Adding upstream version 1.0.2.upstream/1.0.2upstream

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

1 files changed, 337 insertions, 0 deletions

diff --git a/src/2geom/circle.cpp b/src/2geom/circle.cpp
new file mode 100644
index 0000000..934a8d3
--- /dev/null
+++ b/src/2geom/circle.cpp
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+/** @file
+ * @brief Circle shape
+ *//*
+ * Authors:
+ *   Marco Cecchetti <mrcekets at gmail.com>
+ *   Krzysztof Kosiński <tweenk.pl@gmail.com>
+ *
+ * Copyright 2008-2014 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/circle.h>
+#include <2geom/ellipse.h>
+#include <2geom/elliptical-arc.h>
+#include <2geom/numeric/fitting-tool.h>
+#include <2geom/numeric/fitting-model.h>
+
+namespace Geom {
+
+Rect Circle::boundsFast() const
+{
+    Point rr(_radius, _radius);
+    Rect bbox(_center - rr, _center + rr);
+    return bbox;
+}
+
+void Circle::setCoefficients(Coord A, Coord B, Coord C, Coord D)
+{
+    if (A == 0) {
+        THROW_RANGEERROR("square term coefficient == 0");
+    }
+
+    //std::cerr << "B = " << B << "  C = " << C << "  D = " << D << std::endl;
+
+    Coord b = B / A;
+    Coord c = C / A;
+    Coord d = D / A;
+
+    _center[X] = -b/2;
+    _center[Y] = -c/2;
+    Coord r2 = _center[X] * _center[X] + _center[Y] * _center[Y] - d;
+
+    if (r2 < 0) {
+        THROW_RANGEERROR("ray^2 < 0");
+    }
+
+    _radius = std::sqrt(r2);
+}
+
+void Circle::coefficients(Coord &A, Coord &B, Coord &C, Coord &D) const
+{
+    A = 1;
+    B = -2 * _center[X];
+    C = -2 * _center[Y];
+    D = _center[X] * _center[X] + _center[Y] * _center[Y] - _radius * _radius;
+}
+
+std::vector<Coord> Circle::coefficients() const
+{
+    std::vector<Coord> c(4);
+    coefficients(c[0], c[1], c[2], c[3]);
+    return c;
+}
+
+
+Zoom Circle::unitCircleTransform() const
+{
+    Zoom ret(_radius, _center / _radius);
+    return ret;
+}
+
+Zoom Circle::inverseUnitCircleTransform() const
+{
+    if (_radius == 0) {
+        THROW_RANGEERROR("degenerate circle does not have an inverse unit circle transform");
+    }
+
+    Zoom ret(1/_radius, Translate(-_center));
+    return ret;
+}
+
+Point Circle::initialPoint() const
+{
+    Point p(_center);
+    p[X] += _radius;
+    return p;
+}
+
+Point Circle::pointAt(Coord t) const {
+    return _center + Point::polar(t) * _radius;
+}
+
+Coord Circle::valueAt(Coord t, Dim2 d) const {
+    Coord delta = (d == X ? std::cos(t) : std::sin(t));
+    return _center[d] + delta * _radius;
+}
+
+Coord Circle::timeAt(Point const &p) const {
+    if (_center == p) return 0;
+    return atan2(p - _center);
+}
+
+Coord Circle::nearestTime(Point const &p) const {
+    return timeAt(p);
+}
+
+bool Circle::contains(Rect const &r) const
+{
+    for (unsigned i = 0; i < 4; ++i) {
+        if (!contains(r.corner(i))) return false;
+    }
+    return true;
+}
+
+bool Circle::contains(Circle const &other) const
+{
+    Coord cdist = distance(_center, other._center);
+    Coord rdist = fabs(_radius - other._radius);
+    return cdist <= rdist;
+}
+
+bool Circle::intersects(Line const &l) const
+{
+    // http://mathworld.wolfram.com/Circle-LineIntersection.html
+    Coord dr = l.vector().length();
+    Coord r = _radius;
+    Coord D = cross(l.initialPoint(), l.finalPoint());
+    Coord delta = r*r * dr*dr - D*D;
+    if (delta >= 0) return true;
+    return false;
+}
+
+bool Circle::intersects(Circle const &other) const
+{
+    Coord cdist = distance(_center, other._center);
+    Coord rsum = _radius + other._radius;
+    return cdist <= rsum;
+}
+
+
+std::vector<ShapeIntersection> Circle::intersect(Line const &l) const
+{
+    // http://mathworld.wolfram.com/Circle-LineIntersection.html
+    Coord dr = l.vector().length();
+    Coord dx = l.vector().x();
+    Coord dy = l.vector().y();
+    Coord D = cross(l.initialPoint() - _center, l.finalPoint() - _center);
+    Coord delta = _radius*_radius * dr*dr - D*D;
+
+    std::vector<ShapeIntersection> result;
+    if (delta < 0) return result;
+    if (delta == 0) {
+        Coord ix = (D*dy) / (dr*dr);
+        Coord iy = (-D*dx) / (dr*dr);
+        Point ip(ix, iy); ip += _center;
+        result.push_back(ShapeIntersection(timeAt(ip), l.timeAt(ip), ip));
+        return result;
+    }
+
+    Coord sqrt_delta = std::sqrt(delta);
+    Coord signmod = dy < 0 ? -1 : 1;
+
+    Coord i1x = (D*dy + signmod * dx * sqrt_delta) / (dr*dr);
+    Coord i1y = (-D*dx + fabs(dy) * sqrt_delta) / (dr*dr);
+    Point i1p(i1x, i1y); i1p += _center;
+
+    Coord i2x = (D*dy - signmod * dx * sqrt_delta) / (dr*dr);
+    Coord i2y = (-D*dx - fabs(dy) * sqrt_delta) / (dr*dr);
+    Point i2p(i2x, i2y); i2p += _center;
+
+    result.push_back(ShapeIntersection(timeAt(i1p), l.timeAt(i1p), i1p));
+    result.push_back(ShapeIntersection(timeAt(i2p), l.timeAt(i2p), i2p));
+    return result;
+}
+
+std::vector<ShapeIntersection> Circle::intersect(LineSegment const &l) const
+{
+    std::vector<ShapeIntersection> result = intersect(Line(l));
+    filter_line_segment_intersections(result);
+    return result;
+}
+
+std::vector<ShapeIntersection> Circle::intersect(Circle const &other) const
+{
+    std::vector<ShapeIntersection> result;
+
+    if (*this == other) {
+        THROW_INFINITESOLUTIONS();
+    }
+    if (contains(other)) return result;
+    if (!intersects(other)) return result;
+
+    // See e.g. http://mathworld.wolfram.com/Circle-CircleIntersection.html
+    // Basically, we figure out where is the third point of a triangle
+    // with two points in the centers and with edge lengths equal to radii
+    Point cv = other._center - _center;
+    Coord d = cv.length();
+    Coord R = radius(), r = other.radius();
+
+    if (d == R + r) {
+        Point px = lerp(R / d, _center, other._center);
+        Coord T = timeAt(px), t = other.timeAt(px);
+        result.push_back(ShapeIntersection(T, t, px));
+        return result;
+    }
+
+    // q is the distance along the line between centers to the perpendicular line
+    // that goes through both intersections.
+    Coord q = (d*d - r*r + R*R) / (2*d);
+    Point qp = lerp(q/d, _center, other._center);
+
+    // The triangle given by the points:
+    // _center, qp, intersection
+    // is a right triangle. Determine the distance between qp and intersection
+    // using the Pythagorean theorem.
+    Coord h = std::sqrt(R*R - q*q);
+    Point qd = (h/d) * cv.cw();
+
+    // now compute the intersection points
+    Point x1 = qp + qd;
+    Point x2 = qp - qd;
+
+    result.push_back(ShapeIntersection(timeAt(x1), other.timeAt(x1), x1));
+    result.push_back(ShapeIntersection(timeAt(x2), other.timeAt(x2), x2));
+    return result;
+}
+
+/**
+ @param inner a point whose angle with the circle center is inside the angle that the arc spans
+ */
+EllipticalArc *
+Circle::arc(Point const& initial, Point const& inner, Point const& final) const
+{
+    // TODO native implementation!
+    Ellipse e(_center[X], _center[Y], _radius, _radius, 0);
+    return e.arc(initial, inner, final);
+}
+
+bool Circle::operator==(Circle const &other) const
+{
+    if (_center != other._center) return false;
+    if (_radius != other._radius) return false;
+    return true;
+}
+
+D2<SBasis> Circle::toSBasis() const
+{
+    D2<SBasis> B;
+    Linear bo = Linear(0, 2 * M_PI);
+
+    B[0] = cos(bo,4);
+    B[1] = sin(bo,4);
+
+    B = B * _radius + _center;
+
+    return B;
+}
+
+
+void Circle::fit(std::vector<Point> const& points)
+{
+    size_t sz = points.size();
+    if (sz < 2) {
+        THROW_RANGEERROR("fitting error: too few points passed");
+    }
+    if (sz == 2) {
+        _center = points[0] * 0.5 + points[1] * 0.5;
+        _radius = distance(points[0], points[1]) / 2;
+        return;
+    }
+
+    NL::LFMCircle model;
+    NL::least_squeares_fitter<NL::LFMCircle> fitter(model, sz);
+
+    for (size_t i = 0; i < sz; ++i) {
+        fitter.append(points[i]);
+    }
+    fitter.update();
+
+    NL::Vector z(sz, 0.0);
+    model.instance(*this, fitter.result(z));
+}
+
+
+bool are_near(Circle const &a, Circle const &b, Coord eps)
+{
+    // to check whether no point on a is further than eps from b,
+    // we check two things:
+    // 1. if radii differ by more than eps, there is definitely a point that fails
+    // 2. if they differ by less, we check the centers. They have to be closer
+    //    together if the radius differs, since the maximum distance will be
+    //    equal to sum of radius difference and distance between centers.
+    if (!are_near(a.radius(), b.radius(), eps)) return false;
+    Coord adjusted_eps = eps - fabs(a.radius() - b.radius());
+    return are_near(a.center(), b.center(), adjusted_eps);
+}
+
+std::ostream &operator<<(std::ostream &out, Circle const &c)
+{
+    out << "Circle(" << c.center() << ", " << format_coord_nice(c.radius()) << ")";
+    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 :