src/2geom/circle.cpp

76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński/** @file
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * @brief Circle shape
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński *//*
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * Authors:
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński *   Marco Cecchetti <mrcekets at gmail.com>
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński *   Krzysztof Kosiński <tweenk.pl@gmail.com>
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen *
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński * Copyright 2008-2014 Authors
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen *
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * This library is free software; you can redistribute it and/or
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * modify it either under the terms of the GNU Lesser General Public
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * License version 2.1 as published by the Free Software Foundation
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * (the "LGPL") or, at your option, under the terms of the Mozilla
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * Public License Version 1.1 (the "MPL"). If you do not alter this
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * notice, a recipient may use your version of this file under either
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * the MPL or the LGPL.
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen *
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * You should have received a copy of the LGPL along with this library
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * in the file COPYING-LGPL-2.1; if not, write to the Free Software
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * You should have received a copy of the MPL along with this library
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * in the file COPYING-MPL-1.1
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen *
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * The contents of this file are subject to the Mozilla Public License
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * Version 1.1 (the "License"); you may not use this file except in
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * compliance with the License. You may obtain a copy of the License at
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * http://www.mozilla.org/MPL/
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen *
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * OF ANY KIND, either express or implied. See the LGPL or the MPL for
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen * the specific language governing rights and limitations.
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen */
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen#include <2geom/circle.h>
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen#include <2geom/ellipse.h>
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński#include <2geom/elliptical-arc.h>
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen#include <2geom/numeric/fitting-tool.h>
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen#include <2geom/numeric/fitting-model.h>
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosińskinamespace Geom {
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiRect Circle::boundsFast() const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Point rr(_radius, _radius);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Rect bbox(_center - rr, _center + rr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return bbox;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosińskivoid Circle::setCoefficients(Coord A, Coord B, Coord C, Coord D)
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen{
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    if (A == 0) {
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen        THROW_RANGEERROR("square term coefficient == 0");
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen    }
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen    //std::cerr << "B = " << B << "  C = " << C << "  D = " << D << std::endl;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    Coord b = B / A;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    Coord c = C / A;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    Coord d = D / A;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    _center[X] = -b/2;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    _center[Y] = -c/2;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    Coord r2 = _center[X] * _center[X] + _center[Y] * _center[Y] - d;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    if (r2 < 0) {
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen        THROW_RANGEERROR("ray^2 < 0");
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen    }
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    _radius = std::sqrt(r2);
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskivoid Circle::coefficients(Coord &A, Coord &B, Coord &C, Coord &D) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    A = 1;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    B = -2 * _center[X];
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    C = -2 * _center[Y];
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    D = _center[X] * _center[X] + _center[Y] * _center[Y] - _radius * _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<Coord> Circle::coefficients() const
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    std::vector<Coord> c(4);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    coefficients(c[0], c[1], c[2], c[3]);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return c;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiZoom Circle::unitCircleTransform() const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Zoom ret(_radius, _center / _radius);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return ret;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiZoom Circle::inverseUnitCircleTransform() const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (_radius == 0) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        THROW_RANGEERROR("degenerate circle does not have an inverse unit circle transform");
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Zoom ret(1/_radius, Translate(-_center));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return ret;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof KosińskiPoint Circle::initialPoint() const
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński{
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński    Point p(_center);
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński    p[X] += _radius;
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński    return p;
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiPoint Circle::pointAt(Coord t) const {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return _center + Point::polar(t) * _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::valueAt(Coord t, Dim2 d) const {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord delta = (d == X ? std::cos(t) : std::sin(t));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return _center[d] + delta * _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::timeAt(Point const &p) const {
e4369b05aaa20df73a37f4d319ce456865cc74f3Krzysztof Kosiński    if (_center == p) return 0;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return atan2(p - _center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCoord Circle::nearestTime(Point const &p) const {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return timeAt(p);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::contains(Rect const &r) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    for (unsigned i = 0; i < 4; ++i) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        if (!contains(r.corner(i))) return false;
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return true;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::contains(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord cdist = distance(_center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord rdist = fabs(_radius - other._radius);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return cdist <= rdist;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::intersects(Line const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    // http://mathworld.wolfram.com/Circle-LineIntersection.html
b63c6af7aa7f869de42730cf0ffd8b6077d778c5Krzysztof Kosiński    Coord dr = l.vector().length();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord r = _radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord D = cross(l.initialPoint(), l.finalPoint());
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord delta = r*r * dr*dr - D*D;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (delta >= 0) return true;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::intersects(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord cdist = distance(_center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord rsum = _radius + other._radius;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return cdist <= rsum;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(Line const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    // http://mathworld.wolfram.com/Circle-LineIntersection.html
