lc::geo::CubicBezier Class Reference

#include <geobeziercubic.h>

Inheritance diagram for lc::geo::CubicBezier:

Collaboration diagram for lc::geo::CubicBezier:

Public Member Functions
	CubicBezier (const Coordinate &point_a, const Coordinate &point_b, const Coordinate &point_c, const Coordinate &point_d)
	CubicBezier (const CubicBezier &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
virtual std::vector< double >	nearestPointTValue (const Coordinate &coord) const override
	Bezier::nearestPointTValue. More...
virtual 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
Coordinate	_pointD

Detailed Description

Definition at line 15 of file geobeziercubic.h.

Constructor & Destructor Documentation

CubicBezier::CubicBezier	(	const Coordinate &	point_a,
		const Coordinate &	point_b,
		const Coordinate &	point_c,
		const Coordinate &	point_d
	)

Create a new CUBIC Bezier

Definition at line 6 of file geobeziercubic.cpp.

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

CubicBezier::CubicBezier

(

const CubicBezier &

bez

)

Definition at line 10 of file geobeziercubic.cpp.

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

Member Function Documentation

const Area CubicBezier::boundingBox ( ) const

overridevirtual

boundingBox of the bezier

Returns

Area of the bounding box

Implements lc::geo::BezierBase.

Definition at line 15 of file geobeziercubic.cpp.

                                          {

    auto v1 =(_pointB - _pointA)*3;
    auto v2 = (_pointC - _pointB)*3;
    auto v3 = (_pointD - _pointC)*3;

    auto a = v1 - (v2*2) + v3;
    auto b = (v2 - v1)*2;
    auto c = v1;

    std::vector<double> x_roots = lc::Math::quadraticSolver({b.x()/a.x(), c.x()/a.x()});
    std::vector<double> y_roots = lc::Math::quadraticSolver({b.y()/a.y(), b.y()/a.y()});

    std::vector<double> x_{_pointA.x(), _pointB.x(),_pointC.x(), _pointD.x() };
    std::vector<double> y_{_pointA.y(), _pointB.y(),_pointC.y(), _pointD.y() };


    for(const double tx_ : x_roots) {
        if(tx_ > 0. && tx_ < 1.0) {
            auto bez1 = DirectValueAt(tx_);
            x_.push_back(bez1.x());
            y_.push_back(bez1.y());
        }
    }
    for(const double ty_ : y_roots) {
        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 CubicBezier::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 156 of file geobeziercubic.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 > CubicBezier::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 178 of file geobeziercubic.cpp.

                                                                {
    std::vector<Coordinate> v = { _pointA, _pointB, _pointC, _pointD };
    std::vector<Coordinate> ret;
    for(auto i = 0.; i < 1.0; i+=precession) {
        ret.push_back(CasteljauAt(v, i));
    }
    return ret;
}

Coordinate CubicBezier::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 168 of file geobeziercubic.cpp.

                                                    {
    auto t_square = t*t;
    auto t_cube = t_square*t;
    auto one_minus_t = 1 - t;
    auto one_minus_square = one_minus_t*one_minus_t;
    auto one_minus_cube = one_minus_square * one_minus_t;

    return (_pointA*one_minus_cube) + (_pointB*3*one_minus_square*t) + (_pointC*3*one_minus_t*t_square) + (_pointD*t_cube);
}

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

overridevirtual

getCP Returns the control points of the bezier

Returns

Vector of Coordinates.

Implements lc::geo::BezierBase.

Definition at line 123 of file geobeziercubic.cpp.

                                                        {
    std::vector<Coordinate> ret{_pointA, _pointB, _pointC, _pointD};
    return ret;
}

const double CubicBezier::length ( ) const

overridevirtual

length of the Bezier

Returns

double length

Implements lc::geo::BezierBase.

Definition at line 187 of file geobeziercubic.cpp.

                                       {
    return 0; // TODO: no return statement
}

BB_CSPtr CubicBezier::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 227 of file geobeziercubic.cpp.

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

BB_CSPtr CubicBezier::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 208 of file geobeziercubic.cpp.

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

Coordinate CubicBezier::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 79 of file geobeziercubic.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 CubicBezier::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 52 of file geobeziercubic.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 > CubicBezier::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 105 of file geobeziercubic.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});
    std::vector<double> empty(0, 0.);
    return empty; // TODO: no return statement
}

const Coordinate CubicBezier::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 222 of file geobeziercubic.cpp.

                                                   {
    const Coordinate empty;
    return empty; // TODO: no return statement
}

BB_CSPtr CubicBezier::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 250 of file geobeziercubic.cpp.

                                                              {
    return NULL; // TODO: no return statement
}

const lc::geo::Coordinate CubicBezier::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 137 of file geobeziercubic.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;
    return ret; // TODO: no return statement
}

BB_CSPtr CubicBezier::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 191 of file geobeziercubic.cpp.

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

BB_CSPtr CubicBezier::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 199 of file geobeziercubic.cpp.

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

BB_CSPtr CubicBezier::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 254 of file geobeziercubic.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 x4 = _pointD.x();
        auto y4 = _pointD.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 x34 = (x4-x3)*t+x3;
        auto y34 = (y4-y3)*t+y3;

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

        auto x234 = (x34-x23)*t+x23;
        auto y234 = (y34-y23)*t+y23;

        auto x1234 = (x234-x123)*t+x123;
        auto y1234 = (y234-y123)*t+y123;

        return std::make_shared<CubicBezier>(CubicBezier({x1, y1}, {x12, y12}, {x123, y123}, {x1234, y1234}));
}

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

overridevirtual

splitHalf Splits the bezier into two halves.

Returns

Vector of two beziers.

Implements lc::geo::BezierBase.

Definition at line 236 of file geobeziercubic.cpp.

                                                 {
    auto E = (_pointA+_pointB)/2;
    auto F = (_pointB+_pointC)/2;
    auto G = (_pointC+_pointD)/2;
    auto H = (E+F)/2;
    auto J = (F+G)/2;
    auto K = (H+J)/2;

    BB_CSPtr b1 = std::make_shared<CubicBezier>(CubicBezier(_pointA,E,H,K));
    BB_CSPtr b2 = std::make_shared<CubicBezier>(CubicBezier(K,J,G,_pointD));

    return {b1, b2};
}

const Coordinate CubicBezier::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 geobeziercubic.cpp.

                                                    {
    const Coordinate empty;
    return empty; // TODO: no return statement
}

Member Data Documentation

Coordinate lc::geo::CubicBezier::_pointA

private

Definition at line 148 of file geobeziercubic.h.

Coordinate lc::geo::CubicBezier::_pointB

private

Definition at line 149 of file geobeziercubic.h.

Coordinate lc::geo::CubicBezier::_pointC

private

Definition at line 150 of file geobeziercubic.h.

Coordinate lc::geo::CubicBezier::_pointD

private

Definition at line 151 of file geobeziercubic.h.

---

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

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