curve.cpp

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/* Abstract curve type - implementation of default methods
 *
 * Authors:
 *   MenTaLguY <mental@rydia.net>
 *   Marco Cecchetti <mrcekets at gmail.com>
 *   Krzysztof Kosiński <tweenk.pl@gmail.com>
 *   Rafał Siejakowski <rs@rs-math.net>
 * 
 * Copyright 2007-2009 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/curve.h>
#include <2geom/exception.h>
#include <2geom/nearest-time.h>
#include <2geom/sbasis-geometric.h>
#include <2geom/sbasis-to-bezier.h>
#include <2geom/ord.h>
#include <2geom/path-sink.h>
 
namespace Geom 
{
 
Coord Curve::nearestTime(Point const& p, Coord a, Coord b) const
{
    return nearest_time(p, toSBasis(), a, b);
}
 
std::vector<Coord> Curve::allNearestTimes(Point const& p, Coord from, Coord to) const
{
    return all_nearest_times(p, toSBasis(), from, to);
}
 
Coord Curve::length(Coord tolerance) const
{
    return ::Geom::length(toSBasis(), tolerance);
}
 
int Curve::winding(Point const &p) const
{
    try {
        std::vector<Coord> ts = roots(p[Y], Y);
        if(ts.empty()) return 0;
        std::sort(ts.begin(), ts.end());
 
        // skip endpoint roots when they are local maxima on the Y axis
        // this follows the convention used in other winding routines,
        // i.e. that the bottommost coordinate is not part of the shape
        bool ignore_0 = unitTangentAt(0)[Y] <= 0;
        bool ignore_1 = unitTangentAt(1)[Y] >= 0;
 
        int wind = 0;
        for (double t : ts) {
            //std::cout << t << std::endl;
            if ((t == 0 && ignore_0) || (t == 1 && ignore_1)) continue;
            if (valueAt(t, X) > p[X]) { // root is ray intersection
                Point tangent = unitTangentAt(t);
                if (tangent[Y] > 0) {
                    // at the point of intersection, curve goes in +Y direction,
                    // so it winds in the direction of positive angles
                    ++wind;
                } else if (tangent[Y] < 0) {
                    --wind;
                }
            }
        }
        return wind;
    } catch (InfiniteSolutions const &e) {
        // this means we encountered a line segment exactly coincident with the point
        // skip, since this will be taken care of by endpoint roots in other segments
        return 0;
    }
}
 
std::vector<CurveIntersection> Curve::intersect(Curve const &/*other*/, Coord /*eps*/) const
{
    // TODO: approximate as Bezier
    THROW_NOTIMPLEMENTED();
}
 
std::vector<CurveIntersection> Curve::intersectSelf(Coord eps) const
{
    struct Subcurve
    {
        std::unique_ptr<Curve> curve;
        Interval parameter_range;
 
        Subcurve(Curve *piece, Coord from, Coord to)
            : curve{piece}
            , parameter_range{from, to}
        {}
    };
 
    auto const split_into_subcurves = [this] (std::vector<Coord> const &splits) {
        std::vector<Subcurve> result;
        result.reserve(splits.size() + 1);
        Coord previous = 0;
        for (Coord split : splits) {
            // Use global EPSILON since we're operating on normalized curve times.
            if (split < EPSILON || split > 1.0 - EPSILON) {
                continue;
            }
            result.emplace_back(portion(previous, split), previous, split);
            previous = split;
        }
        result.emplace_back(portion(previous, 1.0), previous, 1.0);
        return result;
    };
 
    auto const pairwise_intersect = [=](std::vector<Subcurve> const &subcurves) {
        std::vector<CurveIntersection> result;
        for (unsigned i = 0; i < subcurves.size(); i++) {
            for (unsigned j = i + 1; j < subcurves.size(); j++) {
                auto const xings = subcurves[i].curve->intersect(*subcurves[j].curve, eps);
                for (auto const &xing : xings) {
                    // To avoid duplicate intersections, skip values at exactly 1.
                    if (xing.first == 1. || xing.second == 1.) {
                        continue;
                    }
                    Coord const ti = subcurves[i].parameter_range.valueAt(xing.first);
                    Coord const tj = subcurves[j].parameter_range.valueAt(xing.second);
                    result.emplace_back(ti, tj, xing.point());
                }
            }
        }
        std::sort(result.begin(), result.end());
        return result;
    };
 
    // Monotonic segments cannot have self-intersections. Thus, we can split
    // the curve at critical points of the X or Y coordinate and intersect
    // the portions. However, there's the risk that a juncture between two
    // adjacent portions is mistaken for an intersection due to numerical errors.
    // Hence, we run the algorithm for both the X and Y coordinates and only
    // keep the intersections that show up in both intersection lists.
 
    // Find the critical points of both coordinates.
    std::unique_ptr<Curve> deriv{derivative()};
    auto const crits_x = deriv->roots(0, X);
    auto const crits_y = deriv->roots(0, Y);
    if (crits_x.empty() || crits_y.empty()) {
        return {};
    }
 
    // Split into pieces in two ways and find self-intersections.
    auto const pieces_x = split_into_subcurves(crits_x);
    auto const pieces_y = split_into_subcurves(crits_y);
    auto const crossings_from_x = pairwise_intersect(pieces_x);
    auto const crossings_from_y = pairwise_intersect(pieces_y);
    if (crossings_from_x.empty() || crossings_from_y.empty()) {
        return {};
    }
 
    // Filter the results, only keeping self-intersections found by both approaches.
    std::vector<CurveIntersection> result;
    unsigned index_y = 0;
    for (auto &&candidate_x : crossings_from_x) {
        // Find a crossing corresponding to this one in the y-method collection.
        while (index_y != crossings_from_y.size()) {
            auto const gap = crossings_from_y[index_y].first - candidate_x.first;
            if (std::abs(gap) < EPSILON) {
                // We found the matching intersection!
                result.emplace_back(candidate_x);
                index_y++;
                break;
            } else if (gap < 0.0) {
                index_y++;
            } else {
                break;
            }
        }
    }
    return result;
}
 
Point Curve::unitTangentAt(Coord t, unsigned n) const
{
    std::vector<Point> derivs = pointAndDerivatives(t, n);
    for (unsigned deriv_n = 1; deriv_n < derivs.size(); deriv_n++) {
        Coord length = derivs[deriv_n].length();
        if ( ! are_near(length, 0) ) {
            // length of derivative is non-zero, so return unit vector
            return derivs[deriv_n] / length;
        }
    }
    return Point (0,0);
};
 
void Curve::feed(PathSink &sink, bool moveto_initial) const
{
    std::vector<Point> pts;
    sbasis_to_bezier(pts, toSBasis(), 2); //TODO: use something better!
    if (moveto_initial) {
        sink.moveTo(initialPoint());
    }
    sink.curveTo(pts[0], pts[1], pts[2]);
}
 
} // namespace Geom
 
/*
  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 :