rs_information.cpp

/****************************************************************************
**
** This file is part of the LibreCAD project, a 2D CAD program
**
** Copyright (C) 2015 A. Stebich (librecad@mail.lordofbikes.de)
** Copyright (C) 2010 R. van Twisk (librecad@rvt.dds.nl)
** Copyright (C) 2001-2003 RibbonSoft. All rights reserved.
**
**
** This file may be distributed and/or modified under the terms of the
** GNU General Public License version 2 as published by the Free Software
** Foundation and appearing in the file gpl-2.0.txt included in the
** packaging of this file.
**
** This program is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
** GNU General Public License for more details.
**
** You should have received a copy of the GNU General Public License
** along with this program; if not, write to the Free Software
** Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
**
** This copyright notice MUST APPEAR in all copies of the script!
**
**********************************************************************/

#include <vector>
#include <utility>
#include "rs_information.h"

#include "rs_arc.h"
#include "rs_circle.h"
#include "rs_constructionline.h"
#include "rs_ellipse.h"
#include "rs_line.h"
#include "lc_quadratic.h"
#include "lc_splinepoints.h"


/**
 * Default constructor.
 *
 * @param container The container to which we will add
 *        entities. Usually that's an RS_Graphic entity but
 *        it can also be a polyline, text, ...
 */
RS_Information::RS_Information(RS_EntityContainer& container) {
    this->container = &container;
}



/**
 * @return true: if the entity is a dimensioning enity.
 *         false: otherwise
 */
bool RS_Information::isDimension(RS2::EntityType type) {
    if (type==RS2::EntityDimAligned ||
            type==RS2::EntityDimLinear ||
            type==RS2::EntityDimRadial ||
            type==RS2::EntityDimDiametric ||
            type==RS2::EntityDimAngular) {
        return true;
    } else {
        return false;
    }
}



/**
 * @retval true the entity can be trimmed.
 * i.e. it is in a graphic or in a polyline.
 */
bool RS_Information::isTrimmable(RS_Entity* e) {
    if (e!=NULL) {
        if (e->getParent()!=NULL) {
            if (e->getParent()->rtti()==RS2::EntityPolyline) {
                return true;
            }
            else if (e->getParent()->rtti()==RS2::EntityContainer ||
                     e->getParent()->rtti()==RS2::EntityGraphic ||
                     e->getParent()->rtti()==RS2::EntityBlock) {

                // normal entity:
                return true;
            }
        }
    }

    return false;
}


/**
 * @retval true the two entities can be trimmed to each other;
 * i.e. they are in a graphic or in the same polyline.
 */
bool RS_Information::isTrimmable(RS_Entity* e1, RS_Entity* e2) {
    if (e1!=NULL && e2!=NULL) {
        if (e1->getParent()!=NULL && e2->getParent()!=NULL) {
            if (e1->getParent()->rtti()==RS2::EntityPolyline &&
                    e2->getParent()->rtti()==RS2::EntityPolyline &&
                    e1->getParent()==e2->getParent()) {

                // in the same polyline
                RS_EntityContainer* pl = e1->getParent();
                int idx1 = pl->findEntity(e1);
                int idx2 = pl->findEntity(e2);
                RS_DEBUG->print("RS_Information::isTrimmable: "
                                "idx1: %d, idx2: %d", idx1, idx2);
                if (abs(idx1-idx2)==1 || abs(idx1-idx2)==int(pl->count()-1)) {
                    // directly following entities
                    return true;
                }
                else {
                    // not directly following entities
                    return false;
                }
            }
            else if ((e1->getParent()->rtti()==RS2::EntityContainer ||
                      e1->getParent()->rtti()==RS2::EntityGraphic ||
                      e1->getParent()->rtti()==RS2::EntityBlock) &&
                     (e2->getParent()->rtti()==RS2::EntityContainer ||
                      e2->getParent()->rtti()==RS2::EntityGraphic ||
                      e2->getParent()->rtti()==RS2::EntityBlock)) {

                // normal entities:
                return true;
            }
        }
        else {
            // independent entities with the same parent:
            return (e1->getParent()==e2->getParent());
        }
    }

    return false;
}


/**
 * Gets the nearest end point to the given coordinate.
 *
 * @param coord Coordinate (typically a mouse coordinate)
 *
 * @return the coordinate found or an invalid vector
 * if there are no elements at all in this graphics
 * container.
 */
RS_Vector RS_Information::getNearestEndpoint(const RS_Vector& coord,
        double* dist) const {
    return container->getNearestEndpoint(coord, dist);
}


