds");
+ }
+
+ if (input.isConstant(0)) return from;
+
+ D2<Bezier> bez;
+ if (domain.min() != 0 || domain.max() != 1) {
+ bez = portion(input, domain) - p;
+ partial = true;
+ } else {
+ bez = input - p;
+ }
+
+ // find extrema of the function x(t)^2 + y(t)^2
+ // use the fact that (f^2)' = 2 f f'
+ // this reduces the order of the distance function by 1
+ D2<Bezier> deriv = derivative(bez);
+ std::vector<Coord> ts = (multiply(bez[X], deriv[X]) + multiply(bez[Y], deriv[Y])).roots();
+
+ Coord t = -1, mind = infinity();
+ for (double i : ts) {
+ Coord droot = L2sq(bez.valueAt(i));
+ if (droot < mind) {
+ mind = droot;
+ t = i;
+ }
+ }
+
+ // also check endpoints
+ Coord dinitial = L2sq(bez.at0());
+ Coord dfinal = L2sq(bez.at1());
+
+ if (dinitial < mind) {
+ mind = dinitial;
+ t = 0;
+ }
+ if (dfinal < mind) {
+ //mind = dfinal;
+ t = 1;
+ }
+
+ if (partial) {
+ t = domain.valueAt(t);
+ }
+ return t;
+}
+
+////////////////////////////////////////////////////////////////////////////////
+// D2<SBasis> versions
+
+/*
+ * Return the parameter t of the nearest time value on the portion of the curve "c",
+ * related to the interval [from, to], to the point "p".
+ * The needed curve derivative "dc" is passed as parameter.
+ * The function return the first nearest time value to "p" that is found.
+ */
+
+double nearest_time(Point const& p,
+ D2<SBasis> const& c,
+ D2<SBasis> const& dc,
+ double from, double to )
+{
+ if ( from > to ) std::swap(from, to);
+ if ( from < 0 || to > 1 )
+ {
+ THROW_RANGEERROR("[from,to] interval out of bounds");
+ }
+ if (c.isConstant()) return from;
+ SBasis dd = dot(c - p, dc);
+ //std::cout << dd << std::endl;
+ std::vector<double> zeros = Geom::roots(dd);
+
+ double closest = from;
+ double min_dist_sq = L2sq(c(from) - p);
+ for (double zero : zeros)
+ {
+ double distsq = L2sq(c(zero) - p);
+ if ( min_dist_sq > L2sq(c(zero) - p) )
+ {
+ closest = zero;
+ min_dist_sq = distsq;
+ }
+ }
+ if ( min_dist_sq > L2sq( c(to) - p ) )
+ closest = to;
+ return closest;
+
+}
+
+/*
+ * Return the parameters t of all the nearest points on the portion of
+ * the curve "c", related to the interval [from, to], to the point "p".
+ * The needed curve derivative "dc" is passed as parameter.
+ */
+
+std::vector<double>
+all_nearest_times(Point const &p,
+ D2<SBasis> const &c,
+ D2<SBasis> const &dc,
+ double from, double to)
+{
+ if (from > to) {
+ std::swap(from, to);
+ }
+ if (from < 0 || to > 1) {
+ THROW_RANGEERROR("[from,to] interval out of bounds");
+ }
+
+ std::vector<double> result;
+ if (c.isConstant()) {
+ result.push_back(from);
+ return result;
+ }
+ SBasis dd = dot(c - p, dc);
+
+ std::vector<double> zeros = Geom::roots(dd);
+ std::vector<double> candidates;
+ candidates.push_back(from);
+ candidates.insert(candidates.end(), zeros.begin(), zeros.end());
+ candidates.push_back(to);
+ std::vector<double> distsq;
+ distsq.reserve(candidates.size());
+ for (double candidate : candidates) {
+ distsq.push_back(L2sq(c(candidate) - p));
+ }
+ unsigned closest = 0;
+ double dsq = distsq[0];
+ for (unsigned i = 1; i < candidates.size(); ++i) {
+ if (dsq > distsq[i]) {
+ closest = i;
+ dsq = distsq[i];
+ }
+ }
+ for (unsigned i = 0; i < candidates.size(); ++i) {
+ if (distsq[closest] == distsq[i]) {
+ result.push_back(candidates[i]);
+ }
+ }
+ return result;
+}
+
+
