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| -rw-r--r-- | src/2geom/curve.cpp | 235 |
1 files changed, 235 insertions, 0 deletions
diff --git a/src/2geom/curve.cpp b/src/2geom/curve.cpp new file mode 100644 index 0000000..f79edb3 --- /dev/null +++ b/src/2geom/curve.cpp @@ -0,0 +1,235 @@ +/* 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 +{ + /// Represents a sub-arc of the curve. + struct Subcurve + { + std::unique_ptr<Curve> curve; + Interval parameter_range; + + Subcurve(Curve *piece, Coord from, Coord to) + : curve{piece} + , parameter_range{from, to} + {} + }; + + /// A closure to split the curve into portions at the prescribed split points. + auto const split_into_subcurves = [=](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; + }; + + /// A closure to find pairwise intersections between the passed subcurves. + 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 : |