#include <geoellipse.h>

Inheritance diagram for lc::geo::Ellipse:

Collaboration diagram for lc::geo::Ellipse:

Public Member Functions
	Ellipse (const Coordinate &center, const Coordinate &majorP, double minorRadius, double startAngle, double endAngle, bool reversed=false)

const Coordinate	center () const
	center, Returns Center point of Ellipse More...

const Coordinate	majorP () const
	majorP, Returns major point of the ellipse, relative to center More...

double	minorRadius () const
	minorRadius, Returns the minor radius of ellipse More...

double	startAngle () const
	startAngle, Returns Start elliptic!! angle of ellipse More...

double	endAngle () const
	endAngle, Return the end elliptic!! angle of ellipse More...

Coordinate	getPoint (const double &angle) const
	getPoint, return a point on ellipse with given elliptic angle More...

Coordinate	startPoint () const
	startPoint, start point of ellipse More...

Coordinate	endPoint () const
	endPoint, end point of ellipse More...

std::vector< Coordinate >	findPotentialNearestPoints (const Coordinate &coord) const
	findPotentialNearestPoints More...

Coordinate	nearestPointOnPath (const Coordinate &coord) const
	nearestPointOnPath, (ignore if it arc) More...

Coordinate	nearestPointOnEntity (const Coordinate &coord) const
	nearestPointOnEntity, ( not ignore arc) More...

bool	isArc () const
	isArc More...

bool	isReversed () const

double	ratio () const
	ratio of major radius to minor radius More...

double	majorRadius () const
	Major Radius. More...

double	getAngle () const
	getAngle of MajorP More...

double	getEllipseAngle (const Coordinate &coord) const
	getEllipseAngle More...

bool	isAngleBetween (double angle) const

Ellipse	georotate (const Coordinate &center, const double rotation_angle) const
	rotate an ellipse at a center by an angle More...

Ellipse	geoscale (const Coordinate &center, const Coordinate &factor) const
	scale an ellipse at some center by some factor More...

const maths::Equation	equation () const
	Returns the quadratic equation. More...

virtual void	accept (GeoEntityVisitor &v) const override

Public Member Functions inherited from lc::geo::Base
virtual	~Base ()=default

Public Member Functions inherited from lc::Visitable
virtual	~Visitable ()=default

Private Attributes
const Coordinate	_center

const Coordinate	_majorP

const double	_minorRadius

const double	_startAngle

const double	_endAngle

const bool	_isReversed

Friends
std::ostream &	operator<< (std::ostream &os, const Ellipse &e)

Detailed Description

Definition at line 14 of file geoellipse.h.

Constructor & Destructor Documentation

Ellipse::Ellipse	(	const Coordinate &	center,
		const Coordinate &	majorP,
		double	minorRadius,
		double	startAngle,
		double	endAngle,
		bool	reversed = `false`
	)

Parameters

center
majorP	relative to center
minorRadius
startAngle
endAngle
reversed

Definition at line 10 of file geoellipse.cpp.

                                                                                                                                           :
     _center(center),
     _majorP(majorP),
     _minorRadius(minorRadius),
     _startAngle(startAngle),
     _endAngle(endAngle),
     _isReversed(reversed) {
 
 }

Member Function Documentation

virtual void lc::geo::Ellipse::accept ( GeoEntityVisitor & v ) const

inlineoverridevirtual

Implements lc::Visitable.

Reimplemented in lc::entity::Ellipse.

Definition at line 164 of file geoellipse.h.

164 { v.visit(*this); }

const Coordinate Ellipse::center ( ) const

center, Returns Center point of Ellipse

Returns: geo::Coordinate center

Definition at line 20 of file geoellipse.cpp.

                                        {
     return _center;
 }

double Ellipse::endAngle ( ) const

endAngle, Return the end elliptic!! angle of ellipse

Returns: double endangle

Definition at line 189 of file geoellipse.cpp.

                                {
     return _endAngle;
 }

Coordinate Ellipse::endPoint ( ) const

endPoint, end point of ellipse

Returns: for elliptic arc, return the endPoint, otherwise return end of majorP

Definition at line 202 of file geoellipse.cpp.

                                    {
     return getPoint(endAngle());
 }

const maths::Equation lc::geo::Ellipse::equation ( ) const

inline

Returns the quadratic equation.