/**
 * Gets the nearest point to the given coordinate which is on an entity.
 *
 * @param coord Coordinate (typically a mouse coordinate)
 * @param dist Pointer to a double which will contain the
 *        measured distance after return or NULL
 * @param entity Pointer to a pointer which will point to the
 *        entity on which the point is or NULL
 *
 * @return the coordinate found or an invalid vector
 * if there are no elements at all in this graphics
 * container.
 */
RS_Vector RS_Information::getNearestPointOnEntity(const RS_Vector& coord,
        bool onEntity,
        double* dist,
        RS_Entity** entity) const {

    return container->getNearestPointOnEntity(coord, onEntity, dist, entity);
}


/**
 * Gets the nearest entity to the given coordinate.
 *
 * @param coord Coordinate (typically a mouse coordinate)
 * @param dist Pointer to a double which will contain the
 *             masured distance after return
 * @param level Level of resolving entities.
 *
 * @return the entity found or NULL if there are no elements
 * at all in this graphics container.
 */
RS_Entity* RS_Information::getNearestEntity(const RS_Vector& coord,
        double* dist,
        RS2::ResolveLevel level) const {

    return container->getNearestEntity(coord, dist, level);
}



/**
 * Calculates the intersection point(s) between two entities.
 *
 * @param onEntities true: only return intersection points which are
 *                   on both entities.
 *                   false: return all intersection points.
 *
 * @todo support more entities
 *
 * @return All intersections of the two entities. The tangent flag in
 * RS_VectorSolutions is set if one intersection is a tangent point.
 */
RS_VectorSolutions RS_Information::getIntersection(RS_Entity* e1,
        RS_Entity* e2, bool onEntities) {

    RS_VectorSolutions ret;
    const double tol = 1.0e-4;

    if (e1==NULL || e2==NULL ) {
        RS_DEBUG->print("RS_Information::getIntersection() for NULL entities");
        return ret;
    }
    if (e1->getId() == e2->getId()) {
        RS_DEBUG->print("RS_Information::getIntersection() of the same entity");
        return ret;
    }

    // unsupported entities / entity combinations:
    if (
        e1->rtti()==RS2::EntityMText || e2->rtti()==RS2::EntityMText ||
        e1->rtti()==RS2::EntityText || e2->rtti()==RS2::EntityText ||
        isDimension(e1->rtti()) || isDimension(e2->rtti())) {
        return ret;
    }
    // a little check to avoid doing unneeded intersections, an attempt to avoid O(N^2) increasing of checking two-entity information
    if (onEntities &&
            (! (e1 -> isConstruction() || e2 -> isConstruction() ))
            && (
                e1 -> getMin().x > e2 -> getMax().x
                || e1 -> getMax().x < e2 -> getMin().x
                || e1 -> getMin().y > e2 -> getMax().y
                || e1 -> getMax().y < e2 -> getMin().y
                )
            ) {
            return ret;
    }

    //avoid intersections between line segments the same spline
    /* ToDo: 24 Aug 2011, Dongxu Li, if rtti() is not defined for the parent, the following check for splines may still cause segfault */
    if ( e1->getParent() != NULL && e1->getParent() == e2->getParent()) {
        if ( e1->getParent()->rtti()==RS2::EntitySpline ) {
            //do not calculate intersections from neighboring lines of a spline
            if ( abs(e1->getParent()->findEntity(e1) - e1->getParent()->findEntity(e2)) <= 1 ) {
                return ret;
            }
        }
    }

	if(e1->rtti() == RS2::EntitySplinePoints || e2->rtti() == RS2::EntitySplinePoints)
	{
		ret = LC_SplinePoints::getIntersection(e1, e2);
	}
	else
	{
		const auto&& qf1=e1->getQuadratic();
		const auto&& qf2=e2->getQuadratic();
		ret=LC_Quadratic::getIntersection(qf1,qf2);
	}
    RS_VectorSolutions ret2;
	for(const RS_Vector& vp: ret){
		if ( ! vp.valid) continue;
        if (onEntities==true) {
            //ignore intersections not on entity
            if (!(
                        (e1->isConstruction(true) || e1->isPointOnEntity(vp, tol)) &&
                        (e2->isConstruction(true) || e2->isPointOnEntity(vp, tol))
                        )
                    ) {
//                std::cout<<"Ignored intersection "<<ret.get(i)<<std::endl;
//                std::cout<<"because: e1->isPointOnEntity(ret.get(i), tol)="<<e1->isPointOnEntity(ret.get(i), tol)
//                    <<"\t(e2->isPointOnEntity(ret.get(i), tol)="<<e2->isPointOnEntity(ret.get(i), tol)<<std::endl;
                continue;
            }
        }
        // need to test whether the intersection is tangential
        RS_Vector&& direction1=e1->getTangentDirection(vp);
        RS_Vector&& direction2=e2->getTangentDirection(vp);
        if( direction1.valid && direction2.valid && fabs(fabs(direction1.dotP(direction2)) - sqrt(direction1.squared()*direction2.squared())) < sqrt(tol)*tol )
            ret2.setTangent(true);
        //TODO, make the following tangential test, nearest test work for all entity types

//        RS_Entity   *lpLine = NULL,
//                    *lpCircle = NULL;
//        if( RS2::EntityLine == e1->rtti() && RS2::EntityCircle == e2->rtti()) {
//            lpLine = e1;
//            lpCircle = e2;
//        }
//        else if( RS2::EntityCircle == e1->rtti() && RS2::EntityLine == e2->rtti()) {
//            lpLine = e2;
//            lpCircle = e1;
//        }
//        if( NULL != lpLine && NULL != lpCircle) {
//            double dist = 0.0;
//            RS_Vector nearest = lpLine->getNearestPointOnEntity( lpCircle->getCenter(), false, &dist);

//            // special case: line touches circle tangent
//            if( nearest.valid && fabs( dist - lpCircle->getRadius()) < tol) {
//                ret.set(i,nearest);
//                ret2.setTangent(true);
//            }
//        }
        ret2.push_back(vp);
    }

    return ret2;
}



/**
 * @return Intersection between two lines.
 */
RS_VectorSolutions RS_Information::getIntersectionLineLine(RS_Line* e1,
        RS_Line* e2) {

    RS_VectorSolutions ret;

    if (e1==NULL || e2==NULL) {
        RS_DEBUG->print("RS_Information::getIntersectionLineLin() for NULL entities");
        return ret;
    }

    RS_Vector p1 = e1->getStartpoint();
    RS_Vector p2 = e1->getEndpoint();
    RS_Vector p3 = e2->getStartpoint();
    RS_Vector p4 = e2->getEndpoint();

    double num = ((p4.x-p3.x)*(p1.y-p3.y) - (p4.y-p3.y)*(p1.x-p3.x));
    double div = ((p4.y-p3.y)*(p2.x-p1.x) - (p4.x-p3.x)*(p2.y-p1.y));

	if (fabs(div)>RS_TOLERANCE &&
			fabs(remainder(e1->getAngle1()-e2->getAngle1(), M_PI))>=RS_TOLERANCE*10.) {
		double u = num / div;

		double xs = p1.x + u * (p2.x-p1.x);
		double ys = p1.y + u * (p2.y-p1.y);
		ret = RS_VectorSolutions(RS_Vector(xs, ys));
	}

    // lines are parallel
    else {
        ret = RS_VectorSolutions();
    }

    return ret;
}



/**
 * @return One or two intersection points between given entities.
 */
RS_VectorSolutions RS_Information::getIntersectionLineArc(RS_Line* line,
        RS_Arc* arc) {

    RS_VectorSolutions ret;

    if (line==NULL || arc==NULL) {
        return ret;
    }

    double dist=0.0;
    RS_Vector nearest;
    nearest = line->getNearestPointOnEntity(arc->getCenter(), false, &dist);

    // special case: arc touches line (tangent):
    if (nearest.valid && fabs(dist - arc->getRadius()) < 1.0e-4) {
        ret = RS_VectorSolutions(nearest);
        ret.setTangent(true);
        return ret;
    }

    RS_Vector p = line->getStartpoint();
    RS_Vector d = line->getEndpoint() - line->getStartpoint();
    double d2=d.squared();
    RS_Vector c = arc->getCenter();
    double r = arc->getRadius();
    RS_Vector delta = p - c;
    if (d2<RS_TOLERANCE2) {
        //line too short, still check the whether the line touches the arc
        if ( fabs(delta.squared() - r*r) < 2.*RS_TOLERANCE*r ){
            return RS_VectorSolutions(line->getMiddlePoint());
        }
        return ret;
    }


    //intersection
    // solution = p + t d;
    //| p -c+ t d|^2 = r^2
    // |d|^2 t^2 + 2 (p-c).d t + |p-c|^2 -r^2 = 0
    double a1 = RS_Vector::dotP(delta,d);
    double term1 = a1*a1 - d2*(delta.squared()-r*r);
//        std::cout<<" discriminant= "<<term1<<std::endl;
    if( term1 < - RS_TOLERANCE) {
//        std::cout<<"no intersection\n";
    return ret;
    }else{
        term1=fabs(term1);
//        std::cout<< "term1="<<term1 <<" threshold: "<< RS_TOLERANCE * d2 <<std::endl;
        if( term1 < RS_TOLERANCE * d2 ) {
            //tangential;
//            ret=RS_VectorSolutions(p - d*(a1/d2));
            ret=RS_VectorSolutions(line->getNearestPointOnEntity(c, false));
            ret.setTangent(true);
//        std::cout<<"Tangential point: "<<ret<<std::endl;
            return ret;
        }
        double t = sqrt(fabs(term1));
    //two intersections
     return RS_VectorSolutions( p + d*(t-a1)/d2, p -d*(t+a1)/d2);
    }

//    // root term:
//    term1 = r*r - delta.squared() + term1*term1/d.squared();
//    double term = RS_Math::pow(RS_Vector::dotP(d, delta), 2.0)
//                  - RS_Math::pow(d.magnitude(), 2.0)
//                  * (RS_Math::pow(delta.magnitude(), 2.0) - RS_Math::pow(r, 2.0));
//    std::cout<<"old term= "<<term<<"\tnew term= "<<term1<<std::endl;

//    // no intersection:
//    if (term<0.0) {
//        ret = RS_VectorSolutions() ;
//    }

//    // one or two intersections:
//    else {
//        double t1 = (- RS_Vector::dotP(d, delta) + sqrt(term))
//                    / RS_Math::pow(d.magnitude(), 2.0);
//        double t2;
//        bool tangent = false;

//        // only one intersection:
//        if (fabs(term)<RS_TOLERANCE) {
//            t2 = t1;
//            tangent = true;
//        }

//        // two intersections
//        else {
//            t2 = (-RS_Vector::dotP(d, delta) - sqrt(term))
//                 / RS_Math::pow(d.magnitude(), 2.0);
//        }

//        RS_Vector sol1;
//        RS_Vector sol2(false);

//        sol1 = p + d * t1;

//        if (!tangent) {
//            sol2 = p + d * t2;
//        }

//        ret = RS_VectorSolutions(sol1, sol2);
//        ret.setTangent(tangent);
//    }

//    std::cout<<"ret= "<<ret<<std::endl;
//    return ret;
}



/**
 * @return One or two intersection points between given entities.
 */
RS_VectorSolutions RS_Information::getIntersectionArcArc(RS_Arc* e1,
        RS_Arc* e2) {

    RS_VectorSolutions ret;

    if (e1==NULL || e2==NULL) {
        return ret;
    }

    RS_Vector c1 = e1->getCenter();
    RS_Vector c2 = e2->getCenter();

    double r1 = e1->getRadius();
    double r2 = e2->getRadius();

    RS_Vector u = c2 - c1;

    // concentric
    if (u.magnitude()<1.0e-6) {
        return ret;
    }

    RS_Vector v = RS_Vector(u.y, -u.x);

    double s, t1, t2, term;

    s = 1.0/2.0 * ((r1*r1 - r2*r2)/(RS_Math::pow(u.magnitude(), 2.0)) + 1.0);

    term = (r1*r1)/(RS_Math::pow(u.magnitude(), 2.0)) - s*s;

    // no intersection:
    if (term<0.0) {
        ret = RS_VectorSolutions();
    }

    // one or two intersections:
    else {
        t1 = sqrt(term);
        t2 = -sqrt(term);
        bool tangent = false;

        RS_Vector sol1 = c1 + u*s + v*t1;
        RS_Vector sol2 = c1 + u*s + v*t2;

        if (sol1.distanceTo(sol2)<1.0e-4) {
            sol2 = RS_Vector(false);
            ret = RS_VectorSolutions(sol1);
            tangent = true;
        } else {
            ret = RS_VectorSolutions(sol1, sol2);
        }

        ret.setTangent(tangent);
    }

    return ret;
}

// find intersections between ellipse/arc/circle using quartic equation solver
//
// @author Dongxu Li <dongxuli2011@gmail.com>
//