b63c6af7aa7f869de42730cf0ffd8b6077d778c5Krzysztof Kosiński    Coord dr = l.vector().length();
b63c6af7aa7f869de42730cf0ffd8b6077d778c5Krzysztof Kosiński    Coord dx = l.vector().x();
b63c6af7aa7f869de42730cf0ffd8b6077d778c5Krzysztof Kosiński    Coord dy = l.vector().y();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord D = cross(l.initialPoint() - _center, l.finalPoint() - _center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord delta = _radius*_radius * dr*dr - D*D;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    std::vector<ShapeIntersection> result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (delta < 0) return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (delta == 0) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        Coord ix = (D*dy) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        Coord iy = (-D*dx) / (dr*dr);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        Point ip(ix, iy); ip += _center;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        result.push_back(ShapeIntersection(timeAt(ip), l.timeAt(ip), ip));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        return result;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen    }
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord sqrt_delta = std::sqrt(delta);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord signmod = dy < 0 ? -1 : 1;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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    Point i1p(i1x, i1y); i1p += _center;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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    Point i2p(i2x, i2y); i2p += _center;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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 Kosiński    return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(LineSegment const &l) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    std::vector<ShapeIntersection> result = intersect(Line(l));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    filter_line_segment_intersections(result);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::vector<ShapeIntersection> Circle::intersect(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    std::vector<ShapeIntersection> result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (*this == other) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        THROW_INFINITESOLUTIONS();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (contains(other)) return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (!intersects(other)) return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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    Point cv = other._center - _center;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord d = cv.length();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord R = radius(), r = other.radius();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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        return result;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    // q is the distance along the line between centers to the perpendicular line
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    // that goes through both intersections.
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Coord q = (d*d - r*r + R*R) / (2*d);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Point qp = lerp(q/d, _center, other._center);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
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    Coord h = std::sqrt(R*R - q*q);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Point qd = (h/d) * cv.cw();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    // now compute the intersection points
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Point x1 = qp + qd;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    Point x2 = qp - qd;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    result.push_back(ShapeIntersection(timeAt(x1), other.timeAt(x1), x1));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    result.push_back(ShapeIntersection(timeAt(x2), other.timeAt(x2), x2));
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return result;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen/**
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen @param inner a point whose angle with the circle center is inside the angle that the arc spans
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen */
d37634d73670180f99a3e0ea583621373d90ec4fJohan EngelenEllipticalArc *
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiCircle::arc(Point const& initial, Point const& inner, Point const& final) const
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen{
d37634d73670180f99a3e0ea583621373d90ec4fJohan Engelen    // TODO native implementation!
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    Ellipse e(_center[X], _center[Y], _radius, _radius, 0);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return e.arc(initial, inner, final);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool Circle::operator==(Circle const &other) const
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (_center != other._center) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (_radius != other._radius) return false;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return true;
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof KosińskiD2<SBasis> Circle::toSBasis() const
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen{
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop    D2<SBasis> B;
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop    Linear bo = Linear(0, 2 * M_PI);
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop    B[0] = cos(bo,4);
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop    B[1] = sin(bo,4);
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop
76addc201c409e81eaaa73fe27cc0f79c4db097cKrzysztof Kosiński    B = B * _radius + _center;
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen    return B;
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen}
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskivoid Circle::fit(std::vector<Point> const& points)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    size_t sz = points.size();
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (sz < 2) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        THROW_RANGEERROR("fitting error: too few points passed");
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    if (sz == 2) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        _center = points[0] * 0.5 + points[1] * 0.5;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        _radius = distance(points[0], points[1]) / 2;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        return;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    NL::LFMCircle model;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    NL::least_squeares_fitter<NL::LFMCircle> fitter(model, sz);
c8589a6c7367d09fa756755cef0dd448c7328a71Johan B. C. Engelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    for (size_t i = 0; i < sz; ++i) {
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński        fitter.append(points[i]);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    }
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    fitter.update();
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    NL::Vector z(sz, 0.0);
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    model.instance(*this, fitter.result(z));
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop}
18d56400fb8d667bff7c64b550365d94725bfe6eDiederik van Lierop
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskibool are_near(Circle const &a, Circle const &b, Coord eps)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
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 Kosiński}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosińskistd::ostream &operator<<(std::ostream &out, Circle const &c)
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński{
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    out << "Circle(" << c.center() << ", " << format_coord_nice(c.radius()) << ")";
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński    return out;
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
00f9ca0b3aa57e09f3c3f3632c5427fc03499df5Krzysztof Kosiński}  // end namespace Geom
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen/*
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen  Local Variables:
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen  mode:c++
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
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen  End:
1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4johanengelen*/
a4030d5ca449e7e384bc699cd249ee704faaeab0Chris Morgan// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :