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PPointLine2dC::PPointLine2dC(void) PPointLine2dC::PPointLine2dC(CCoordT,CCoordT) PPointLine2dC::PPointLine2dC(const Point2dC &) PPointLine2dC::PPointLine2dC(const Vector2dC &) PPointLine2dC::PPointLine2dC(PCoordT,PCoordT,PCoordT) PPointLine2dC::PPointLine2dC(const PPointLine2dC &,const PPointLine2dC &) PPointLine2dC::PPointLine2dC(const PPointLine2dC &) PPointLine2dC::operator=(const PPointLine2dC &) PPointLine2dC::operator[](IndexT) const PPointLine2dC::operator[](IndexT) PPointLine2dC::operator()(IndexT) const PPointLine2dC::Scale(void) const PPointLine2dC::P1(void) const PPointLine2dC::P2(void) const PPointLine2dC::P3(void) const PPointLine2dC::P1(void) PPointLine2dC::P2(void) PPointLine2dC::P3(void) PPointLine2dC::X(void) const PPointLine2dC::Y(void) const PPointLine2dC::PPointLine2d(void) const PPointLine2dC::PPointLine2d(void) PPointLine2dC::operator==(const PPointLine2dC &) const PPointLine2dC::operator!=(const PPointLine2dC &) const PPointLine2dC::IsIdealPoint(void) const PPointLine2dC::IsIdealLine(void) const PPointLine2dC::IsValid(void) const PPointLine2dC::Set(const PPointLine2dC &) PPointLine2dC::Set(const PCoordT,const PCoordT,const PCoordT) PPointLine2dC::MaxIndex(void) const PPointLine2dC::MinIndex(void) const PPointLine2dC::AbsMaxIndex(void) const PPointLine2dC::AbsMinIndex(void) const PPointLine2dC::Sum(void) const PPointLine2dC::SumAbs(void) const PPointLine2dC::operator+=(const PPointLine2dC &) PPointLine2dC::operator-=(const PPointLine2dC &) PPointLine2dC::operator*=(const RealT) PPointLine2dC::operator/=(const RealT) PPointLine2dC::operator+(const PPointLine2dC &) const PPointLine2dC::operator*(const RealT) const PPointLine2dC::operator/(const RealT) const PPointLine2dC::operator&(const PPointLine2dC &) const PPointLine2dC::PPointLine2d(const PPointLine2dC &) const

PPointLine2dC
Point - plane in 2D projective space
include	"amma/PPtLi2d.hh"
User Level:	Default
Library:	Mpg2
Example:	exMat2d.cc
Section:	Geometry.Projective.2-D
In Scope:	std

Comments:
The class represents a point/line in 2 dimensional projective space. An object contains 3 real numbers which serve as its projective coordinates. An object can be treated as a point and its dual line and vice versa in any time. This feature reflects the dual relationship of points and lines in 2D projective space. The index of coordinates starts from 0.

private Point3dC

PLine2dC
PPoint2dC

typedef Point3dC::CoordT PCoordT;

A projective coordinate.

typedef Point3dC::CoordT CCoordT;

An cartesian coordinate.

PPointLine2dC()

Constructs the point/line whose coordinates are zeros, eg. non-existing projective object.

PPointLine2dC(CCoordT x,CCoordT y)

Constructs the point/line (x, y, 1). x,y represent either point Cartesian coordinates or a line normal expressed as vector Cartesian coordinates.

PPointLine2dC(const Point2dC & p)

Constructs the projective point/line (p.X(), p.Y(), 1) related to the Euclidian point 'p'.

PPointLine2dC(const Vector2dC & v)

Constructs the projective point/line (v.X(), v.Y(), 0) related to the Euclidian direction 'v'.

PPointLine2dC(PCoordT p1,PCoordT p2,PCoordT p3)

Constructs the point/line (p1, p2, p3).

PPointLine2dC(const PPointLine2dC & p0,const PPointLine2dC & p1)

Constructs the projective point/line determined by two projective lines/points, resp.

PPointLine2dC(const PPointLine2dC & p)

Copy constructor.

const PPointLine2dC & operator=(const PPointLine2dC & p)

Assigment of a point/line 'p'. Access to the object items. ---------------------------

const PCoordT & operator[](IndexT i) const

Returns the value of the i-th coordinate.

