lc::geo::Bezier Class Reference

#include <geobezier.h>

Inheritance diagram for lc::geo::Bezier:

Collaboration diagram for lc::geo::Bezier:

Public Member Functions
	Bezier (const Coordinate &point_a, const Coordinate &point_b, const Coordinate &point_c)
	Bezier (const Bezier &bez)
virtual const std::vector < Coordinate >	getCP () const override
	getCP Returns the control points of the bezier More...
virtual const Area	boundingBox () const override
	boundingBox of the bezier More...
virtual Coordinate	nearestPointOnPath (const Coordinate &coord) const override
	nearestPointOnPath of the bezier More...
virtual Coordinate	nearestPointOnEntity (const Coordinate &coord) const override
	nearestPointOnEntity of the bezier More...
virtual Coordinate	CasteljauAt (std::vector< Coordinate > points, double t) const override
	CasteljauAt Coordinate of bezier at time t. More...
virtual Coordinate	DirectValueAt (double t) const override
	DirectValueAt Coordinate of bezier at time t calculated numerically. More...
virtual const std::vector < Coordinate >	Curve (double precession) override
	Curve Creates a bezier curve for drawing with some precession value. More...
virtual const double	length () const override
	length of the Bezier More...
virtual const Coordinate	tangent (double t) const override
	tangent of the bezeir More...
virtual const Coordinate	normal (double t) const override
	normal of the bezier at time t More...
virtual std::vector< BB_CSPtr >	splitHalf () const override
	splitHalf Splits the bezier into two halves. More...
virtual BB_CSPtr	splitAtT (double t) const override
	splitAtT Splits bezier at specific time. More...
virtual BB_CSPtr	offset (const geo::Coordinate &offset) const override
	offset offsets the bezier. More...
virtual BB_CSPtr	rotate (const geo::Coordinate &center, double angle) const override
	rotate the bezier at specific center and some angle More...
virtual BB_CSPtr	scale (const geo::Coordinate &center, const geo::Coordinate &factor) const override
	scale the bezier at specific center by some factor More...
virtual BB_CSPtr	move (const geo::Coordinate &offset) const override
	move the bezeir by some offset More...
virtual BB_CSPtr	mirror (const geo::Coordinate &axis1, const geo::Coordinate &axis2) const override
	mirror a bezier around a line More...
Public Member Functions inherited from lc::geo::BezierBase
	BezierBase ()
virtual	~BezierBase ()
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 Member Functions
std::vector< double >	nearestPointTValue (const Coordinate &coord) const override
	Bezier::nearestPointTValue. More...
const lc::geo::Coordinate	returnCasesForNearestPoint (double min_distance, const lc::geo::Coordinate &coord, const Coordinate &ret) const override
	Bezier::returnCasesForNearestPoint. More...

Private Attributes
Coordinate	_pointA
Coordinate	_pointB
Coordinate	_pointC

Friends
std::ostream &	operator<< (std::ostream &os, const Bezier &bez)

Detailed Description

Definition at line 15 of file geobezier.h.

Constructor & Destructor Documentation

Bezier::Bezier	(	const Coordinate &	point_a,
		const Coordinate &	point_b,
		const Coordinate &	point_c
	)

Create a new Bezier

Definition at line 6 of file geobezier.cpp.

    : _pointA(point_a), _pointB(point_b), _pointC(point_c) {
}

Bezier::Bezier

(

const Bezier &

bez

)

Definition at line 10 of file geobezier.cpp.

                                :
    _pointA(bez._pointA), _pointB(bez._pointB),
    _pointC(bez._pointC) {

}

Member Function Documentation

const Area Bezier::boundingBox ( ) const

overridevirtual

boundingBox of the bezier

Returns

Area of the bounding box

Implements lc::geo::BezierBase.

Definition at line 21 of file geobezier.cpp.

                                     {

    /*
     * T = A-B/(A - 2B + C)
     */
    auto tx_ = (_pointA.x() - _pointB.x())/(_pointA.x() - (_pointB.x()*2.0) + _pointC.x());
    auto ty_ = (_pointA.y() - _pointB.y())/(_pointA.y() - (_pointB.y()*2.0) + _pointC.y());
    std::vector<double> x_{_pointA.x(), _pointC.x() };
    std::vector<double> y_{_pointA.y(), _pointC.y() };

    if(tx_ > 0. && tx_ < 1.0) {
        auto bez1 = DirectValueAt(tx_);
        x_.push_back(bez1.x());
        y_.push_back(bez1.y());
    }

    if(ty_ > 0. && ty_ < 1.0) {
        auto bez2 = DirectValueAt(ty_);
        x_.push_back(bez2.x());
        y_.push_back(bez2.y());
    }

    std::sort(x_.begin(), x_.end());
    std::sort(y_.begin(), y_.end());

    return Area(geo::Coordinate(x_.front(), y_.front()), geo::Coordinate (x_.back() ,y_.back()));
}

Coordinate Bezier::CasteljauAt ( std::vector< Coordinate >  points, double  t  ) const

overridevirtual

CasteljauAt Coordinate of bezier at time t.

