Adding upstream version 1.3.upstream/1.3upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 274 insertions, 0 deletions

diff --git a/src/2geom/point.cpp b/src/2geom/point.cpp
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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 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 :