RS_VectorSolutions RS_Information::getIntersectionEllipseEllipse(RS_Ellipse* e1, RS_Ellipse* e2) {
    RS_VectorSolutions ret;

    if (e1==NULL || e2==NULL ) {
        return ret;
    }
    if (
        (e1->getCenter() - e2 ->getCenter()).squared() < RS_TOLERANCE2 &&
        (e1->getMajorP() - e2 ->getMajorP()).squared() < RS_TOLERANCE2 &&
        fabs(e1->getRatio() - e2 ->getRatio()) < RS_TOLERANCE
    ) { // overlapped ellipses, do not do overlap
        return ret;
    }
    RS_Ellipse ellipse01(NULL,e1->getData());

    RS_Ellipse *e01= & ellipse01;
    if( e01->getMajorRadius() < e01->getMinorRadius() ) e01->switchMajorMinor();
    RS_Ellipse ellipse02(NULL,e2->getData());
    RS_Ellipse *e02= &ellipse02;
    if( e02->getMajorRadius() < e02->getMinorRadius() ) e02->switchMajorMinor();
    //transform ellipse2 to ellipse1's coordinates
    RS_Vector shiftc1=- e01->getCenter();
    double shifta1=-e01->getAngle();
    e02->move(shiftc1);
    e02->rotate(shifta1);
//    RS_Vector majorP2=e02->getMajorP();
    double a1=e01->getMajorRadius();
    double b1=e01->getMinorRadius();
    double x2=e02->getCenter().x,
           y2=e02->getCenter().y;
    double a2=e02->getMajorRadius();
    double b2=e02->getMinorRadius();

    if( e01->getMinorRadius() < RS_TOLERANCE || e01 -> getRatio()< RS_TOLERANCE) {
        // treate e01 as a line
        RS_LineData ldata0(RS_Vector(-a1,0.),RS_Vector(a1,0.));
        RS_Line *l0=new RS_Line(e1->getParent(),ldata0);
        ret= getIntersectionEllipseLine(l0, e02);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }
    if( e02->getMinorRadius() < RS_TOLERANCE || e02 -> getRatio()< RS_TOLERANCE) {
        // treate e02 as a line
        RS_LineData ldata0(RS_Vector(-a2,0.),RS_Vector(a2,0.));
        RS_Line *l0=new RS_Line(e1->getParent(),ldata0);
        l0->rotate(RS_Vector(0.,0.),e02->getAngle());
        l0->move(e02->getCenter());
        ret= getIntersectionEllipseLine(l0, e01);
        ret.rotate(-shifta1);
        ret.move(-shiftc1);
        return ret;
    }

    //ellipse01 equation:
    //	x^2/(a1^2) + y^2/(b1^2) - 1 =0
    double t2= - e02->getAngle();
    //ellipse2 equation:
    // ( (x - u) cos(t) - (y - v) sin(t))^2/a^2 + ( (x - u) sin(t) + (y-v) cos(t))^2/b^2 =1
    // ( cos^2/a^2 + sin^2/b^2) x^2 +
    // ( sin^2/a^2 + cos^2/b^2) y^2 +
    //  2 sin cos (1/b^2 - 1/a^2) x y +
    //  ( ( 2 v sin cos - 2 u cos^2)/a^2 - ( 2v sin cos + 2 u sin^2)/b^2) x +
    //  ( ( 2 u sin cos - 2 v sin^2)/a^2 - ( 2u sin cos + 2 v cos^2)/b^2) y +
    //  (u cos - v sin)^2/a^2 + (u sin + v cos)^2/b^2 -1 =0
    // detect whether any ellipse radius is zero
    double cs=cos(t2),si=sin(t2);
    double ucs=x2*cs,usi=x2*si,
           vcs=y2*cs,vsi=y2*si;
    double cs2=cs*cs,si2=1-cs2;
    double tcssi=2.*cs*si;
    double ia2=1./(a2*a2),ib2=1./(b2*b2);
    std::vector<double> m(0,0.);
    m.push_back( 1./(a1*a1)); //ma000
    m.push_back( 1./(b1*b1)); //ma011
    m.push_back(cs2*ia2 + si2*ib2); //ma100
    m.push_back(cs*si*(ib2 - ia2)); //ma101
    m.push_back(si2*ia2 + cs2*ib2); //ma111
    m.push_back(( y2*tcssi - 2.*x2*cs2)*ia2 - ( y2*tcssi+2*x2*si2)*ib2); //mb10
    m.push_back( ( x2*tcssi - 2.*y2*si2)*ia2 - ( x2*tcssi+2*y2*cs2)*ib2); //mb11
    m.push_back((ucs - vsi)*(ucs-vsi)*ia2+(usi+vcs)*(usi+vcs)*ib2 -1.); //mc1
    auto&& vs0=RS_Math::simultaneousQuadraticSolver(m);
    shifta1 = - shifta1;
    shiftc1 = - shiftc1;
	for(RS_Vector vp: vs0){
        vp.rotate(shifta1);
        vp.move(shiftc1);
        ret.push_back(vp);
    }
    return ret;
}