Returns: Equation

Definition at line 153 of file geoellipse.h.

                                                      {
                     auto ce0 = _majorP.squared();
                     auto ce2 = this->ratio() * this->ratio() * ce0;
 
                     if (ce0 < LCTOLERANCE * LCTOLERANCE || ce2 < LCTOLERANCE * LCTOLERANCE) {
                         return maths::Equation();
                     }
 
                     return maths::Equation(1. / ce0, 0., 1. / ce2, 0., 0., -1.).rotate(getAngle()).move(_center);
                 }

std::vector< Coordinate > Ellipse::findPotentialNearestPoints ( const Coordinate & coord ) const

findPotentialNearestPoints

Parameters

coord,the point of which we search

Returns

Definition at line 88 of file geoellipse.cpp.

                                                                                        {
     std::vector<Coordinate> pnp;
     pnp.push_back(this->startPoint());
     pnp.push_back(this->endPoint());
 
     double ellipseAngle = this->getAngle();
 
     Coordinate trcoord = coord-_center;
     trcoord = trcoord.rotate(Coordinate(0, 0), -ellipseAngle);
 
     double b = _minorRadius;
     double a = _majorP.magnitude();
 
     double x=trcoord.x(),y=trcoord.y();
 
     double twoa2b2=2*(a*a-b*b);
     double twoax=2*a*x;
     double twoby=2*b*y;
     double a0=twoa2b2*twoa2b2;
     std::vector<double> ce(4,0.);
     std::vector<double> roots(0,0.);
 
     if(a0 > LCTOLERANCE) { // a != b , ellipse
         ce[0]=-2.*twoax/twoa2b2;
         ce[1]= (twoax*twoax+twoby*twoby)/a0-1.;
         ce[2]= - ce[0];
         ce[3]= -twoax*twoax/a0;
         //std::cout<<"1::find cosine, variable c, solve(c^4 +("<<ce[0]<<")*c^3+("<<ce[1]<<")*c^2+("<<ce[2]<<")*c+("<<ce[3]<<")=0,c)\n";
         roots=Math::quarticSolver(ce);
     } else {//a=b, quadratic equation for circle
         a0=twoby/twoax;
         roots.push_back(sqrt(1./(1.+a0*a0)));
         roots.push_back(-roots[0]);
     }
 
     if(roots.size() == 0) {
         //this should not happen
         std::cout<<"(a= "<<a<<" b= "<<b<<" x= "<<x<<" y= "<<y<<" )\n";
         std::cout<<"finding minimum for ("<<x<<"-"<<a<<"*cos(t))^2+("<<y<<"-"<<b<<"*sin(t))^2\n";
         std::cout<<"2::find cosine, variable c, solve(c^4 +("<<ce[0]<<")*c^3+("<<ce[1]<<")*c^2+("<<ce[2]<<")*c+("<<ce[3]<<")=0,c)\n";
         std::cout<<ce[0]<<' '<<ce[1]<<' '<<ce[2]<<' '<<ce[3]<<std::endl;
         std::cerr<<"lcmath::geoellipse::findPotentialNearestPoints() finds no root from quartic, this should not happen\n";
         return pnp;
     }
 
 
     for(size_t i=0; i<roots.size(); i++) {
         double const s=twoby*roots[i]/(twoax-twoa2b2*roots[i]); //sine
         double const d2=twoa2b2+(twoax-2.*roots[i]*twoa2b2)*roots[i]+twoby*s;
         if (d2<0) continue; // fartherest
         Coordinate t(a*roots[i], b*s);
         //double d=(t-trcoord).magnitude();
         //double angle = atan2(roots[i],s);
         // std::cout<<i<<" Find Point: cos= "<<roots[i]<<" sin= "<<s<<" angle= "<<angle<<" ds2= "<<d<<" d="<<d2<<std::endl;
         t = t.rotate(ellipseAngle);
         t = t + _center;
         pnp.push_back(t);
     }
     return pnp;
 }

Ellipse Ellipse::georotate	(	const Coordinate &	center,
		const double	rotation_angle
	)		const

rotate an ellipse at a center by an angle

Parameters

center	of rotation
rotation_angle

Returns: Rotated Ellipse

Definition at line 82 of file geoellipse.cpp.