Parameters

points	Vector of CP of bezier
t	Time t

Returns

Coordinate at time t

Implements lc::geo::BezierBase.

Definition at line 145 of file geobezier.cpp.

                                                                           {
    if(points.size() == 1) return points.front();
    else {
        int size_ = points.size();
        std::vector<Coordinate> new_vec;
        for(int i = 1; i < size_; i++) {
            new_vec.push_back(points[i-1] * (1.0-t) + points[i] * t);
        }
        return CasteljauAt(new_vec, t);
    }
}

const std::vector< Coordinate > Bezier::Curve ( double  precession )

overridevirtual

Curve Creates a bezier curve for drawing with some precession value.

Parameters

precession

of the curve

Returns

Vector of Coordinates to be joined.

Implements lc::geo::BezierBase.

Definition at line 165 of file geobezier.cpp.

                                                           {
    std::vector<Coordinate> v = { _pointA, _pointB, _pointC };
    std::vector<Coordinate> ret;
    for(auto i = 0.; i < 1.; i+=precession) {
        ret.push_back(CasteljauAt(v, i));
    }
    return ret;
}

Coordinate Bezier::DirectValueAt ( double  t ) const

overridevirtual

DirectValueAt Coordinate of bezier at time t calculated numerically.

Parameters

t

Time t

Returns

Coordinate at time t

Implements lc::geo::BezierBase.

Definition at line 157 of file geobezier.cpp.

                                               {
    auto one_minus_t = 1 - t;
    auto t_square = t*t;
    auto one_minus_t_square = one_minus_t * one_minus_t;
    auto two_a_b  = 2 * one_minus_t * t;
    return (_pointA * one_minus_t_square) + (_pointB * two_a_b) + (_pointC * t_square);
}

const std::vector< geo::Coordinate > Bezier::getCP ( ) const

overridevirtual

getCP Returns the control points of the bezier

Returns

Vector of Coordinates.

Implements lc::geo::BezierBase.

Definition at line 16 of file geobezier.cpp.

                                                   {
    return {_pointA, _pointB, _pointC };
}

const double Bezier::length ( ) const

overridevirtual

length of the Bezier

Returns

double length

Implements lc::geo::BezierBase.

Definition at line 174 of file geobezier.cpp.

                                  {

     auto  Bx = 2*(_pointB.x() - _pointA.x());
     auto  By = 2*(_pointB.y() - _pointA.y());
     auto  Ax = _pointA.x() - (_pointB.x()*2.0) + _pointC.x();
     auto  Ay = _pointA.y() - (_pointB.y()*2.0) + _pointC.y();

     auto A = 4*(Ax*Ax + Ay*Ay);
     auto B = 4*(Ax*Bx + Ay*By);
     auto C = Bx*Bx + By*By;

     auto Sabc = 2*std::sqrt(A+B+C);
     auto A_2 = std::sqrt(A);
     auto A_32 = 2*A*A_2;
     auto C_2 = 2*std::sqrt(C);
     auto BA = B/A_2;

     return ( A_32 * Sabc + A_2 * B * (Sabc - C_2) + (4 * C * A - B * B) * std::log((2* A_2 + BA + Sabc)/(BA + C_2))) / (4 * A_32);
}

BB_CSPtr Bezier::mirror ( const geo::Coordinate &  axis1, const geo::Coordinate &  axis2  ) const

overridevirtual

mirror a bezier around a line

Parameters

axis1	first coordinate of line to be mirrored about
axis2	second coordinate of line to be mirrored about

Returns

mirrored bezier

Implements lc::geo::BezierBase.

Definition at line 246 of file geobezier.cpp.

                                                                                    {
    auto z = std::make_shared<const Bezier>(_pointA.mirror(axis1, axis2),
                  _pointB.mirror(axis1, axis2),
                  _pointC.mirror(axis1, axis2)
                  );
    return z;
}

BB_CSPtr Bezier::move ( const geo::Coordinate &  offset ) const

overridevirtual

move the bezeir by some offset

Parameters

offset

coordinate of move

Returns

moved bezier

Implements lc::geo::BezierBase.

Definition at line 209 of file geobezier.cpp.

                                                       {
    auto z = std::make_shared<const Bezier>(_pointA + offset,
                  _pointB + offset,
                  _pointC + offset
                  );
    return z;
}

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

overridevirtual

nearestPointOnEntity of the bezier

Parameters

coord

Coordinate to be compared with

Returns

Coordinate of nearest point

Implements lc::geo::BezierBase.