//wrapper to do Circle-Ellipse and Arc-Ellipse using Ellipse-Ellipse intersection
RS_VectorSolutions RS_Information::getIntersectionCircleEllipse(RS_Circle* c1,
        RS_Ellipse* e1) {
    RS_VectorSolutions ret;
    if (c1==NULL || e1==NULL) {
        return ret;
    }

    RS_EllipseData d(
        c1->getCenter(),
        RS_Vector(c1->getRadius(),0.),
        1.0,
        0.,
        2.*M_PI,
        false);
    RS_Ellipse * e2= new RS_Ellipse(c1->getParent(),d);
    return getIntersectionEllipseEllipse(e1,e2);
}

RS_VectorSolutions RS_Information::getIntersectionArcEllipse(RS_Arc * a1,
        RS_Ellipse* e1) {
    RS_VectorSolutions ret;
    if (a1==NULL || e1==NULL) {
        return ret;
    }
    RS_EllipseData d(
        a1->getCenter(),
        RS_Vector(a1->getRadius(),0.),
        1.0,
        a1->getAngle1(),
        a1->getAngle2(),
        a1->isReversed());
    RS_Ellipse * e2= new RS_Ellipse(a1->getParent(),d);
    return getIntersectionEllipseEllipse(e1,e2);
}





/**
 * @return One or two intersection points between given entities.
 */
RS_VectorSolutions RS_Information::getIntersectionEllipseLine(RS_Line* line,
        RS_Ellipse* ellipse) {

    RS_VectorSolutions ret;

    if (line==NULL || ellipse==NULL) {
        return ret;
    }

    // rotate into normal position:

    double rx = ellipse->getMajorRadius();
    if(rx<RS_TOLERANCE) {
        //zero radius ellipse
        RS_Vector vp(line->getNearestPointOnEntity(ellipse->getCenter(), true));
        if((vp-ellipse->getCenter()).squared() <RS_TOLERANCE2){
            //center on line
            ret.push_back(vp);
        }
        return ret;
    }
    RS_Vector angleVector = ellipse->getMajorP().scale(RS_Vector(1./rx,-1./rx));
    double ry = rx*ellipse->getRatio();
    RS_Vector center = ellipse->getCenter();
    RS_Vector a1 = line->getStartpoint().rotate(center, angleVector);
    RS_Vector a2 = line->getEndpoint().rotate(center, angleVector);
//    RS_Vector origin = a1;
    RS_Vector dir = a2-a1;
    RS_Vector diff = a1 - center;
    RS_Vector mDir = RS_Vector(dir.x/(rx*rx), dir.y/(ry*ry));
    RS_Vector mDiff = RS_Vector(diff.x/(rx*rx), diff.y/(ry*ry));

    double a = RS_Vector::dotP(dir, mDir);
    double b = RS_Vector::dotP(dir, mDiff);
    double c = RS_Vector::dotP(diff, mDiff) - 1.0;
    double d = b*b - a*c;

//    std::cout<<"RS_Information::getIntersectionEllipseLine(): d="<<d<<std::endl;
    if (d < - 1.e3*RS_TOLERANCE*sqrt(RS_TOLERANCE)) {
        RS_DEBUG->print("RS_Information::getIntersectionLineEllipse: outside 0");
        return ret;
    }
    if( d < 0. ) d=0.;
    double root = sqrt(d);
    double t_a = -b/a;
    double t_b = root/a;
    //        double t_b = (-b + root) / a;

    ret.push_back(a1.lerp(a2,t_a+t_b));
    RS_Vector vp(a1.lerp(a2,t_a-t_b));
    if ( (ret.get(0)-vp).squared()>RS_TOLERANCE2) {
        ret.push_back(vp);
    }
    angleVector.y *= -1.;
    ret.rotate(center, angleVector);
//    std::cout<<"found Ellipse-Line intersections: "<<ret.getNumber()<<std::endl;
//    std::cout<<ret<<std::endl;
    RS_DEBUG->print("RS_Information::getIntersectionEllipseLine(): done");
    return ret;
}


/**
 * Checks if the given coordinate is inside the given contour.
 *
 * @param point Coordinate to check.
 * @param contour One or more entities which shape a contour.
 *         If the given contour is not closed, the result is undefined.
 *         The entities don't need to be in a specific order.
 * @param onContour Will be set to true if the given point it exactly
 *         on the contour.
 */
bool RS_Information::isPointInsideContour(const RS_Vector& point,
        RS_EntityContainer* contour, bool* onContour) {

    if (contour==NULL) {
        RS_DEBUG->print(RS_Debug::D_WARNING,
                        "RS_Information::isPointInsideContour: contour is NULL");
        return false;
    }

    if (point.x < contour->getMin().x || point.x > contour->getMax().x ||
            point.y < contour->getMin().y || point.y > contour->getMax().y) {
        return false;
    }

    double width = contour->getSize().x+1.0;

    bool sure;
    int counter;
    int tries = 0;
    double rayAngle = 0.0;
    do {
        sure = true;

        // create ray:
        RS_Vector v;
        v.setPolar(width*10.0, rayAngle);
        RS_Line ray(NULL, RS_LineData(point, point+v));
        counter = 0;
        RS_VectorSolutions sol;

        if (onContour!=NULL) {
            *onContour = false;
        }

        for (RS_Entity* e = contour->firstEntity(RS2::ResolveAll);
                e!=NULL;
                e = contour->nextEntity(RS2::ResolveAll)) {

            // intersection(s) from ray with contour entity:
            sol = RS_Information::getIntersection(&ray, e, true);

            for (int i=0; i<=1; ++i) {
                RS_Vector p = sol.get(i);

                if (p.valid) {
                    // point is on the contour itself
                    if (p.distanceTo(point)<1.0e-5) {
                        if (onContour!=NULL) {
                            *onContour = true;
                        }
                    } else {
                        if (e->rtti()==RS2::EntityLine) {
                            RS_Line* line = (RS_Line*)e;

                            // ray goes through startpoint of line:
                            if (p.distanceTo(line->getStartpoint())<1.0e-4) {
                                if (RS_Math::correctAngle(line->getAngle1())<M_PI) {
                                    sure = false;
                                }
                            }

                            // ray goes through endpoint of line:
                            else if (p.distanceTo(line->getEndpoint())<1.0e-4) {
                                if (RS_Math::correctAngle(line->getAngle2())<M_PI) {
                                    sure = false;
                                }
                            }
                            // else: ray goes through the line


                                counter++;
                            
                        } else if (e->rtti()==RS2::EntityArc) {
                            RS_Arc* arc = (RS_Arc*)e;

                            if (p.distanceTo(arc->getStartpoint())<1.0e-4) {
                                double dir = arc->getDirection1();
                                if ((dir<M_PI && dir>=1.0e-5) ||
                                        ((dir>2*M_PI-1.0e-5 || dir<1.0e-5) &&
                                         arc->getCenter().y>p.y)) {
                                    counter++;
                                    sure = false;
                                }
                            }
                            else if (p.distanceTo(arc->getEndpoint())<1.0e-4) {
                                double dir = arc->getDirection2();
                                if ((dir<M_PI && dir>=1.0e-5) ||
                                        ((dir>2*M_PI-1.0e-5 || dir<1.0e-5) &&
                                         arc->getCenter().y>p.y)) {
                                    counter++;
                                    sure = false;
                                }
                            } else {
                                counter++;
                            }
                        } else if (e->rtti()==RS2::EntityCircle) {
                            // tangent:
                            if (i==0 && sol.get(1).valid==false) {
                                if (!sol.isTangent()) {
                                    counter++;
                                } else {
                                    sure = false;
                                }
                            } else if (i==1 || sol.get(1).valid==true) {
                                counter++;
                            }
                        } else if (e->rtti()==RS2::EntityEllipse) {
                            RS_Ellipse* ellipse=static_cast<RS_Ellipse*>(e);
                            if(ellipse->isArc()){
                                if (p.distanceTo(ellipse->getStartpoint())<1.0e-4) {
                                    double dir = ellipse->getDirection1();
                                    if ((dir<M_PI && dir>=1.0e-5) ||
                                            ((dir>2*M_PI-1.0e-5 || dir<1.0e-5) &&
                                             ellipse->getCenter().y>p.y)) {
                                        counter++;
                                        sure = false;
                                    }
                                }
                                else if (p.distanceTo(ellipse->getEndpoint())<1.0e-4) {
                                    double dir = ellipse->getDirection2();
                                    if ((dir<M_PI && dir>=1.0e-5) ||
                                            ((dir>2*M_PI-1.0e-5 || dir<1.0e-5) &&
                                             ellipse->getCenter().y>p.y)) {
                                        counter++;
                                        sure = false;
                                    }
                                } else {
                                    counter++;
                                }
                            }else{
                                // tangent:
                                if (i==0 && sol.get(1).valid==false) {
                                    if (!sol.isTangent()) {
                                        counter++;
                                    } else {
                                        sure = false;
                                    }
                                } else if (i==1 || sol.get(1).valid==true) {
                                    counter++;
                                }
                            }
                        }
                    }
                }
            }
        }

        rayAngle+=0.02;
        tries++;
    }
    while (!sure && rayAngle<2*M_PI && tries<6);

    // remove double intersections:
    /*
       QList<RS_Vector> is2;
       bool done;
    RS_Vector* av;
       do {
           done = true;
           double minDist = RS_MAXDOUBLE;
           double dist;
        av = NULL;
           for (RS_Vector* v = is.first(); v!=NULL; v = is.next()) {
               dist = point.distanceTo(*v);
               if (dist<minDist) {
                   minDist = dist;
                   done = false;
                        av = v;
               }
           }

        if (!done && av!=NULL) {
                is2.append(*av);
        }
       } while (!done);
    */

    return ((counter%2)==1);
}


RS_VectorSolutions RS_Information::createQuadrilateral(const RS_EntityContainer& container)
{
	RS_VectorSolutions ret;
	if(container.count()!=4) return ret;
	RS_EntityContainer c(container);
	std::vector<RS_Line*> lines;
	for (RS_Entity* e=c.firstEntity(RS2::ResolveNone);
		 e!=NULL;
		 e=c.nextEntity(RS2::ResolveNone)) {
		if(e->rtti()!=RS2::EntityLine) return ret;
		lines.push_back(static_cast<RS_Line*>(e));
	}
	if(lines.size()!=4) return ret;

	//neigbours;
	std::vector<RS_Vector> vertices;
	for(unsigned i=0; i<3; ++i){
		for(unsigned j=i+1; j<4; ++j){
			RS_VectorSolutions&& sol=RS_Information::getIntersectionLineLine(lines[i], lines[j]);
			if(sol.size()){
				vertices.push_back(sol.at(0));
			}
		}
	}

//	std::cout<<"vertices.size()="<<vertices.size()<<std::endl;

	switch (vertices.size()){
	default:
		return ret;
	case 4:
		break;
	case 5:
	case 6:
		for(RS_Line* pl: lines){
			const double a0=pl->getDirection1();
			std::vector<std::vector<RS_Vector>::iterator> left;
			std::vector<std::vector<RS_Vector>::iterator> right;
			for(auto it=vertices.begin(); it != vertices.end(); ++it){
				RS_Vector&& dir=*it - pl->getNearestPointOnEntity(*it, false);
				if(dir.squared()<RS_TOLERANCE15) continue;
//				std::cout<<"angle="<<remainder(dir.angle() - a0, 2.*M_PI)<<std::endl;
				if(remainder(dir.angle() - a0, 2.*M_PI) > 0.)
					left.push_back(it);
				else
					right.push_back(it);

				if(left.size()==2 && right.size()==1){
					vertices.erase(right[0]);
					break;
				} else if(left.size()==1 && right.size()==2){
					vertices.erase(left[0]);
					break;
				}
			}
			if(vertices.size()==4) break;
		}
		break;
	}

	RS_Vector center(0., 0.);
	for(const RS_Vector& vp: vertices)
		center += vp;
	center *= 0.25;
	std::sort(vertices.begin(), vertices.end(), [&center](const RS_Vector& a, const RS_Vector&b)->bool{
		return center.angleTo(a)<center.angleTo(b);
	});
	for(const RS_Vector& vp: vertices){
		ret.push_back(vp);
//		std::cout<<"vp="<<vp<<std::endl;
	}
	return ret;
}