point.cpp

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/*
 *  Authors:
 *    Michael G. Sloan <mgsloan@gmail.com>
 *    Nathan Hurst <njh@njhurst.com>
 *    Krzysztof Kosiński <tweenk.pl@gmail.com>
 *
 * Copyright (C) 2006-2009 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 <assert.h>
#include <math.h>
#include <2geom/angle.h>
#include <2geom/coord.h>
#include <2geom/point.h>
#include <2geom/transforms.h>
 
namespace Geom {
 
Point Point::polar(Coord angle) {
    Point ret;
    Coord remainder = Angle(angle).radians0();
    if (are_near(remainder, 0) || are_near(remainder, 2*M_PI)) {
        ret[X] = 1;
        ret[Y] = 0;
    } else if (are_near(remainder, M_PI/2)) {
        ret[X] = 0;
        ret[Y] = 1;
    } else if (are_near(remainder, M_PI)) {
        ret[X] = -1;
        ret[Y] = 0;
    } else if (are_near(remainder, 3*M_PI/2)) {
        ret[X] = 0;
        ret[Y] = -1;
    } else {
        sincos(angle, ret[Y], ret[X]);
    }
    return ret;
}
 
void Point::normalize() {
    double len = hypot(_pt[0], _pt[1]);
    if(len == 0) return;
    if(std::isnan(len)) return;
    static double const inf = HUGE_VAL;
    if(len != inf) {
        *this /= len;
    } else {
        unsigned n_inf_coords = 0;
        /* Delay updating pt in case neither coord is infinite. */
        Point tmp;
        for ( unsigned i = 0 ; i < 2 ; ++i ) {
            if ( _pt[i] == inf ) {
                ++n_inf_coords;
                tmp[i] = 1.0;
            } else if ( _pt[i] == -inf ) {
                ++n_inf_coords;
                tmp[i] = -1.0;
            } else {
                tmp[i] = 0.0;
            }
        }
        switch (n_inf_coords) {
            case 0: {
                /* Can happen if both coords are near +/-DBL_MAX. */
                *this /= 4.0;
                len = hypot(_pt[0], _pt[1]);
                assert(len != inf);
                *this /= len;
                break;
            }
            case 1: {
                *this = tmp;
                break;
            }
            case 2: {
                *this = tmp * sqrt(0.5);
                break;
            }
        }
    }
}
 
Coord L1(Point const &p) {
    Coord d = 0;
    for ( int i = 0 ; i < 2 ; i++ ) {
        d += fabs(p[i]);
    }
    return d;
}
 
Coord LInfty(Point const &p) {
    Coord const a(fabs(p[0]));
    Coord const b(fabs(p[1]));
    return ( a < b || std::isnan(b)
             ? b
             : a );
}
 
bool is_zero(Point const &p) {
    return ( p[0] == 0 &&
             p[1] == 0   );
}
 
bool is_unit_vector(Point const &p, Coord eps) {
    return are_near(L2(p), 1.0, eps);
}
Coord atan2(Point const &p) {
    return std::atan2(p[Y], p[X]);
}
 
Coord angle_between(Point const &a, Point const &b) {
    return std::atan2(cross(a,b), dot(a,b));
}
 
Point unit_vector(Point const &a)
{
    Point ret(a);
    ret.normalize();
    return ret;
}
Point abs(Point const &b)
{
    Point ret;
    if (b[Y] < 0.0) {
        ret = -b;
    } else if (b[Y] == 0.0) {
        ret = b[X] < 0.0 ? -b : b;
    } else {
        ret = b;
    }
    return ret;
}
 
Point &Point::operator*=(Affine const &m) {
    double x = _pt[X], y = _pt[Y];
    for(int i = 0; i < 2; i++) {
        _pt[i] = x * m[i] + y * m[i + 2] + m[i + 4];
    }
    return *this;
}
 
Point constrain_angle(Point const &A, Point const &B, unsigned int n, Point const &dir)
{
    // for special cases we could perhaps use explicit testing (which might be faster)
    if (n == 0.0) {
        return B;
    }
    Point diff(B - A);
    double angle = -angle_between(diff, dir);
    double k = round(angle * (double)n / (2.0*M_PI));
    return A + dir * Rotate(k * 2.0 * M_PI / (double)n) * L2(diff);
}
 
std::ostream &operator<<(std::ostream &out, Geom::Point const &p)
{
    return out << "(" << format_coord_nice(p[X]) << ", "
                      << format_coord_nice(p[Y]) << ")";
}
 
} // 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 :