MbPlacement3D Class Reference

Local coordinate system in three dimensional space. More...

#include <mb_placement3d.h>

Collaboration diagram for MbPlacement3D:

Public Member Functions
MbPlacement3D &	Init ()
	Initialize identity matrix of a direct transformation (the global coordinate system).
MbPlacement3D &	Init (const MbPlacement3D &)
	Initialize by a placement.
MbPlacement3D &	Init (const MbMatrix3D &matr)
	Initialize by a matrix.
void	Init (const MbCartPoint3D &initOrigin, const MbVector3D &initAxisZ)
	Initialize by point and vector (Z-axis) with arbitrary X-axis.
MbPlacement3D &	Init (const MbCartPoint3D &p, const MbVector3D &axisZ, const MbVector3D &axisX, bool left=false)
	Initialize by the origin and vectors of X and Z axes.
MbPlacement3D &	Init (const MbCartPoint3D &p, const MbCartPoint3D &axisX, const MbCartPoint3D &axisY, bool left=false)
	Initialize by the origin and points of X and Y axes.
MbPlacement3D &	Init (const MbCartPoint3D &p, const MbVector3D &axisZ, bool left)
	Initialize by Z-axis and arbitrary X-axis.
MbPlacement3D &	Init (const MbPlacement3D &pl, double distance)
	Initialize by placement with a shift.
MbPlacement3D &	Init (const MbCartPoint3D &p, const MbPlacement3D &pl)
	Initialize by origin and orienting placement.
MbPlacement3D &	Init (const MbCartPoint3D &org)
	Initialize by origin.
MbPlacement3D &	InitXY (const MbCartPoint3D &p, const MbVector3D &axisX, const MbVector3D &axisY, bool reset)
	Initialize by a point and two vectors (X and Y axes).
MbPlacement3D &	InitXZ (const MbCartPoint3D &p, const MbVector3D &axisX, const MbVector3D &axisZ)
	Initialize by a point and two vectors (X and Z axes).
MbPlacement3D &	InitYZ (const MbCartPoint3D &p, const MbVector3D &axisY, const MbVector3D &axisZ)
	Initialize by a point and two vectors (Y and Z axes).
bool	Init (const MbPlacement3D &pl, double ang, const MbCurve3D &c, double t)
	Initialize by curve and angle to plane.
bool	Init (const MbCartPoint3D &p, const MbCurve3D &c, double t)
	Initialize by point and curve.
bool	Init (const MbCurve3D &, const MbCartPoint3D &, bool checkPlanar)
	Initialize by point, perpendicularly to curve.
bool	Init (const MbLine3D &, const MbCartPoint3D &)
	Initialize by a line and a point.
bool	Init (const MbLine3D &, const MbVector3D &)
	Initialize by a line and a vector.
bool	Init (const MbLine3D &l1, const MbLine3D &l2)
	Initialize by two lines.
bool	Init (const MbCurve3D &, double t, bool checkPlanar)
	Initialize perpendicularly to a curve by a parameter on the curve.
void	Update (const MbPlacement3D &, VERSION version, bool fuzzy_null=true)
	Bind placement to another coordinates.
void	Update (const MbPlacement3D &, const MbPlacement3D &)
	Bind placement to another coordinates.
void	UpdateFromNull (VERSION version, bool fuzzy_null=true)
	Bind placement to the local zero.
bool	IsSingle () const
	Check coincidence with the global coordinate system (i.e. the direct matrix of a coordinate system is unit).
bool	IsTranslation () const
	Check if a coordinate system is translated relative to the global coordinate system.
bool	IsRotation () const
	Check if the coordinate system is rotated relative to the global coordinate system.
bool	IsLeft () const
	Check if a coordinate system is left.
bool	IsRight () const
	Check if a coordinate system is right.
bool	IsOrt () const
	Check if a coordinate system is orthogonal, but not normalized.
bool	IsOrthogonal () const
	Get orthogonality property of coordinate system.
bool	IsAffine () const
	Check if a coordinate system is affine (otherwise it is orthonormalized).
bool	IsNormal () const
	Check if coordinate system is orthonormalized.
bool	IsUnSet () const
	Check whether bit flags are not set.
bool	IsUnit (double eps=Math::lengthEpsilon) const
	Get attribute of the unit placement.
bool	IsUnit (double &sqX, double &sqY, double &sqZ, double eps=Math::lengthEpsilon) const
	Get attribute of unit placement and squares of orts.
bool	IsTranslationStandard () const
	Check if the axes of a coordinate system are coincident to the standard one (right orthonormalized coordinate system).
bool	IsCircular () const
	Check if a coordinate system is orthogonal with axes X and Y of equal length (circle moves to circle).
bool	IsCircular (double &lxy) const
	Check if a coordinate system is orthogonal with axes X and Y of equal length (circle moves to circle).
bool	IsIsotropic () const
	Check if a coordinate system is orthogonal with axes X and Y of equal length.
bool	IsIsotropic (double &l) const
	Check if a coordinate system is orthogonal with axes X and Y of equal length.
const MbCartPoint3D &	GetOrigin () const
	Get the origin of a coordinate system.
const MbVector3D &	GetAxisZ () const
	Get the Z-axis.
const MbVector3D &	GetAxisX () const
	Get the X-axis.
const MbVector3D &	GetAxisY () const
	Get the Y-axis.
MbCartPoint3D &	SetOrigin ()
	Get the origin of a local coordinate system.
MbVector3D &	SetAxisZ ()
	Get the Z-axis.
MbVector3D &	SetAxisX ()
	Get the X-axis.
MbVector3D &	SetAxisY ()
	Get the Y-axis.
void	SetOrigin (const MbCartPoint3D &o)
	Set the origin of a local coordinate system.
void	SetAxisZ (const MbVector3D &a)
	Set the Z-axis.
void	SetAxisX (const MbVector3D &a)
	Set the X-axis.
void	SetAxisY (const MbVector3D &a)
	Set the Y-axis.
void	AxisZInvert ()
	Invert the Z-axis.
void	AxisXInvert ()
	Invert the X-axis.
void	AxisYInvert ()
	Invert the Y-axis.
void	SetFlag (bool bLeft, bool bAffine=false, bool bOrt=true) const
	Set the flag of state.
void	SetRight ()
	Set the coordinate system as right.
MbPlacement3D &	Transform (const MbMatrix3D &)
	Transform according to the matrix.
MbPlacement3D &	Move (const MbVector3D &)
	Translate along a vector.
MbPlacement3D &	Rotate (const MbAxis3D &axis, double angle)
	Rotate at a given angle around an axis.
MbPlacement3D &	Scale (double sx, double sy, double sz)
	Scale.
MbPlacement3D &	Scale (double s)
	Scale.
bool	IsSame (const MbPlacement3D &other, double accuracy) const
	Determine whether an object is equal?
void	GetMatrixInto (MbMatrix3D &) const
	Get the matrix of transformation to the local coordinate system: r=R*into (inverse matrix).
MbMatrix3D	GetMatrixInto () const
	Get the matrix of transformation to the local coordinate system: r=R*into (inverse matrix).
void	GetMatrixFrom (MbMatrix3D &) const
	Get the matrix of transformation from the local coordinate system: R=r*from (direct matrix).
MbMatrix3D	GetMatrixFrom () const
	Get the matrix of transformation from the local coordinate system: R=r*from (direct matrix).
void	Symmetry (MbMatrix3D &) const
	Get the matrix of symmetry with respect to the XY-plane.
bool	GetMatrixToPlace (const MbPlacement3D &p, MbMatrix &matr, double eps=Math::angleRegion) const
	Get the matrix of transformation to place.
void	GetMatrixToPlace (const MbPlacement3D &p, MbMatrix3D &matr) const
	Get the matrix of transformation to place.
double	DistanceToPoint (const MbCartPoint3D &to) const
	Calculate the distance to a point.
void	PointProjection (const MbCartPoint3D &p, MbCartPoint3D &pOn) const
	Find point projection to XY-plane.
void	VectorProjection (const MbVector3D &v, double &x, double &y) const
	Find the vector of projection to XY-plane.
void	PointProjection (const MbCartPoint3D &p, double &x, double &y) const
	Find the point projection to XY-plane.
bool	DirectPointProjection (const MbCartPoint3D &p, const MbVector3D &v, double &x, double &y) const
	Find the point projection to XY-plane along a vector in either of two directions.
bool	NearDirectPointProjection (const MbCartPoint3D &p, const MbVector3D &v, double &x, double &y, bool onlyPositiveDirection) const
	Find the point projection to XY-plane in direction of the vector.
void	PointOn (double x, double y, MbCartPoint3D &p) const
	Get the projection of a point on XY-plane.
void	PointOn (const MbCartPoint &r, MbCartPoint3D &p) const
	Get the space point by a point on XY-plane.
void	VectorOn (const MbVector &r, MbVector3D &p) const
	Get the space vector by a vector on XY-plane.
void	VectorOn (const MbDirection &r, MbVector3D &p) const
	Get the space vector by a vector on XY-plane.
void	Normal (MbVector3D &n) const
	Get the normal of the plane XY of a local coordinate system, the Z axis is not taken into account here.
MbVector3D	Normal () const
	Get the normal of the plane XY of a local coordinate system, the Z axis is not taken into account here.
MbeItemLocation	PointRelative (const MbCartPoint3D &pnt, double eps=ANGLE_REGION) const
	Get point location relative to the plane.
MbeItemLocation	CubeRelative (const MbCube &cube, double eps=ANGLE_REGION) const
	Get bounding box location relative to the plane.
bool	Colinear (const MbPlacement3D &with, double eps=Math::angleRegion) const
	Check collinearity.
bool	NormalColinear (const MbPlacement3D &with, double eps=Math::angleRegion) const
	Check collinearity of normals.
bool	Complanar (const MbPlacement3D &with, double eps=Math::angleRegion) const
	Check complanarity.
bool	Orthogonal (const MbAxis3D &, double &x, double &y, double eps=Math::angleRegion) const
	Check orthogonality.
void	AdaptToPlace (const MbPlacement3D &)
	Match with the place by rotation till the parallelism and translation along place normal.
double	Angle (const MbVector3D &v) const
	Angle to Z-axis.
double	Angle (const MbPlacement3D &) const
	Angle between Z-axes of the placements.
double	GetNormalAngle (const MbVector3D &) const
	Get the sine of angle between a vector and the plane.
void	Reset ()
	Recalculate the coordinate system for changed internal data.
void	Invert (MbMatrix *=nullptr)
	Invert.
bool	LineIntersectionPoint (const MbCartPoint3D &origin, const MbVector3D &direction, MbCartPoint3D &p, double &d, double eps=ANGLE_EPSILON) const
	Find the nearest point of intersection with line. More...
bool	PlanesIntersection (const MbPlacement3D &place, MbCartPoint3D &p, MbVector3D &axis, double eps=ANGLE_EPSILON) const
	Get the point and direction of planes intersection line.
MbeNewtonResult	CurveIntersectNewton (const MbCurve3D &curve, bool ext, double funcEpsilon, size_t iterLimit, double &u, double &v, double &t) const
	Intersection plane XY with a curve.
MbeNewtonResult	NearestPoints (const MbCurve3D &curve, bool ext, double &u0, double &v0, double &t0, double &dmin, bool tCalc) const
	Calculate parameters of the nearest points of surface and curve.
void	TransformPoint (const MbMatrix3D &, MbCartPoint &) const
	Transform 2D-point to another 2D-point.
double	GetXEpsilon () const
	Give the minimum distinguishable value of U parameter.
double	GetYEpsilon () const
	Get the minimum distinguishable value of V parameter.
bool	SetRoundedValue (bool total, double eps)
	Round.
bool	operator== (const MbPlacement3D &) const
	Check for equality.
bool	operator!= (const MbPlacement3D &) const
	Check for inequality.
void	operator= (const MbPlacement3D &)
	Assign another coordinate system.
MbPlacement3D	operator* (const MbPlacement3D &p) const
	Multiply by a local coordinate system: P = this * p (as of matrix multiplication).
void	Normalize ()
	Orthogonalize and normalize axes of a local coordinate system.
bool	IsShift (const MbPlacement3D &, MbVector3D &, bool &isSame, double accuracy=LENGTH_EPSILON) const
	Check if the object is a translation.
bool	IsShiftZ (const MbPlacement3D &other, MbVector3D &vect, double accuracy) const
	Check if the object is a shift of the current one along axis Z?
bool	IsDegenerate (double lenEps=Math::metricRegion, double angEps=Math::angleRegion) const
	Check for degeneracy.
void	GetPointFrom (double x0, double y0, double z0, MbCartPoint3D &p, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Get the point in the global coordinate system by local coordinates.
void	GetVectorFrom (double x1, double y1, double z1, MbVector3D &v, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Get the vector in the global coordinate system by local coordinates.
void	GetPointFrom (MbCartPoint3D &p, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a point from a local coordinate system to the global coordinate system.
void	GetVectorFrom (MbVector3D &v, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a vector from a local coordinate system to the global coordinate system.
void	GetPointInto (MbCartPoint3D &p, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a point from the global coordinate system to a local coordinate system.
void	GetVectorInto (MbVector3D &v, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a vector from the global coordinate system to a local coordinate system.
void	GetPointAndDerivesFrom (MbCartPoint3D &point, MbVector3D &firstDer, MbVector3D &secondDer, MbVector3D &thirdDer, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a point and the first three derivatives from a local coordinate system to the global coordinate system.
void	GetPointAndDerivesInto (MbCartPoint3D &point, MbVector3D &firstDer, MbVector3D &secondDer, MbVector3D &thirdDer, MbeLocalSystemType3D type=ls_CartesianSystem) const
	Transform a point and the first three derivatives from the global coordinate system to a local coordinate system.
void	GetProperties (MbProperties &)
	Get properties of the object.
void	SetProperties (const MbProperties &)
	Set properties of the object.
The constructors.
	MbPlacement3D ()
	Default constructor.
	MbPlacement3D (const MbCartPoint3D &org)
	Constructor by point.
	MbPlacement3D (const MbVector3D &axisX, const MbVector3D &axisY, const MbCartPoint3D &org)
	Constructor by point and two vectors.
	MbPlacement3D (const MbPlacement3D &place)
	Copy-constructor.
	MbPlacement3D (const MbMatrix3D &matr)
	Constructor by matrix.
	MbPlacement3D (const MbCartPoint3D &org, const MbVector3D &axisZ, const MbVector3D &axisX, bool l=false)
	Constructor by point and two vectors.
	MbPlacement3D (const MbCartPoint3D &org, const MbCartPoint3D &px, const MbCartPoint3D &py, bool l=false)
	Constructor by three points.
	MbPlacement3D (const MbCartPoint3D &org, const MbVector3D &axisZ, bool l=false)
	Constructor by point and vector (Z-axis) with arbitrary X-axis.

Static Public Attributes
static const MbPlacement3D	global
	A constant of the global coordinate system.

Detailed Description

Local coordinate system in three dimensional space.

Local coordinate system in three dimensional space.
Local coordinate system is described by the initial point and three non-parallel vectors. In most cases the system of coordinates is right, and vectors of system are orthonormalized. A coordinate system can become left and not orthonormalized via transformations. Local coordinate system is Cartesian. A point is defined by three coordinates x, y, z in the Cartesian coordinate system.
A local coordinate system may act both as a cylindrical or a sphricial coordinate system.
A point in a cylindrical coordinate system is defined by three coordinates r, f, z:
r, f - polar coordinates of point projection to the main plane;
r - length of radius-vector projection;
f - polar angle of radius-vector projection;
z - z-axis (the distance from point to the main plane).
When a local coordinate system is used as a cylindrical coordinate system, it is considered that:
the origin of a cylindrical coordinate system is coincident to the origin of Cartesian coordinate system;
Oz-axis of a cylindrical coordinate system is coincident to Oz-axis of the Cartesian coordinate system;
the main plane of a cylindrical coordinate system is coincident to Oxy-plane of the Cartesian coordinate system;
the polar axis of a cylindrical coordinate system is coincident to Ox-axis of the Cartesian coordinate system;
the polar angle f of a cylindrical coordinate system is counted from Ox-axis to the positive direction of Oy-axis.
A point in a spherical coordinate system is defined by three coordinates r, f, w:
r - distance from the origin to a point (length of radius-vector);
f - the angle between radius-vector projection to the plane and a ray on the plane (longitude);
w - the angle between radius-vector and the normal of spherical coordinate system plane (polar distance).
When a local coordinate system is used as a spherical coordinate system, it is considered that:
the origin of a spherical coordinate system is coincident to the origin of the Cartesian coordinate system;
the ray perpendicular to the plane of a spherical coordinate system is coincident to Oz-axis of the Cartesian coordinate system;
the plane of a spherical coordinate system is coincident to Oxy-plane of the Cartesian coordinate system;
the angle f of a spherical coordinate system is counted from Ox-axis to the positive direction of Oy-axis.
To speed up transformation of coordinates the local coordinate system has additional data - flag of state.
Use Get... methods to obtain data of a coordinate system from the outside.
To modify data of a coordinate system from the outside use Set... methods that automatically reset the flag of the system to the unspecified state.

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The documentation for this class was generated from the following file:

• mb_placement3d.h