PUBLIC

PPoint1dC::PPoint1dC(void) PPoint1dC::PPoint1dC(CCoordT) PPoint1dC::PPoint1dC(PCoordT,PCoordT) PPoint1dC::PPoint1dC(const PPoint1dC &) PPoint1dC::operator=(const PPoint1dC &) PPoint1dC::operator[](IndexT) const PPoint1dC::operator[](IndexT) PPoint1dC::operator()(IndexT) const PPoint1dC::Scale(void) const PPoint1dC::P1(void) const PPoint1dC::P2(void) const PPoint1dC::P1(void) PPoint1dC::P2(void) PPoint1dC::X(void) const PPoint1dC::PPoint1d(void) const PPoint1dC::PPoint1d(void) PPoint1dC::operator==(const PPoint1dC &) const PPoint1dC::operator!=(const PPoint1dC &) const PPoint1dC::IsIdeal(void) const PPoint1dC::IsColinear(const PPoint1dC &,const PPoint1dC &) const PPoint1dC::IsValid(void) const PPoint1dC::Set(const PPoint1dC &) PPoint1dC::Set(const PCoordT,const PCoordT) PPoint1dC::MaxIndex(void) const PPoint1dC::MinIndex(void) const PPoint1dC::AbsMaxIndex(void) const PPoint1dC::AbsMinIndex(void) const PPoint1dC::Sum(void) const PPoint1dC::SumAbs(void) const PPoint1dC::operator+=(const PPoint1dC &) PPoint1dC::operator-=(const PPoint1dC &) PPoint1dC::operator*=(const RealT) PPoint1dC::operator/=(const RealT) PPoint1dC::operator+(const PPoint1dC &) const PPoint1dC::operator*(const RealT) const PPoint1dC::operator/(const RealT) const PPoint1dC::Translation(const PPoint1dC &) const PPoint1dC::operator&(const PPoint1dC &) const

PPoint1dC
Point in 1D projective space
include	"amma/PPoint1d.hh"
User Level:	Default
Library:	Mpg1
Example:	exMat2d.cc
Section:	Geometry.Projective.1-D
In Scope:	std

Comments:
The class represents a point in 1 dimensional projective space. The point contains 2 real numbers which serve as its projective coordinates.

private Point2dC

typedef Point2dC::CoordT PCoordT;

A projective coordinate.

typedef Point2dC::CoordT CCoordT;

An cartesian coordinate.

PPoint1dC()

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

PPoint1dC(CCoordT x)

Constructs the point (x, 1).

PPoint1dC(PCoordT p1,PCoordT p2)

Constructs the point (p1, p2).

PPoint1dC(const PPoint1dC & p)

Copy constructor.

const PPoint1dC & operator=(const PPoint1dC & p)

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

const PCoordT & operator[](IndexT i) const

Returns the value of the (i+1)-th projective coordinate.

PCoordT & operator[](IndexT i)

Access the value of the (i+1)-th projective coordinate.

CCoordT operator()(IndexT i) const

Returns the value of the (i+1)-th Cartesian coordinate. The function does not check if the point is ideal or not or the range of the index 'i'.

PCoordT Scale() const

Returns the value of the last projective coordinate P2().

const PCoordT & P1() const

Returns the value of the 1-st coordinate.

const PCoordT & P2() const

Returns the value of the 2-st coordinate.

PCoordT & P1()

Returns the value of the 1-st coordinate.

PCoordT & P2()

Returns the value of the 2-st coordinate.

CCoordT X() const

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

const PPoint1dC & PPoint1d() const

Access to this constant object.

PPoint1dC & PPoint1d()

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

BooleanT operator==(const PPoint1dC & p) const

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

BooleanT operator!=(const PPoint1dC & p) const

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

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 PPoint1dC & q2,const PPoint1dC & q3) const

Returns always TRUE.

BooleanT IsValid() const

Returns TRUE if the sum of absolute values of the projective coordinates is bigger than the threshold 'Point2dC::zeroDistance'. Setting of the coordinates. ---------------------------

void Set(const PPoint1dC & p)

Sets both coordinates according to the values of the point 'p'.

void Set(const PCoordT p1,const PCoordT p2)

Sets the 1-st coordinate to be 'p1' and the 2nd one to be 'p2'. 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 projective coordinates. Arithmetical operations. ------------------------

const PPoint1dC & operator+=(const PPoint1dC & point)

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

const PPoint1dC & operator-=(const PPoint1dC & point)

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

const PPoint1dC & operator*=(const RealT alpha)

Multiplies both coordinates by 'alpha'.

const PPoint1dC & operator/=(const RealT alpha)

Divides both coordinates by 'alpha'.

PPoint1dC operator+(const PPoint1dC & point) const

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

PPoint1dC operator*(const RealT alpha) const

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

PPoint1dC operator/(const RealT alpha) const

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

PPoint1dC Translation(const PPoint1dC & newOrigin) const

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

RealT operator&(const PPoint1dC & p) const

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