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OrthoProjection2to1dC::OrthoProjection2to1dC(void) OrthoProjection2to1dC::OrthoProjection2to1dC(const Point2dC &,const Point2dC &) OrthoProjection2to1dC::OrthoProjection2to1dC(const Point2dC &,const Vector2dC &) OrthoProjection2to1dC::OrthoProjection2to1dC(const OrthoProjection2to1dC &) OrthoProjection2to1dC::operator()(const Point2dC &) const OrthoProjection2to1dC::operator[](const Point2dC &) const OrthoProjection2to1dC::operator()(const Coor1DT &) const OrthoProjection2to1dC::T(const Point2dC &) const OrthoProjection2to1dC::ODistance(const Point2dC &) const OrthoProjection2to1dC::Distance(const Point2dC &) const OrthoProjection2to1dC::operator()(const OrthoProjection2to1dC::Coor1DT &) const

OrthoProjection2to1dC
Orthogonal projection between 1D and 2D spaces
include	"amma/OProj1a2.hh"
User Level:	Default
Library:	Mpm123
Example:	exMat2d.cc
Section:	Geometry.Transforms
In Scope:	std

Comments:
The class OrthoProjection2to1dC represents orthogonal projection from 2D space into the 1D space.

typedef double Coor1DT;

The coordinate in 1D space.

typedef double DistanceT;

Distance.

Point2dC coorOrigin;

The origin of the coordinate system of 1D space expressed in 2D coordinate system.

Vector2dC unitDirection;

The direction of the 1D space expressed in 2D coordinate system.

OrthoProjection2to1dC()

Non-existing projection. All point are projected into the point (0,0).

OrthoProjection2to1dC(const Point2dC & origin,const Point2dC & plusPoint)

The projection mapping will project 2D points into 1D points belonging to the 1D space (line). The embedded line is defined in 2D space by the origin point and another arbitrary point different from the origin lying in the positive half of the line.

OrthoProjection2to1dC(const Point2dC & origin,const Vector2dC & plusDirection)

The projection mapping will project 2D points into 1D points belonging to the 1D space (line). The embedded line is defined in 2D space by the origin point and an arbitrary vector different from zero vector pointing into the positive half of the line.

OrthoProjection2to1dC(const OrthoProjection2to1dC & p)

Copy constructor. Projections. ------------

Coor1DT operator()(const Point2dC & p) const

Returns the coordinate of the orthogonal projection of the 2D point 'p'. The returned point coordinate is expressed in the coordinate system of the 1D space (line).

Point2dC operator[](const Point2dC & p) const

Returns the coordinates of the orthogonal projection of the 2D point 'p'. The returned point coordinate is expressed in the coordinate system of the 2D space.

Point2dC operator()(const Coor1DT & p) const

Returns the 2D coordinates of the point 'p' belonging to the embedded 1D space. Coordinate system relationships. --------------------------------

Point2dC T(const Point2dC & p) const

The embedded 1D space coordinate system is added another coordinate to create positive oriented 2D coordinate system A. The coordinates of the point 'p' are transformed into the coordinate system A and returned.

DistanceT ODistance(const Point2dC & p) const

Returns the oriented orthogonal distance between the point 'p' and the embedded 1D space. The distance is positive if the point 'p' is in the half space which is determined by the positive part of the added coordinate to create positive oriented 2D coordinate system, eg. the same half space as the normal vector points to.

DistanceT Distance(const Point2dC & p) const

Returns the orthogonal distance between the point 'p' and the embedded 1D space.

Point2dC operator()(const OrthoProjection2to1dC::Coor1DT & p) const