                                                                                                   {
     return Ellipse(center().rotate(rotation_center, rotation_angle),
                     majorP().rotate(rotation_center, rotation_angle),
                     minorRadius(), startAngle(), endAngle());
 }

Ellipse Ellipse::geoscale	(	const Coordinate &	center,
		const Coordinate &	factor
	)		const

scale an ellipse at some center by some factor

Parameters

center	of scaling
factor	of scaling

Returns: scaled ellipse

Definition at line 44 of file geoellipse.cpp.

                                                                                   {
     geo::Coordinate vp1(this->majorP());
     double a(vp1.magnitude());
     geo::Coordinate vp2(vp1.x() * 1. / a, vp1.y() * 1. / a);
     geo::Coordinate startPoint;
     geo::Coordinate endPoint;
 
     if (isArc()) {
         startPoint = this->startPoint();
         endPoint = this->endPoint();
     }
 
     double ct = vp2.x();
     double ct2 = ct * ct; // cos^2 angle
     double st = vp2.y();
     double st2 = 1.0 - ct2; // sin^2 angle
     double kx2 = factor.x() * factor.x();
     double ky2 = factor.y() * factor.y();
     double b = (this->minorRadius() / this->majorP().magnitude()) * a;
     double cA = 0.5 * a * a * (kx2 * ct2 + ky2 * st2);
     double cB = 0.5 * b * b * (kx2 * st2 + ky2 * ct2);
     double cC = a * b * ct * st * (ky2 - kx2);
     geo::Coordinate vp(cA - cB, cC);
     geo::Coordinate vp3(a, b);
     geo::Coordinate vp4(vp3.scale(geo::Coordinate(vp.angle() * 0.5)));
     geo::Coordinate vp5(vp4.rotate(geo::Coordinate(ct, st)));
     geo::Coordinate vp6(vp5.scale(factor));
     double z = cA + cB;
     double x = vp.magnitude();
     double ratio = std::sqrt((z - x) / (z + x));
     double minor_ = vp6.magnitude() * ratio;
 
     return Ellipse(this->center().scale(center, factor), vp6,
                                                     minor_,
                                                     isArc() ? this->getEllipseAngle(startPoint) : 0.,
                                                     isArc() ? this->getEllipseAngle(endPoint) : 2.*M_PI);
 }

double Ellipse::getAngle ( ) const

getAngle of MajorP

Returns: double majorP angle

Definition at line 40 of file geoellipse.cpp.

                                {
     return _majorP.angle();
 }

double Ellipse::getEllipseAngle ( const Coordinate & coord ) const

getEllipseAngle

Parameters

coord,a point on ellipse, not actually required to be on ellipse

Returns: elliptic angle to the position of coord

Definition at line 218 of file geoellipse.cpp.

                                                              {
     Coordinate offset = coord - _center;
     Coordinate point = offset.rotate(-_majorP.angle());
     return atan2(point.y() * _majorP.magnitude(), point.x() * _minorRadius);
 }

Coordinate Ellipse::getPoint ( const double & angle ) const

getPoint, return a point on ellipse with given elliptic angle

Parameters

angle,elliptic!! angle in radians

Returns: coordinates of a point on ellipse with given elliptic angle

Definition at line 193 of file geoellipse.cpp.

                                                       {
     const double a = majorP().magnitude();
     const double b = minorRadius();
     return _center + Coordinate(a * cos(angle), b * sin(angle)).rotate(Coordinate(0., 0.), majorP().angle());
 }

bool lc::geo::Ellipse::isAngleBetween ( double angle ) const

inline

Definition at line 127 of file geoellipse.h.

                                                         {
                     if (!isArc())
                         return true;
                     return Math::isAngleBetween(angle, _startAngle, _endAngle, !_isReversed);
                 }

bool Ellipse::isArc ( ) const

isArc

Returns: true if entity is an elliptic arc

Definition at line 214 of file geoellipse.cpp.

                           {
     return Math::getAngleDifferenceShort(_startAngle, _endAngle, _isReversed) > LCARCTOLERANCE;
 }

bool Ellipse::isReversed ( ) const

Return values

true	if the arc is reversed (clockwise),
false	otherwise

Definition at line 206 of file geoellipse.cpp.