Definition at line 76 of file geobezier.cpp.

                                                                     {
    auto min_distance = std::numeric_limits<double>::max();

    Coordinate ret;

    auto tValues = nearestPointTValue(coord);

    for (auto val : tValues) {
        if(val > 0 && val < 1) {
            geo::Coordinate point_on_path = DirectValueAt(val);
            auto raw_distance = coord.distanceTo(point_on_path);
            if(raw_distance < min_distance) {
                ret = point_on_path;
                min_distance = raw_distance;
            }
        }
    }

    return returnCasesForNearestPoint(min_distance, coord, ret);
}

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

overridevirtual

nearestPointOnPath of the bezier

Parameters

coord

Coordinate to be compared with

Returns

Coordinate of nearest point

Implements lc::geo::BezierBase.

Definition at line 49 of file geobezier.cpp.

                                                                   {

    /*
     * Difference between nearest point on path and
     * nearest point on entity for a bezier curve is that
     * for calculating the nearest point on entity you check
     * that if the value of "t" is between 0 and 1
     * whereas for nearest point on path, you don't check that
     */

    auto min_distance = std::numeric_limits<double>::max();
    Coordinate ret;

    auto tValues = nearestPointTValue(coord);

    for (auto val : tValues) {
        geo::Coordinate point_on_path = DirectValueAt(val);
        auto raw_distance = coord.distanceTo(point_on_path);
        if(raw_distance < min_distance) {
            ret = point_on_path;
            min_distance = raw_distance;
        }
    }

    return returnCasesForNearestPoint(min_distance, coord, ret);
}

std::vector< double > Bezier::nearestPointTValue ( const Coordinate &  coord ) const

overrideprivatevirtual

Bezier::nearestPointTValue.

Parameters

coord

The pointt from where nearest point is to be found

Returns

vector of t values for bezier

Implements lc::geo::BezierBase.

Definition at line 102 of file geobezier.cpp.

                                                                               {
    auto pos = _pointA - coord;

    auto Ax = _pointB.x() - _pointA.x();
    auto Ay = _pointB.y() - _pointA.y();
    auto Bx = _pointA.x() - (_pointB.x()*2.0) + _pointC.x();
    auto By = _pointA.y() - (_pointB.y()*2.0) + _pointC.y();

    auto a = Bx * Bx + By * By;
    auto b = (3 * (Ax * Bx + Ay * By)) / a;
    auto c = (2 * (Ax * Ax + Ay * Ay) + pos.x() * Bx + pos.y() * By) / a;
    auto d = (pos.x() * Ax + pos.y() * Ay) / a;

    return lc::Math::cubicSolver({b, c, d});
}

const Coordinate Bezier::normal ( double  t ) const

overridevirtual

normal of the bezier at time t

Parameters

t

time t

Returns

Coordinate of normal

Implements lc::geo::BezierBase.

Definition at line 227 of file geobezier.cpp.

                                              {
    auto  Bx = _pointB.x() - _pointA.x();
    auto  By = _pointB.y() - _pointA.y();
    auto  Ax = _pointA.x() - (_pointB.x()*2.0) + _pointC.x();
    auto  Ay = _pointA.y() - (_pointB.y()*2.0) + _pointC.y();

    auto tanx = Ay * t + By;
    auto tany = -(Ax * t + Bx);

    auto lNorm = std::sqrt(tanx * tanx + tany * tany);

    if (lNorm > 0)  {
        tanx /= lNorm;
        tany /= lNorm;
    }

    return Coordinate(tanx, tany);
}

BB_CSPtr Bezier::offset ( const geo::Coordinate &  offset ) const

overridevirtual

offset offsets the bezier.

Parameters

offset

offsect coordinate

Returns

offsetted bezier

Implements lc::geo::BezierBase.

Definition at line 265 of file geobezier.cpp.

                                                         {
    //auto tx_ = (_pointA.x() - _pointB.x())/(_pointA.x() - (_pointB.x()*2.0) + _pointC.x());
    //auto ty_ = (_pointA.y() - _pointB.y())/(_pointA.y() - (_pointB.y()*2.0) + _pointC.y());

//    if(tx_ > 0. && tx_ < 1.0) {
//        auto bez1 = DirectValueAt(tx_);
//        x_.push_back(bez1.x());
//        y_.push_back(bez1.y());
//    }

//    if(ty_ > 0. && ty_ < 1.0) {
//        auto bez2 = DirectValueAt(ty_);
//        x_.push_back(bez2.x());
//        y_.push_back(bez2.y());
//    }

    return NULL; // TODO: no return statement
}

const lc::geo::Coordinate Bezier::returnCasesForNearestPoint ( double  min_distance, const lc::geo::Coordinate &  coord, const Coordinate &  ret  ) const

overrideprivatevirtual

Bezier::returnCasesForNearestPoint.

