curve.cpp revision 76addc201c409e81eaaa73fe27cc0f79c4db097c
/* Abstract curve type - implementation of default methods
*
* Authors:
* MenTaLguY <mental@rydia.net>
* Marco Cecchetti <mrcekets at gmail.com>
* Krzysztof Kosiński <tweenk.pl@gmail.com>
*
* 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>
//#include <iostream>
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 ingore_0 = unitTangentAt(0)[Y] <= 0;
bool ignore_1 = unitTangentAt(1)[Y] >= 0;
int wind = 0;
for (std::size_t i = 0; i < ts.size(); ++i) {
Coord t = ts[i];
//std::cout << t << std::endl;
if ((t == 0 && ingore_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
{
std::vector<CurveIntersection> result;
// Monotonic segments cannot have self-intersections.
// Thus, we can split the curve at roots and intersect the portions.
std::vector<Coord> splits;
std::auto_ptr<Curve> deriv(derivative());
splits = deriv->roots(0, X);
if (splits.empty()) {
return result;
}
deriv.reset();
splits.push_back(1.);
boost::ptr_vector<Curve> parts;
Coord previous = 0;
for (unsigned i = 0; i < splits.size(); ++i) {
if (splits[i] == 0.) continue;
parts.push_back(portion(previous, splits[i]));
previous = splits[i];
}
Coord prev_i = 0;
for (unsigned i = 0; i < parts.size()-1; ++i) {
Interval dom_i(prev_i, splits[i]);
prev_i = splits[i];
Coord prev_j = 0;
for (unsigned j = i+1; j < parts.size(); ++j) {
Interval dom_j(prev_j, splits[j]);
prev_j = splits[j];
std::vector<CurveIntersection> xs = parts[i].intersect(parts[j], eps);
for (unsigned k = 0; k < xs.size(); ++k) {
// to avoid duplicated intersections, skip values at exactly 1
if (xs[k].first == 1. || xs[k].second == 1.) continue;
Coord ti = dom_i.valueAt(xs[k].first);
Coord tj = dom_j.valueAt(xs[k].second);
CurveIntersection real(ti, tj, xs[k].point());
result.push_back(real);
}
}
}
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 :