                                {
     return _isReversed;
 }

const Coordinate Ellipse::majorP ( ) const

majorP, Returns major point of the ellipse, relative to center

Returns: geo::Coordinate majorP

Definition at line 24 of file geoellipse.cpp.

                                        {
     return _majorP;
 }

double Ellipse::majorRadius ( ) const

Major Radius.

Returns: double Major radius

Definition at line 36 of file geoellipse.cpp.

                                   {
     return _majorP.magnitude();
 }

double Ellipse::minorRadius ( ) const

minorRadius, Returns the minor radius of ellipse

Returns: double minor radius

Definition at line 28 of file geoellipse.cpp.

                                   {
     return _minorRadius;
 }

Coordinate Ellipse::nearestPointOnEntity ( const Coordinate & coord ) const

nearestPointOnEntity, ( not ignore arc)

Parameters

coord,the point of which we search

Returns: nearest point on the ellipse Entity

Definition at line 167 of file geoellipse.cpp.

                                                                       {
     Coordinate res;
     double minDist = DBL_MAX;
     std::vector<Coordinate> potencialPoinst = this->findPotentialNearestPoints(coord);
 
 
     for (auto verifiedPoint: potencialPoinst)
     {
         if (this->isAngleBetween(verifiedPoint.angle()))
         {
             double d = verifiedPoint.distanceTo(coord);
             if (d<minDist)
             {
                 minDist = verifiedPoint.distanceTo(coord);
                 res = verifiedPoint;
             }
         }
     };
 
     return res;
 }

Coordinate Ellipse::nearestPointOnPath ( const Coordinate & coord ) const

nearestPointOnPath, (ignore if it arc)

Parameters

coord,the point of which we search

Returns: nearest point on the ellipse path

Definition at line 149 of file geoellipse.cpp.

                                                                     {
     Coordinate res;
     auto minDist = DBL_MAX;
     std::vector<Coordinate> potencialPoinst = this->findPotentialNearestPoints(coord);
 
     for (auto& verifiedPoint: potencialPoinst)
     {
         double d = verifiedPoint.distanceTo(coord);
         if (d<minDist)
         {
             minDist = verifiedPoint.distanceTo(coord);
             res = verifiedPoint;
         }
     };
 
     return res;
 }

double Ellipse::ratio ( ) const

ratio of major radius to minor radius

Returns: double ratio

Definition at line 210 of file geoellipse.cpp.

                             {
     return _majorP.magnitude() / _minorRadius;
 }

double Ellipse::startAngle ( ) const

startAngle, Returns Start elliptic!! angle of ellipse

Returns: double startangle

Definition at line 32 of file geoellipse.cpp.

                                  {
     return _startAngle;
 }

Coordinate Ellipse::startPoint ( ) const

startPoint, start point of ellipse

Returns: for elliptic arc, return the startPoint, otherwise return end of majorP

Definition at line 199 of file geoellipse.cpp.

                                      {
     return getPoint(startAngle());
 }

Friends And Related Function Documentation

std::ostream& operator<<	(	std::ostream &	os,
		const Ellipse &	e
	)

friend

Definition at line 167 of file geoellipse.h.

                                                                                 {
                     os << "Ellipse(center=" << e._center << " majorP=" << e._majorP << " minorRadius=" << e._minorRadius << " startAngle=" << e._startAngle << " endAngle=" << e._endAngle << " isReversed=" << e._isReversed << ")";
                     return os;
                 }

Member Data Documentation

const Coordinate lc::geo::Ellipse::_center

private

Definition at line 172 of file geoellipse.h.

const double lc::geo::Ellipse::_endAngle

private

Definition at line 176 of file geoellipse.h.

const bool lc::geo::Ellipse::_isReversed

private

Definition at line 177 of file geoellipse.h.

const Coordinate lc::geo::Ellipse::_majorP

private

Definition at line 173 of file geoellipse.h.

const double lc::geo::Ellipse::_minorRadius

private

Definition at line 174 of file geoellipse.h.

const double lc::geo::Ellipse::_startAngle

private

Definition at line 175 of file geoellipse.h.

The documentation for this class was generated from the following files:

lckernel/cad/geometry/geoellipse.h
lckernel/cad/geometry/geoellipse.cpp

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation