PPointPlane3dC - Point - plane in 3D projective space

Developer Documentation

Centre for Vision, Speech & Signal Processing

Comments:
The class represents a point/plane in 3 dimensional projective space. An object contains 4 real numbers which serve as its projective coordinates. An object can be treated as a point and its dual plane and vice versa in any time. This feature reflects the dual relationship of points and planes in 3D projective space.

Parent Classes:

Point4dC

Derived Classes:

PPoint3dC

PPlane3dC

Typedefs:

typedef Point4dC::CoordT PCoordT;: A projective coordinate.
typedef Point4dC::CoordT CCoordT;: An cartesian coordinate.

Methods:

PPointPlane3dC(): Constructs the point/plane whose coordinates are zeros, eg. non-existing projective object.
PPointPlane3dC(CCoordT x,CCoordT y,CCoordT z): Constructs the point/plane (x, y, z, 1). x,y,z represent either point Cartesian coordinates or plane normal expressed as vector Cartesian coordinates.
PPointPlane3dC(const Point3dC & p): Constructs the projective point/line (p.X(), p.Y(), p.Z(), 1) related to the Euclidian point 'p'.
PPointPlane3dC(const Vector3dC & v): Constructs the projective point/line (v.X(), v.Y(), v.Z(), 0) related to the Euclidian direction 'v'.
PPointPlane3dC(PCoordT p0,PCoordT p1,PCoordT p2,PCoordT p3): Constructs the point/plane (p0, p1, p2, p3).
PPointPlane3dC(const PlaneABCD3dC & p): Constructs the projective point/plane corresponding to the Euclidian plane 'p'.
PPointPlane3dC(const PPointPlane3dC & p0,const PPointPlane3dC & p1,const PPointPlane3dC & p2): Constructs the projective point/plane determined by three projective planes/points, resp.
PPointPlane3dC(const PPointPlane3dC & p): Copy constructor.
const PPointPlane3dC & operator=(const PPointPlane3dC & p): Assigment of point/plane. Access to the object parameters. --------------------------------
const PCoordT & operator[](IndexT i) const: Returns the value of the (i+1)-th coordinate.
PCoordT & operator[](IndexT i): Access the value of the (i+1)-th coordinate.
CCoordT operator()(IndexT i) const: Returns the value of the (i+1)-th Cartesian coordinate. The function does not check if the point/plane is ideal or not or the range of the index 'i'.
PCoordT Scale() const: Returns the value of the last projective coordinate P4().
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.
const PCoordT & P4() const: Returns the value of the 4th 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.
PCoordT & P4(): Returns the value of the 4th coordinate.
CCoordT X() const: Returns the value of the 1. Cartesian coordinate. The function does not check if the point/plane is ideal or not.
CCoordT Y() const: Returns the value of the 2. Cartesian coordinate. The function does not check if the point/plane is ideal or not.
CCoordT Z() const: Returns the value of the 3. Cartesian coordinate. The function does not check if the point/plane is ideal or not.
Point3dC Point3d() const: Returns the point in 3D Euiclidian space corresponding to this projective object. This object is treated as a projective point. It is not checked if the projective point is ideal or not.
const PPointPlane3dC & PPointPlane3d() const: Access to this constant object.
PPointPlane3dC & PPointPlane3d(): Access to the point/plane. Logical conditions. -------------------
BooleanT operator==(const PPointPlane3dC & p) const: Returns TRUE iff 2 points/planes are the same projective point/plane. Two projective points/planes are equal iff their 4D Cartesian representants are equal.
BooleanT operator!=(const PPointPlane3dC & p) const: Returns TRUE iff 2 points/planes are different projective points/planes. Two projective points/planes are different iff they are not equal in the sense of the operator '=='.
BooleanT IsIdealPoint() const: Returns TRUE iff this point/plane 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 'Point4dC::relZero'.
BooleanT IsIdealPlane() const: Returns TRUE iff this point/plane represents an ideal projective plane. The plane is an ideal projective plane if the absolute value of the ratio (Abs(P1)+Abs(P2()+Abs(P3))/Scale() is smaller or equal to the threshold 'Point4dC::relZero'.
BooleanT IsValid() const: Returns TRUE if the sum of absolute values of the projective coordinates is bigger than the threshold 'Point4dC::zeroDistance'. Setting of the coordinates. ---------------------------
void Set(const PPointPlane3dC & p): Sets both coordinates according to the values of the point/plane 'p'.
void Set(const PCoordT p1,const PCoordT p2,const PCoordT p3,const PCoordT p4): Sets the 1-st coordinate to be 'p1', the 2nd one to be 'p2', the 3rd one to be 'p3', and the 4th one to be 'p4'. 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 PPointPlane3dC & operator+=(const PPointPlane3dC & p): Adds the values of the coordinates of the 'p' to this point/plane.
const PPointPlane3dC & operator-=(const PPointPlane3dC & p): Subtracts the values of the coordinates of the 'p' from this point/plane.
const PPointPlane3dC & operator*=(const RealT alpha): Multiplies all coordinates by 'alpha'.
const PPointPlane3dC & operator/=(const RealT alpha): Divides all coordinates by 'alpha'.
PPointPlane3dC operator+(const PPointPlane3dC & p) const: Returns the point/plane which is the sum of this point and the 'p'.
PPointPlane3dC operator*(const RealT alpha) const: Returns the point/plane which coordinates are multiplied by 'alpha'.
PPointPlane3dC operator/(const RealT alpha) const: Returns the point/plane which coordinates are divided by 'alpha'. Geometrical operations. -----------------------
RealT operator&(const PPointPlane3dC & p) const: Returns the sum P1()*p.P1() + P2()*p.P2() + P3()*p.P3() + P4()*p.P4(). In 3 dimensional Euclidian vector space the result is equivalent to dot product of 2 vectors.
PPointPlane3dC Translation(const PPointPlane3dC & newOrigin) const: Returns the point/plane with projective coordinates related to the new origin 'newOrigin'.
RealT AdjointDet(RealT b00,RealT b01,RealT b02,RealT b10,RealT b11,RealT b12,RealT b20,RealT b21,RealT b22): Computes the determinant of the matrix 3x3 created from b[ij] elements.
PPointPlane3dC(const Point4dC & p): Creates the projective point/plane in 3D space from values of the point 'p'.
PPointPlane3dC operator*(RealT lambda,const PPointPlane3dC & p)
PPointPlane3dC operator/(RealT lambda,const PPointPlane3dC & p)
istream & operator>>(istream & inS,PPointPlane3dC & point)
void Set(const PPointPlane3dC::PCoordT p1,const PPointPlane3dC::PCoordT p2,const PPointPlane3dC::PCoordT p3,const PPointPlane3dC::PCoordT p4)

Programmer:Radek Marik, Documentation by CxxDoc: Tue Mar 20 10:49:27 2001

PPointPlane3dC

Point - plane in 3D projective space

include	"amma/PPtPl3d.hh"
User Level:	Default
Library:	Mpg3
Example:	exMat2d.cc
Section:	Geometry.Projective.3-D
In Scope:	std