PCoordT & operator[](IndexT i)

Access the value of the i-th coordinate.

CCoordT operator()(IndexT i) const

Returns the value of the i-th Cartesian coordinate. The function does not check if the point/line is ideal or not or the range of the index 'i'.

PCoordT Scale() const

Returns the value of the last projective coordinate P3().

const PCoordT & P1() const

Returns the value of the 1st coordinate.

const PCoordT & P2() const

Returns the value of the 2nd coordinate.

const PCoordT & P3() const

Returns the value of the 3rd coordinate.

PCoordT & P1()

Returns the value of the 1st coordinate.

PCoordT & P2()

Returns the value of the 2nd coordinate.

PCoordT & P3()

Returns the value of the 3rd coordinate.

CCoordT X() const

Returns the value of the 1. Cartesian coordinate. The function does not check if the point/line is ideal or not.

CCoordT Y() const

Returns the value of the 2. Cartesian coordinate. The function does not check if the point/line is ideal or not.

const PPointLine2dC & PPointLine2d() const

Access to this constant object.

PPointLine2dC & PPointLine2d()

Access to the point/line. Logical conditions. -------------------

BooleanT operator==(const PPointLine2dC & p) const

Returns TRUE iff 2 points/lines are the same projective point/line. Two projective points/lines are equal iff their 3D Cartesian representants are equal.

BooleanT operator!=(const PPointLine2dC & p) const

Returns TRUE iff 2 points/lines are different projective points/lines. Two projective points/lines are different iff they are not equal in the sense of the operator '=='.

BooleanT IsIdealPoint() const

Returns TRUE iff this point/line represents an ideal projective point. The point is an ideal projective point if the absolute value of the ratio Scale()/SumAbs() is smaller or equal to the threshold 'Point3dC::relZero'.

BooleanT IsIdealLine() const

Returns TRUE iff this point/line represents an ideal projective plane. The plane is an ideal projective plane if the absolute value of the ratio (Abs(P1)+Abs(P2())/Scale() is smaller or equal to the threshold 'Point3dC::relZero'.

BooleanT IsValid() const

Returns TRUE if the sum of absolute values of the projective coordinates is bigger than the threshold 'Point3dC::zeroDistance'. Setting of the coordinates. ---------------------------

void Set(const PPointLine2dC & p)

Sets coordinates according to the values of the point/line 'p'.

void Set(const PCoordT p1,const PCoordT p2,const PCoordT p3)

Sets the 1-st coordinate to be 'p1', the 2nd one to be 'p2', and the 3rd one to be 'p3'. Information about extrems. --------------------------

IndexT MaxIndex() const

Returns the index of the maximum coordinate.

IndexT MinIndex() const

Returns the index of the minimum coordinate.

IndexT AbsMaxIndex() const

Returns the index of the maximum coordinate in absolute value.

IndexT AbsMinIndex() const

Returns the index of the minimum coordinate in absolute value.

PCoordT Sum() const

Returns the sum of coordinates.

PCoordT SumAbs() const

Returns the sum of absolute value of coordinates. Arithmetical operations. ------------------------

const PPointLine2dC & operator+=(const PPointLine2dC & p)

Adds the values of the coordinates of the 'p' to this point/line.

const PPointLine2dC & operator-=(const PPointLine2dC & p)

Subtracts the values of the coordinates of the 'p' from this point/line.

const PPointLine2dC & operator*=(const RealT alpha)

Multiplies all coordinates by 'alpha'.

const PPointLine2dC & operator/=(const RealT alpha)

Divides all coordinates by 'alpha'.

PPointLine2dC operator+(const PPointLine2dC & p) const

Returns the point/line which is the sum of this point and the 'p'.

PPointLine2dC operator*(const RealT alpha) const

Returns the point/line which coordinates are multiplied by 'alpha'.

PPointLine2dC operator/(const RealT alpha) const

Returns the point/line which coordinates are divided by 'alpha'. Geometrical operations. -----------------------

RealT operator&(const PPointLine2dC & p) const

Returns the sum P1()*p.P1() + P2()*p.P2() + P3()*p.P3(). In 3 dimensional Euclidian vector space the result is equivalent to dot product of 2 vectors.

PPointLine2dC PPointLine2d(const PPointLine2dC & p) const

Returns the projective line/point determined by this point/line and the point/line 'p'.