PLine2dC - Plane in 3D projective space

User Documentation

Centre for Vision, Speech & Signal Processing

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

Parent Classes:

PPointLine2dC

Typedefs:

typedef PPointLine2dC::PCoordT PCoordT;: A projective coordinate.
typedef PPointLine2dC::CCoordT CCoordT;: An cartesian coordinate.

Methods:

PLine2dC(): Constructs the line whose coordinates are zeros, eg. non-existing projective line.
PLine2dC(const Vector2dC & n,RealT d): Constructs the projective line equivalent to the Euiclidian line determined by the equation n.X()*x + n.Y()*y + d = 0.
PLine2dC(const Point2dC & p1,const Point2dC & p2): Constructs the projective line passing through two Euclidian points p1, p2.
PLine2dC(const Point2dC & p,const Vector2dC & v): Constructs the projective line passing through the Euclidian point 'p' and the Euclidian line direction vector 'v'.
PLine2dC(const Line2dPVC & l): Constructs the projective line from the Euclidian line 'l'.
PLine2dC(const Line2dPPC & l): Constructs the projective line from the Euclidian line 'l'.
PLine2dC(PCoordT p1,PCoordT p2,PCoordT p3): Constructs the line (p1, p2, p3).
PLine2dC(const PPointLine2dC & p0,const PPointLine2dC & p1): Constructs the line passing through two projective points 'p0' and 'p1'.
PLine2dC(const PPointLine2dC & p): Constructs the line from the point/line object 'p'.
PLine2dC(const PLine2dC & p): Copy constructor.
const PLine2dC & operator=(const PLine2dC & p): Assigment of point. Access to the object. ---------------------
Vector2dC Normal() const: Returns the normal of a corresponding Euclidian line. If this projective line is ideal the function returns the zero vector.
const PLine2dC & PLine2d() const: Access to this constant object.
PLine2dC & PLine2d(): Access to the point. Logical conditions. -------------------
BooleanT IsIdeal() const: Returns TRUE iff this line is an ideal projective line. The line is an ideal projective line if the absolute value of the ratio Scale()/SumAbs() is smaller or equal to the threshold 'Point3dC::relZero'. Arithmetical operations. ------------------------
const PLine2dC & operator*=(const RealT alpha): Multiplies all coordinates by 'alpha'.
const PLine2dC & operator/=(const RealT alpha): Divides all coordinates by 'alpha'.
PLine2dC operator*(const RealT alpha) const: Returns the line which coordinates are multiplied by 'alpha'.
PLine2dC operator/(const RealT alpha) const: Returns the line which coordinates are divided by 'alpha'. Geometrical constructions. --------------------------
PPoint2dC Intersection(const PLine2dC & l) const: Returns the projective point that is the intersection of both lines.
PLine2dC operator*(RealT lambda,const PLine2dC & p)
PLine2dC operator/(RealT lambda,const PLine2dC & p)
istream & operator>>(istream & inS,PLine2dC & point)

#include "amma/PPtLi2d.hh"

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'.

Programmer:Radek Marik, Documentation by CxxDoc: Tue Mar 20 10:48:08 2001

PLine2dC

Plane in 3D projective space

include	"amma/PLine2d.hh"
User Level:	Default
Library:	Mpg2
Example:	exMat2d.cc
Section:	Geometry.Projective.2-D
In Scope:	std