Adding upstream version 1.3.upstream/1.3upstream

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

1 files changed, 322 insertions, 0 deletions

diff --git a/src/2geom/nearest-time.cpp b/src/2geom/nearest-time.cpp
new file mode 100644
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--- /dev/null
+++ b/src/2geom/nearest-time.cpp
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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
+
+