Description

The Plane class stores an oriented plane in 3D.

The plane is defined by its (unit) normal vector and parameter d, which is the signed distance of the plane from the origin of the coordinate system.

The following holds for all points on the plane:

normal % point + d = 0

The plane parameters are accessed via public data members, normal and d.

If the plane is invalid (cannot be constructed), the plane normal is set to a null vector.

#include <Plane.h>

Public Member Functions
	Plane ()

	Plane (const Vector3d &nn, double dd)

	Plane (const UnitVector3d &nn, double dd)

	Plane (const Point3d &, const UnitVector3d &)

	Plane (const Point3d &, const Vector3d &)
	< More...

	Plane (const Point3d &, const Point3d &, const Point3d &)

	Plane (const Point3d &, const Vector3d &, const Vector3d &)

	Plane (const Point3d plg[], size_t n)
	Create plane from a polygon of vertices (n >=3). More...

	Plane (const Point3d plg[], size_t n, const Vector3d &normal)
	The plane normal is given, just calculate the 'd' parameter from all polygon vertices. More...

Plane	operator- () const

double	dist (const Point3d &p) const

Point3d	project (const Point3d &) const

Vector3d	project (const Vector3d &) const

Line3d	project (const Line3d &) const

Line3d	operator* (const Plane &) const

Point3d	operator* (const Line3d &) const

void	OffsetByDistance (double dDist)
	Offset the Plane by the given distance. More...

bool	intersectsInPoint (const Line3d &l, Point3d &pt, double &dParam) const
	Returns true if the plane and line intersect in a single point. More...

bool	intersectsInLine (const Plane &pl, Line3d &line) const
	Returns true if the planes intersect in a line. Returns the line if true. More...

bool	isValid () const

bool	isEqual (const Plane &, double dDistTol=WSM_DISTANCE_TOL, double dAngleTol2=WSM_ANGLE_TOL2) const
	isEqual function. More...

bool	isEquivalent (const Plane &, double dDistTol=WSM_DISTANCE_TOL, double dAngleTol2=WSM_ANGLE_TOL2) const
	Returns true if geometrically the planes with possibly reversed normals. More...

Plane &	negate ()

bool	pointIntersectsNegativeSide (const Point3d &pt, double dTol=WSM_MACHINE_TOL) const
	Returns true if pt lies on the Plane or the negative side of the Plane. More...

bool	boxIntersectsNegativeSide (const Interval3d &box, double dTol=WSM_MACHINE_TOL) const
	Returns true if box intersects the negative side of the Plane. More...

bool	boxLiesOnNegativeSide (const Interval3d &box, double dTol=WSM_MACHINE_TOL) const
	Returns true if box lies on the negative side of the Plane. More...

void	operator*= (const Transf3d &)

Static Public Member Functions
static Plane	fromPoints (const Point3d pts[], size_t pointCount, bool checkPlanarity)
	Create a plane from the given set of coplanar points. More...

static Plane	fromPointsUsingThreeNoncollinearPnts (const Point3d pts[], size_t pointCount, bool bCheckPlanarity, int &resultStatus, double dTol=WSM_MACHINE_TOL, bool bTryAgain=false)
	Create a plane from the first three non-collinear points. More...

Public Attributes
UnitVector3d	normal
	Public data members. More...

double	d

Constructor & Destructor Documentation

WSM::Plane::Plane ( )

WSM::Plane::Plane	(	const Vector3d &	nn,
		double	dd
	)

inline

WSM::Plane::Plane	(	const UnitVector3d &	nn,
		double	dd
	)

inline

WSM::Plane::Plane	(	const Point3d &	p,
		const UnitVector3d &	norm
	)

inline

WSM::Plane::Plane	(	const Point3d &	p,
		const Vector3d &	norm
	)

inline

<

WSM::Plane::Plane	(	const Point3d &	,
		const Point3d &	,
		const Point3d &
	)

WSM::Plane::Plane	(	const Point3d &	,
		const Vector3d &	,
		const Vector3d &
	)

WSM::Plane::Plane	(	const Point3d	plg[],
		size_t	n
	)

Create plane from a polygon of vertices (n >=3).

All polygon vertices are used to calculate the plane coefficients to make the formula symmetrical.

WSM::Plane::Plane	(	const Point3d	plg[],
		size_t	n,
		const Vector3d &	normal
	)

The plane normal is given, just calculate the 'd' parameter from all polygon vertices.

Member Function Documentation

bool WSM::Plane::boxIntersectsNegativeSide	(	const Interval3d &	box,
		double	dTol = `WSM_MACHINE_TOL`
	)		const

Returns true if box intersects the negative side of the Plane.

bool WSM::Plane::boxLiesOnNegativeSide	(	const Interval3d &	box,
		double	dTol = `WSM_MACHINE_TOL`
	)		const

Returns true if box lies on the negative side of the Plane.

double WSM::Plane::dist ( const Point3d & p ) const

inline

static Plane WSM::Plane::fromPoints	(	const Point3d	pts[],
		size_t	pointCount,
		bool	checkPlanarity
	)

static

Create a plane from the given set of coplanar points.

Returns a null plane if the points do not define a plane. Unlike the Plane constructor that takes a closed polygon, the set of points here is just any set of points and the method tries to do some kind of a best fit plane from them

static Plane WSM::Plane::fromPointsUsingThreeNoncollinearPnts	(	const Point3d	pts[],
		size_t	pointCount,
		bool	bCheckPlanarity,
		int &	resultStatus,
		double	dTol = `WSM_MACHINE_TOL`,
		bool	bTryAgain = `false`
	)

static

Create a plane from the first three non-collinear points.

resultStatus: can be 0, -1, -2. 0: succeeds to find the plane constructed by three non-collinear points;-1: fails to find 3 non-collinear points; -2: fails to satisfy the planarity. dTol is the tolerance use to check if the points are collinear and planar. If bTryAgain is true, on failure tries again using points more optimal then the first three non-collinear points.

bool WSM::Plane::intersectsInLine	(	const Plane &	pl,
		Line3d &	line
	)		const

Returns true if the planes intersect in a line. Returns the line if true.

bool WSM::Plane::intersectsInPoint	(	const Line3d &	l,
		Point3d &	pt,
		double &	dParam
	)		const

Returns true if the plane and line intersect in a single point.

Returns the parameter of intersection if true. Note when the l and the Plane are coincident, the origin point of l is returned. Do we need to add a version that is strict and fails in the case of coincidence?

bool WSM::Plane::isEqual	(	const Plane &	pla,
		double	dDistTol = `WSM_DISTANCE_TOL`,
		double	dAngleTol2 = `WSM_ANGLE_TOL2`
	)		const

inline

isEqual function.

Note dAngleTol2 relates to the angle between the normals by 2 - 2 cos(angle) = dAngleTol2. So angle = arccos(1 - dAngleTol2 / 2). The default dAngleTol2 = WSM_ANGLE_TOL2 means equal normals differ by an angle of no more than 5.7295e-9 degrees.

Parameters

[in]	dDistTol
[in]	dAngleTol2

bool WSM::Plane::isEquivalent	(	const Plane &	pla,
		double	dDistTol = `WSM_DISTANCE_TOL`,
		double	dAngleTol2 = `WSM_ANGLE_TOL2`
	)		const

inline

Returns true if geometrically the planes with possibly reversed normals.

isEquivalent function.

Parameters

[in]	dTol
[in]	dAngleTol2
[in]	dDistTol

bool WSM::Plane::isValid ( ) const

inline

Plane& WSM::Plane::negate ( )

inline

void WSM::Plane::OffsetByDistance ( double dDist )

inline

Offset the Plane by the given distance.

Line3d WSM::Plane::operator* ( const Plane & ) const

Point3d WSM::Plane::operator* ( const Line3d & ) const

void WSM::Plane::operator*= ( const Transf3d & )

Plane WSM::Plane::operator- ( ) const

inline

bool WSM::Plane::pointIntersectsNegativeSide	(	const Point3d &	pt,
		double	dTol = `WSM_MACHINE_TOL`
	)		const

Returns true if pt lies on the Plane or the negative side of the Plane.

Point3d WSM::Plane::project ( const Point3d & ) const

Vector3d WSM::Plane::project ( const Vector3d & ) const

Line3d WSM::Plane::project ( const Line3d & ) const

Member Data Documentation

double WSM::Plane::d

UnitVector3d WSM::Plane::normal

Public data members.

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

WSM/Plane.h

Description

Public Member Functions

Static Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation