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-rw-r--r--src/2geom/circle.cpp291
1 files changed, 243 insertions, 48 deletions
diff --git a/src/2geom/circle.cpp b/src/2geom/circle.cpp
index d021882ea..553981a72 100644
--- a/src/2geom/circle.cpp
+++ b/src/2geom/circle.cpp
@@ -1,10 +1,11 @@
-/*
- * Circle Curve
- *
+/** @file
+ * @brief Circle shape
+ *//*
* Authors:
- * Marco Cecchetti <mrcekets at gmail.com>
+ * Marco Cecchetti <mrcekets at gmail.com>
+ * Krzysztof Kosiński <tweenk.pl@gmail.com>
*
- * Copyright 2008 authors
+ * 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
@@ -30,77 +31,241 @@
* the specific language governing rights and limitations.
*/
-
#include <2geom/circle.h>
#include <2geom/ellipse.h>
-#include <2geom/svg-elliptical-arc.h>
+#include <2geom/elliptical-arc.h>
#include <2geom/numeric/fitting-tool.h>
#include <2geom/numeric/fitting-model.h>
+namespace Geom {
-
-namespace Geom
+Rect Circle::boundsFast() const
{
+ Point rr(_radius, _radius);
+ Rect bbox(_center - rr, _center + rr);
+ return bbox;
+}
-void Circle::set(double A, double B, double C, double D)
+void Circle::setCoefficients(Coord A, Coord B, Coord C, Coord D)
{
- if (A == 0)
- {
+ if (A == 0) {
THROW_RANGEERROR("square term coefficient == 0");
}
//std::cerr << "B = " << B << " C = " << C << " D = " << D << std::endl;
- double b = B / A;
- double c = C / A;
- double d = D / A;
+ Coord b = B / A;
+ Coord c = C / A;
+ Coord d = D / A;
- m_centre[X] = -b/2;
- m_centre[Y] = -c/2;
- double r2 = m_centre[X] * m_centre[X] + m_centre[Y] * m_centre[Y] - d;
+ _center[X] = -b/2;
+ _center[Y] = -c/2;
+ Coord r2 = _center[X] * _center[X] + _center[Y] * _center[Y] - d;
- if (r2 < 0)
- {
+ if (r2 < 0) {
THROW_RANGEERROR("ray^2 < 0");
}
- m_ray = std::sqrt(r2);
+ _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;
+}
-void Circle::set(std::vector<Point> const& points)
+std::vector<Coord> Circle::coefficients() const
{
- size_t sz = points.size();
- if (sz < 3)
- {
- THROW_RANGEERROR("fitting error: too few points passed");
+ 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");
}
- NL::LFMCircle model;
- NL::least_squeares_fitter<NL::LFMCircle> fitter(model, sz);
- for (size_t i = 0; i < sz; ++i)
- {
- fitter.append(points[i]);
+ 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;
}
- fitter.update();
+ return true;
+}
- NL::Vector z(sz, 0.0);
- model.instance(*this, fitter.result(z));
+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.versor().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.versor().length();
+ Coord dx = l.versor().x();
+ Coord dy = l.versor().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,
- bool _svg_compliant)
+Circle::arc(Point const& initial, Point const& inner, Point const& final) const
{
// TODO native implementation!
- Ellipse e(center(X), center(Y), ray(), ray(), 0);
- return e.arc(initial, inner, final, _svg_compliant);
+ Ellipse e(_center[X], _center[Y], _radius, _radius, 0);
+ return e.arc(initial, inner, final);
}
-D2<SBasis> Circle::toSBasis()
+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);
@@ -108,27 +273,57 @@ D2<SBasis> Circle::toSBasis()
B[0] = cos(bo,4);
B[1] = sin(bo,4);
- B = B * m_ray + m_centre;
+ B = B * _radius + _center;
return B;
}
-void
-Circle::getPath(std::vector<Path> &path_out) {
- Path pb;
- D2<SBasis> B = toSBasis();
+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;
+ }
- pb.append(SBasisCurve(B));
+ NL::LFMCircle model;
+ NL::least_squeares_fitter<NL::LFMCircle> fitter(model, sz);
- path_out.push_back(pb);
-}
+ 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));
+}
-} // end namespace Geom
+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:
generated by cgit v1.2.3 (git 2.25.1) at 2026-05-19 03:40:31 +0000