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+/**
+ * \file
+ * \brief Cartesian point / 2D vector and related operations
+ *//*
+ * Authors:
+ * Michael G. Sloan <mgsloan@gmail.com>
+ * Nathan Hurst <njh@njhurst.com>
+ * Krzysztof KosiƄski <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 :