Parameters

distance	at minimum T
coord	coordinate from where the minimum distance is to be found
ret	coordinate value at minimum T

Returns

nearest point

Implements lc::geo::BezierBase.

Definition at line 127 of file geobezier.cpp.

                                          {
    auto distance_to_A = coord.distanceTo(_pointA);
    auto distance_to_C = coord.distanceTo(_pointC);

    // Point is on curve
    if(min_distance < distance_to_A && min_distance < distance_to_C) {
        return ret;
    }
    // Point is on starting of Curve
    if (distance_to_A < distance_to_C) {
        return _pointA;
    }
    // Point is end of curve
    return _pointC;
}

BB_CSPtr Bezier::rotate ( const geo::Coordinate &  center, double  angle  ) const

overridevirtual

rotate the bezier at specific center and some angle

Parameters

center	of rotation
angle	of rotation

Returns

rotated bezier

Implements lc::geo::BezierBase.

Definition at line 194 of file geobezier.cpp.

                                                                       {
    auto z = std::make_shared<const Bezier>(_pointA.rotate(center, angle),
                  _pointB.rotate(center, angle),
                  _pointC.rotate(center, angle));
    return z;
}

BB_CSPtr Bezier::scale ( const geo::Coordinate &  center, const geo::Coordinate &  factor  ) const

overridevirtual

scale the bezier at specific center by some factor

Parameters

center	of scale
factor	of scale

Returns

Scaled bezier

Implements lc::geo::BezierBase.

Definition at line 201 of file geobezier.cpp.

                                                                                     {
    auto z = std::make_shared<const Bezier>(_pointA.scale(center, factor),
                                            _pointB.scale(center, factor),
                                            _pointC.scale(center, factor)
                                            );
    return z;
}

BB_CSPtr Bezier::splitAtT ( double  t ) const

overridevirtual

splitAtT Splits bezier at specific time.

Parameters

t

Time t

Returns

Split bezier.

Implements lc::geo::BezierBase.

Definition at line 284 of file geobezier.cpp.

                                        {
        auto x1 = _pointA.x();
        auto y1 = _pointA.y();

        auto x2 = _pointB.x();
        auto y2 = _pointB.y();

        auto x3 = _pointC.x();
        auto y3 = _pointC.y();

        auto x12 = (x2-x1)*t+x1;
        auto y12 = (y2-y1)*t+y1;

        auto x23 = (x3-x2)*t+x2;
        auto y23 = (y3-y2)*t+y2;

        auto x123 = (x23-x12)*t+x12;
        auto y123 = (y23-y12)*t+y12;

        return std::make_shared<Bezier>(Bezier({x1, y1}, {x12, y12}, {x123, y123}));
}

std::vector< BB_CSPtr > Bezier::splitHalf ( ) const

overridevirtual

splitHalf Splits the bezier into two halves.

Returns

Vector of two beziers.

Implements lc::geo::BezierBase.

Definition at line 254 of file geobezier.cpp.

                                            {
    auto AB = (_pointA + _pointB) / 2;
    auto BC = (_pointB + _pointC) / 2;
    auto D = (AB + BC)/2;

    BB_CSPtr b1 = std::make_shared<Bezier>(Bezier(_pointA, AB, D));
    BB_CSPtr b2 = std::make_shared<Bezier>(Bezier(D, BC, _pointC));

    return {b1, b2};
}

const Coordinate Bezier::tangent ( double  t ) const

overridevirtual

tangent of the bezeir

Parameters

t

time T

Returns

Coordinate of tangent

Implements lc::geo::BezierBase.

Definition at line 217 of file geobezier.cpp.

                                               {
    auto  Bx = _pointB.x() - _pointA.x();
    auto  By = _pointB.y() - _pointA.y();
    auto  Ax = _pointA.x() - (_pointB.x()*2.0) + _pointC.x();
    auto  Ay = _pointA.y() - (_pointB.y()*2.0) + _pointC.y();
    auto tanx = Ax * t + Bx;
    auto tany = Ay * t + By;
    return Coordinate(tanx, tany);
}

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  os, const Bezier &  bez  )

friend

Definition at line 149 of file geobezier.h.

                                                                                 {
                    os << "Bezier(A=" << bez._pointA << " radius=" << bez._pointB << " startAngle=" << bez._pointC << ")";
                    return os;
                }

Member Data Documentation

Coordinate lc::geo::Bezier::_pointA

private

Definition at line 155 of file geobezier.h.

Coordinate lc::geo::Bezier::_pointB

private

Definition at line 156 of file geobezier.h.

Coordinate lc::geo::Bezier::_pointC

private

Definition at line 157 of file geobezier.h.

---

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

• lckernel/cad/geometry/geobezier.h
• lckernel/cad/geometry/geobezier.cpp