circle.cpp revision e4369b05aaa20df73a37f4d319ce456865cc74f3
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * @brief Circle shape
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * Marco Cecchetti <mrcekets at gmail.com>
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * Krzysztof Kosiński <tweenk.pl@gmail.com>
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * Copyright 2008-2014 Authors
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * This library is free software; you can redistribute it and/or
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76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosińskivoid Circle::setCoefficients(Coord A, Coord B, Coord C, Coord D)
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen THROW_RANGEERROR("square term coefficient == 0");
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen //std::cerr << "B = " << B << " C = " << C << " D = " << D << std::endl;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński Coord r2 = _center[X] * _center[X] + _center[Y] * _center[Y] - d;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskivoid Circle::coefficients(Coord &A, Coord &B, Coord &C, Coord &D) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński D = _center[X] * _center[X] + _center[Y] * _center[Y] - _radius * _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<Coord> Circle::coefficients() const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiZoom Circle::inverseUnitCircleTransform() const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński THROW_RANGEERROR("degenerate circle does not have an inverse unit circle transform");
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Zoom ret(1/_radius, Translate(-_center));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński return _center + Point::polar(t) * _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::valueAt(Coord t, Dim2 d) const {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord delta = (d == X ? std::cos(t) : std::sin(t));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::timeAt(Point const &p) const {
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński if (_center == p) return 0;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::nearestTime(Point const &p) const {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::contains(Rect const &r) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński for (unsigned i = 0; i < 4; ++i) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (!contains(r.corner(i))) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::contains(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord cdist = distance(_center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord rdist = fabs(_radius - other._radius);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::intersects(Line const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // http://mathworld.wolfram.com/Circle-LineIntersection.html
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord D = cross(l.initialPoint(), l.finalPoint());
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (delta >= 0) return true;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::intersects(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord cdist = distance(_center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(Line const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // http://mathworld.wolfram.com/Circle-LineIntersection.html
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord D = cross(l.initialPoint() - _center, l.finalPoint() - _center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord delta = _radius*_radius * dr*dr - D*D;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(timeAt(ip), l.timeAt(ip), ip));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord i1x = (D*dy + signmod * dx * sqrt_delta) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord i1y = (-D*dx + fabs(dy) * sqrt_delta) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord i2x = (D*dy - signmod * dx * sqrt_delta) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord i2y = (-D*dx - fabs(dy) * sqrt_delta) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(timeAt(i1p), l.timeAt(i1p), i1p));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(timeAt(i2p), l.timeAt(i2p), i2p));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(LineSegment const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński std::vector<ShapeIntersection> result = intersect(Line(l));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński filter_line_segment_intersections(result);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (*this == other) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // See e.g. http://mathworld.wolfram.com/Circle-CircleIntersection.html
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // Basically, we figure out where is the third point of a triangle
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // with two points in the centers and with edge lengths equal to radii
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (d == R + r) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Point px = lerp(R / d, _center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord T = timeAt(px), t = other.timeAt(px);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(T, t, px));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // q is the distance along the line between centers to the perpendicular line
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // that goes through both intersections.
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Point qp = lerp(q/d, _center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // The triangle given by the points:
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // _center, qp, intersection
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // is a right triangle. Determine the distance between qp and intersection
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // using the Pythagorean theorem.
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // now compute the intersection points
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(timeAt(x1), other.timeAt(x1), x1));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński result.push_back(ShapeIntersection(timeAt(x2), other.timeAt(x2), x2));
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen @param inner a point whose angle with the circle center is inside the angle that the arc spans
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCircle::arc(Point const& initial, Point const& inner, Point const& final) const
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen // TODO native implementation!
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński Ellipse e(_center[X], _center[Y], _radius, _radius, 0);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::operator==(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (_center != other._center) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (_radius != other._radius) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskivoid Circle::fit(std::vector<Point> const& points)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński THROW_RANGEERROR("fitting error: too few points passed");
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński _center = points[0] * 0.5 + points[1] * 0.5;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński _radius = distance(points[0], points[1]) / 2;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński NL::least_squeares_fitter<NL::LFMCircle> fitter(model, sz);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool are_near(Circle const &a, Circle const &b, Coord eps)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // to check whether no point on a is further than eps from b,
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // we check two things:
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // 1. if radii differ by more than eps, there is definitely a point that fails
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // 2. if they differ by less, we check the centers. They have to be closer
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // together if the radius differs, since the maximum distance will be
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński // equal to sum of radius difference and distance between centers.
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński if (!are_near(a.radius(), b.radius(), eps)) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński Coord adjusted_eps = eps - fabs(a.radius() - b.radius());
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński return are_near(a.center(), b.center(), adjusted_eps);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::ostream &operator<<(std::ostream &out, Circle const &c)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński out << "Circle(" << c.center() << ", " << format_coord_nice(c.radius()) << ")";
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński} // end namespace Geom
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen Local Variables:
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen c-file-style:"stroustrup"
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen indent-tabs-mode:nil
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen fill-column:99
a4030d5ca449e7e384bc699cd249ee704faaeab0Chris Morgan// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :