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OrthoProjection3to2dC::OrthoProjection3to2dC(void) OrthoProjection3to2dC::OrthoProjection3to2dC(const Point3dC &,const Point3dC &,const Point3dC &) OrthoProjection3to2dC::OrthoProjection3to2dC(const Point3dC &,const Vector3dC &,const Vector3dC &) OrthoProjection3to2dC::OrthoProjection3to2dC(const OrthoProjection3to2dC &) OrthoProjection3to2dC::operator()(const Point3dC &) const OrthoProjection3to2dC::operator[](const Point3dC &) const OrthoProjection3to2dC::operator()(const Point2dC &) const OrthoProjection3to2dC::T(const Point3dC &) const OrthoProjection3to2dC::ODistance(const Point3dC &) const OrthoProjection3to2dC::Normal(void) const OrthoProjection3to2dC::Distance(const Point3dC &) const

OrthoProjection3to2dC
Orthogonal projection between 2D and 3D spaces
include	"amma/OProj2a3.hh"
User Level:	Default
Library:	Mpm123
Example:	exMat2d.cc
Section:	Geometry.Transforms
In Scope:	std

Comments:
The class OrthoProjection3to2dC represents orthogonal projection from 3D space into the 2D space. The class is optimized to perform projections quickly.

TriOrthoC

typedef RealT DistanceT;

Distance.

OrthoProjection3to2dC()

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

OrthoProjection3to2dC(const Point3dC & origin,const Point3dC & xPoint,const Point3dC & xyPoint)

The projection mapping will project 3D points into 2D points belonging to the embedded 2D space (plane). The embedded plane is defined in 3D space by the origin point, by the point 'xPoint' belonging to the positive half of the x coordinate of the embedded plane, and another arbitrary point different from the 'origin' and 'xPoint' lying in the positive y coordinate half space of the plane.

OrthoProjection3to2dC(const Point3dC & origin,const Vector3dC & xDirection,const Vector3dC & xyDirection)

The projection mapping will project 3D points into 2D points belonging to the embedded 2D space (plane). The embedded plane is defined in 3D space by the origin point, by the vector 'xDirection' defining the positive direction of the x coordinate of the embedded plane, and another vector 'xyDirection' different from zero vector and the vector 'xDirection' pointing into the positive y coordinate half space of the plane.

OrthoProjection3to2dC(const OrthoProjection3to2dC & p)

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

Point2dC operator()(const Point3dC & p) const

Returns the coordinate of the orthogonal projection of the 3D point 'p'. The returned point coordinates are expressed in the coordinate system of the 2D space (plane).

Point3dC operator[](const Point3dC & p) const

Returns the coordinates of the orthogonal projection of the 3D point 'p'. The returned point coordinates are expressed in the coordinate system of the 3D space.

Point3dC operator()(const Point2dC & p) const

Returns the 3D coordinates of the point 'p' belonging to the embedded 2D space. Coordinate system relationships. --------------------------------

Point3dC T(const Point3dC & p) const

The embedded 2D space coordinate system is added another coordinate to create the positive oriented 3D coordinate system A. The coordinates of the point 'p' are transformed into the coordinate system A and returned.

DistanceT ODistance(const Point3dC & p) const

Returns the oriented orthogonal distance between the point 'p' and the embedded 2D 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.

Vector3dC Normal() const

Returns the unit normal vector of the embedded 2D space. The normal vector with the coordinate system of the embedded 2D space defines the positively oriented 3D coordinate system.

DistanceT Distance(const Point3dC & p) const

Returns the orthogonal distance between the point 'p' and the embedded 2D space.