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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
{
/// 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 :
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