+////////////////////////////////////////////////////////////////////////////////
+// Piecewise< D2<SBasis> > versions
+
+
+double nearest_time(Point const &p,
+ Piecewise< D2<SBasis> > const &c,
+ double from, double to)
+{
+ if (from > to) std::swap(from, to);
+ if (from < c.cuts[0] || to > c.cuts[c.size()]) {
+ THROW_RANGEERROR("[from,to] interval out of bounds");
+ }
+
+ unsigned si = c.segN(from);
+ unsigned ei = c.segN(to);
+ if (si == ei) {
+ double nearest =
+ nearest_time(p, c[si], c.segT(from, si), c.segT(to, si));
+ return c.mapToDomain(nearest, si);
+ }
+
+ double t;
+ double nearest = nearest_time(p, c[si], c.segT(from, si));
+ unsigned int ni = si;
+ double dsq;
+ double mindistsq = distanceSq(p, c[si](nearest));
+ Rect bb;
+ for (unsigned i = si + 1; i < ei; ++i) {
+ bb = *bounds_fast(c[i]);
+ dsq = distanceSq(p, bb);
+ if ( mindistsq <= dsq ) continue;
+
+ t = nearest_time(p, c[i]);
+ dsq = distanceSq(p, c[i](t));
+ if (mindistsq > dsq) {
+ nearest = t;
+ ni = i;
+ mindistsq = dsq;
+ }
+ }
+ bb = *bounds_fast(c[ei]);
+ dsq = distanceSq(p, bb);
+ if (mindistsq > dsq) {
+ t = nearest_time(p, c[ei], 0, c.segT(to, ei));
+ dsq = distanceSq(p, c[ei](t));
+ if (mindistsq > dsq) {
+ nearest = t;
+ ni = ei;
+ }
+ }
+ return c.mapToDomain(nearest, ni);
+}
+
+std::vector<double>
+all_nearest_times(Point const &p,
+ Piecewise< D2<SBasis> > const &c,
+ double from, double to)
+{
+ if (from > to) {
+ std::swap(from, to);
+ }
+ if (from < c.cuts[0] || to > c.cuts[c.size()]) {
+ THROW_RANGEERROR("[from,to] interval out of bounds");
+ }
+
+ unsigned si = c.segN(from);
+ unsigned ei = c.segN(to);
+ if ( si == ei )
+ {
+ std::vector<double> all_nearest =
+ all_nearest_times(p, c[si], c.segT(from, si), c.segT(to, si));
+ for (double & i : all_nearest)
+ {
+ i = c.mapToDomain(i, si);
+ }
+ return all_nearest;
+ }
+ std::vector<double> all_t;
+ std::vector< std::vector<double> > all_np;
+ all_np.push_back( all_nearest_times(p, c[si], c.segT(from, si)) );
+ std::vector<unsigned> ni;
+ ni.push_back(si);
+ double dsq;
+ double mindistsq = distanceSq( p, c[si](all_np.front().front()) );
+ Rect bb;
+
+ for (unsigned i = si + 1; i < ei; ++i) {
+ bb = *bounds_fast(c[i]);
+ dsq = distanceSq(p, bb);
+ if ( mindistsq < dsq ) continue;
+ all_t = all_nearest_times(p, c[i]);
+ dsq = distanceSq( p, c[i](all_t.front()) );
+ if ( mindistsq > dsq )
+ {
+ all_np.clear();
+ all_np.push_back(all_t);
+ ni.clear();
+ ni.push_back(i);
+ mindistsq = dsq;
+ }
+ else if ( mindistsq == dsq )
+ {
+ all_np.push_back(all_t);
+ ni.push_back(i);
+ }
+ }
+ bb = *bounds_fast(c[ei]);
+ dsq = distanceSq(p, bb);
+ if (mindistsq >= dsq) {
+ all_t = all_nearest_times(p, c[ei], 0, c.segT(to, ei));
+ dsq = distanceSq( p, c[ei](all_t.front()) );
+ if (mindistsq > dsq) {
+ for (double & i : all_t) {
+ i = c.mapToDomain(i, ei);
+ }
+ return all_t;
+ } else if (mindistsq == dsq) {
+ all_np.push_back(all_t);
+ ni.push_back(ei);
+ }
+ }
+ std::vector<double> all_nearest;
+ for (unsigned i = 0; i < all_np.size(); ++i) {
+ for (unsigned int j = 0; j < all_np[i].size(); ++j) {
+ all_nearest.push_back( c.mapToDomain(all_np[i][j], ni[i]) );
+ }
+ }
+ all_nearest.erase(std::unique(all_nearest.begin(), all_nearest.end()),
+ all_nearest.end());
+ return all_nearest;
+}
+
+} // end namespace Geom
+
+
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