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Diffstat (limited to 'src/2geom/point.cpp')
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diff --git a/src/2geom/point.cpp b/src/2geom/point.cpp new file mode 100644 index 0000000..cbe53c4 --- /dev/null +++ b/src/2geom/point.cpp @@ -0,0 +1,274 @@ +/** + * \file + * \brief Cartesian point / 2D vector and related operations + *//* + * 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 { + +/** + * @class Point + * @brief Two-dimensional point that doubles as a vector. + * + * Points in 2Geom are represented in Cartesian coordinates, e.g. as a pair of numbers + * that store the X and Y coordinates. Each point is also a vector in \f$\mathbb{R}^2\f$ + * from the origin (point at 0,0) to the stored coordinates, + * and has methods implementing several vector operations (like length()). + * + * @section OpNotePoint Operator note + * + * Most operators are provided by Boost operator helpers, so they are not visible in this class. + * If @a p, @a q, @a r denote points, @a s a floating-point scalar, and @a m a transformation matrix, + * then the following operations are available: + * @code + p += q; p -= q; r = p + q; r = p - q; + p *= s; p /= s; q = p * s; q = s * p; q = p / s; + p *= m; q = p * m; q = m * p; + @endcode + * It is possible to left-multiply a point by a matrix, even though mathematically speaking + * this is undefined. The result is a point identical to that obtained by right-multiplying. + * + * @ingroup Primitives */ + +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; +} + +/** @brief Normalize the vector representing the point. + * After this method returns, the length of the vector will be 1 (unless both coordinates are + * zero - the zero point will be returned then). The function tries to handle infinite + * coordinates gracefully. If any of the coordinates are NaN, the function will do nothing. + * @post \f$-\epsilon < \left|this\right| - 1 < \epsilon\f$ + * @see unit_vector(Geom::Point const &) */ +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; + } + } + } +} + +/** @brief Compute the first norm (Manhattan distance) of @a p. + * This is equal to the sum of absolutes values of the coordinates. + * @return \f$|p_X| + |p_Y|\f$ + * @relates Point */ +Coord L1(Point const &p) { + Coord d = 0; + for ( int i = 0 ; i < 2 ; i++ ) { + d += fabs(p[i]); + } + return d; +} + +/** @brief Compute the infinity norm (maximum norm) of @a p. + * @return \f$\max(|p_X|, |p_Y|)\f$ + * @relates Point */ +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 ); +} + +/** @brief True if the point has both coordinates zero. + * NaNs are treated as not equal to zero. + * @relates Point */ +bool is_zero(Point const &p) { + return ( p[0] == 0 && + p[1] == 0 ); +} + +/** @brief True if the point has a length near 1. The are_near() function is used. + * @relates Point */ +bool is_unit_vector(Point const &p, Coord eps) { + return are_near(L2(p), 1.0, eps); +} +/** @brief Return the angle between the point and the +X axis. + * @return Angle in \f$(-\pi, \pi]\f$. + * @relates Point */ +Coord atan2(Point const &p) { + return std::atan2(p[Y], p[X]); +} + +/** @brief Compute the angle between a and b relative to the origin. + * The computation is done by projecting b onto the basis defined by a, rot90(a). + * @return Angle in \f$(-\pi, \pi]\f$. + * @relates Point */ +Coord angle_between(Point const &a, Point const &b) { + return std::atan2(cross(a,b), dot(a,b)); +} + +/** @brief Create a normalized version of a point. + * This is equivalent to copying the point and calling its normalize() method. + * The returned point will be (0,0) if the argument has both coordinates equal to zero. + * If any coordinate is NaN, this function will do nothing. + * @param a Input point + * @return Point on the unit circle in the same direction from origin as a, or the origin + * if a has both coordinates equal to zero + * @relates Point */ +Point unit_vector(Point const &a) +{ + Point ret(a); + ret.normalize(); + return ret; +} +/** @brief Return the "absolute value" of the point's vector. + * This is defined in terms of the default lexicographical ordering. If the point is "larger" + * that the origin (0, 0), its negation is returned. You can check whether + * the points' vectors have the same direction (e.g. lie + * on the same line passing through the origin) using + * @code abs(a).normalize() == abs(b).normalize() @endcode + * To check with some margin of error, use + * @code are_near(abs(a).normalize(), abs(b).normalize()) @endcode + * Although naively this should take the absolute value of each coordinate, such an operation + * is not very useful. + * @relates Point */ +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; +} + +/** @brief Transform the point by the specified matrix. */ +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; +} + +/** @brief Snap the angle B - A - dir to multiples of \f$2\pi/n\f$. + * The 'dir' argument must be normalized (have unit length), otherwise the result + * is undefined. + * @return Point with the same distance from A as B, with a snapped angle. + * @post distance(A, B) == distance(A, result) + * @post angle_between(result - A, dir) == \f$2k\pi/n, k \in \mathbb{N}\f$ + * @relates Point */ +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, const Geom::Point &p) +{ + out << "(" << format_coord_nice(p[X]) << ", " + << format_coord_nice(p[Y]) << ")"; + return out; +} + +} // end 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 : |