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PPoint2dC::PPoint2dC(void) PPoint2dC::PPoint2dC(CCoordT,CCoordT) PPoint2dC::PPoint2dC(const Point2dC &) PPoint2dC::PPoint2dC(PCoordT,PCoordT,PCoordT) PPoint2dC::PPoint2dC(const PPoint2dC &) PPoint2dC::PPoint2dC(const PPointLine2dC &) PPoint2dC::PPoint2dC(const PPointLine2dC &,const PPointLine2dC &) PPoint2dC::operator=(const PPoint2dC &) PPoint2dC::PPoint2d(void) const PPoint2dC::PPoint2d(void) PPoint2dC::Point2d(void) const PPoint2dC::IsIdeal(void) const PPoint2dC::IsColinear(const PPoint2dC &,const PPoint2dC &) const PPoint2dC::operator+=(const PPoint2dC &) PPoint2dC::operator-=(const PPoint2dC &) PPoint2dC::operator*=(const RealT) PPoint2dC::operator/=(const RealT) PPoint2dC::operator+(const PPoint2dC &) const PPoint2dC::operator*(const RealT) const PPoint2dC::operator/(const RealT) const PPoint2dC::Translation(const PPoint2dC &) const PPoint2dC::PLine(const PPoint2dC &) const 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

PPoint2dC
Point in 2D projective space
include	"amma/PPoint2d.hh"
User Level:	Default
Library:	Mpg2
Example:	exMat2d.cc
Section:	Geometry.Projective.2-D
In Scope:	std

Comments:
The class represents a point in 2 dimensional projective space. The point contains 3 real numbers which serve as its projective coordinates.

public PPointLine2dC

typedef PPointLine2dC::PCoordT PCoordT;

A projective coordinate.

typedef PPointLine2dC::CCoordT CCoordT;

An cartesian coordinate.

PPoint2dC()

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

PPoint2dC(CCoordT x,CCoordT y)

Constructs the point (x, y, 1).

PPoint2dC(const Point2dC & p)

Constructs the point (p.x, p.y, 1).

PPoint2dC(PCoordT p1,PCoordT p2,PCoordT p3)

Constructs the point (p1, p2, p3).

PPoint2dC(const PPoint2dC & p)

Copy constructor.

PPoint2dC(const PPointLine2dC & p)

Creates the projective point from the projective point/line.

PPoint2dC(const PPointLine2dC & l0,const PPointLine2dC & l1)

Constructs the projective point as intersection of two projective line 'l0' and 'l1'.

const PPoint2dC & operator=(const PPoint2dC & p)

Assigment of point. Access to the object. --------------------------

const PPoint2dC & PPoint2d() const

Access to this constant object.

PPoint2dC & PPoint2d()

Access to the point.

Point2dC Point2d() const

Returns the point in Euclidian space related to this projective point. It is assumed that the point is not ideal. The function does not check if the point is ideal or not. Logical conditions. -------------------

BooleanT IsIdeal() const

Returns TRUE iff this point is 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 'Point2dC::relZero'.

BooleanT IsColinear(const PPoint2dC & q2,const PPoint2dC & q3) const

Returns TRUE iff this point and the points 'q2' and 'q3' are colinear. Arithmetical operations. ------------------------

const PPoint2dC & operator+=(const PPoint2dC & point)

Adds the values of the coordinates of the 'point' to this point.

const PPoint2dC & operator-=(const PPoint2dC & point)

Subtracts the values of the coordinates of the 'point' from this point.

const PPoint2dC & operator*=(const RealT alpha)

Multiplies both coordinates by 'alpha'.

const PPoint2dC & operator/=(const RealT alpha)

Divides both coordinates by 'alpha'.

PPoint2dC operator+(const PPoint2dC & point) const

Returns the point which is the sum of this point and the 'point'.

PPoint2dC operator*(const RealT alpha) const

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

PPoint2dC operator/(const RealT alpha) const

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

PPoint2dC Translation(const PPoint2dC & newOrigin) const

Returns the point with projective coordinates related to the new origin 'newOrigin'.

PLine2dC PLine(const PPoint2dC & p) const

Returns the projective line passing through this point and the point 'p'.

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'.