#include <opennurbs_point.h>

Public Member Functions
	ON_PlaneEquation ()

	ON_PlaneEquation (double xx, double yy, double zz, double dd)

ON_3dPoint	ClosestPointTo (ON_3dPoint point) const

bool	Create (ON_3dPoint P, ON_3dVector N)

ON_3dVector	Direction () const

double	DirectionLength () const

void	Dump (class ON_TextLog &) const

bool	IsNearerThan (const class ON_BezierCurve &bezcrv, double s0, double s1, int sample_count, double endpoint_tolerance, double interior_tolerance, double smin, double smax) const

int	IsParallelTo (const ON_PlaneEquation &other, double angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE) const

bool	IsSet () const

bool	IsUnitized () const

bool	IsValid () const

double	MaximumAbsoluteValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const

double	MaximumCoefficient () const

double	MaximumValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const

double	MaximumValueAt (const class ON_CurveLeafBox &crvleafbox) const

double	MaximumValueAt (const class ON_SurfaceLeafBox &srfleafbox) const

double	MaximumValueAt (const ON_BoundingBox &bbox) const

double	MinimumValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const

double	MinimumValueAt (const class ON_CurveLeafBox &crvleafbox) const

double	MinimumValueAt (const class ON_SurfaceLeafBox &srfleafbox) const

double	MinimumValueAt (const ON_BoundingBox &bbox) const

ON_PlaneEquation	NegatedPlaneEquation () const

bool	operator!= (const ON_PlaneEquation &) const

bool	operator== (const ON_PlaneEquation &) const

double &	operator[] (int)

double	operator[] (int) const

double &	operator[] (unsigned int)

double	operator[] (unsigned int) const

bool	Transform (const ON_Xform &xform)

ON_PlaneEquation	UnitizedPlaneEquation () const

ON_3dVector	UnitNormal () const

double	ValueAt (double x, double y, double z) const

double *	ValueAt (int Pcount, const ON_3dPoint P, double value, double value_range[2]) const

double *	ValueAt (int Pcount, const ON_3fPoint P, double value, double value_range[2]) const

double	ValueAt (ON_3dPoint P) const

double	ValueAt (ON_3dVector P) const

double	ValueAt (ON_4dPoint P) const

ON_Interval	ValueRange (const class ON_3dPointListRef &point_list) const

ON_Interval	ValueRange (const ON_SimpleArray< ON_3dPoint > &point_list) const

ON_Interval	ValueRange (const ON_SimpleArray< ON_3fPoint > &point_list) const

ON_Interval	ValueRange (size_t point_index_count, const unsigned int *point_index_list, const class ON_3dPointListRef &point_list) const

ON_Interval	ValueRange (size_t point_index_count, size_t point_index_stride, const unsigned int *point_index_list, const class ON_3dPointListRef &point_list) const

ON_Interval	ValueRange (size_t point_list_count, const ON_3dPoint *point_list) const

ON_Interval	ValueRange (size_t point_list_count, const ON_3fPoint *point_list) const

double	ZeroTolerance () const

Static Public Member Functions
static const ON_PlaneEquation	CreateFromPointAndNormal (ON_3dPoint point, ON_3dVector normal)

static const ON_PlaneEquation	CreateFromThreePoints (ON_3dPoint pointA, ON_3dPoint pointB, ON_3dPoint pointC)

static void	Set (ON_PlaneEquation &plane_equation, double x, double y, double z, double d)

Public Attributes
double	d
	4th coefficient of the plane equation. More...

double	x

double	y

double	z

Static Public Attributes
static const ON_PlaneEquation	NanPlaneEquation
	(ON_DBL_QNAN,ON_DBL_QNAN,ON_DBL_QNAN,ON_DBL_QNAN) More...

static const ON_PlaneEquation	UnsetPlaneEquation
	(ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE) More...

static const ON_PlaneEquation	WorldXY
	(0,0,1,0) More...

static const ON_PlaneEquation	WorldYZ
	(1,0,0,0) More...

static const ON_PlaneEquation	WorldZX
	(0,1,0,0) More...

static const ON_PlaneEquation	ZeroPlaneEquation
	(0.0,0.0,0.0,0.0) More...

Detailed Description

Description: Typically the vector portion is a unit vector and m_d = -(x*P.x + y*P.y + z*P.z) for a point P on the plane.

Constructor & Destructor Documentation

◆ ON_PlaneEquation() [1/2]

ON_PlaneEquation::ON_PlaneEquation ( )

◆ ON_PlaneEquation() [2/2]

ON_PlaneEquation::ON_PlaneEquation	(	double	xx,
		double	yy,
		double	zz,
		double	dd
	)

Member Function Documentation

◆ ClosestPointTo()

ON_3dPoint ON_PlaneEquation::ClosestPointTo ( ON_3dPoint point ) const

Description: Get point on plane that is closest to a given point. Parameters: point - [in] Returns: A 3d point on the plane that is closest to the input point.

◆ Create()

bool ON_PlaneEquation::Create	(	ON_3dPoint	P,
		ON_3dVector	N
	)

Description: Sets (x,y,z) to a unitized N and then sets d = -(x*P.x + y*P.y + z*P.z). Parameters: P - [in] point on the plane N - [in] vector perpendicular to the plane Returns: true if input is valid.

◆ CreateFromPointAndNormal()

static const ON_PlaneEquation ON_PlaneEquation::CreateFromPointAndNormal	(	ON_3dPoint	point,
		ON_3dVector	normal
	)

static

Returns: If point is valid and normal is nonzero, a unitized plane equation is returned. Otherwise ON_PlaneEquation::NanPlaneEquation is returned.

◆ CreateFromThreePoints()

static const ON_PlaneEquation ON_PlaneEquation::CreateFromThreePoints	(	ON_3dPoint	pointA,
		ON_3dPoint	pointB,
		ON_3dPoint	pointC
	)

static

Returns: If the three points are valid and not collinear, a unitized plane equation is returned. Otherwise ON_PlaneEquation::NanPlaneEquation is returned.

◆ Direction()

ON_3dVector ON_PlaneEquation::Direction ( ) const

Returns: Direction (x,y,z)

◆ DirectionLength()

double ON_PlaneEquation::DirectionLength ( ) const

◆ Dump()

void ON_PlaneEquation::Dump ( class ON_TextLog & ) const

◆ IsNearerThan()

bool ON_PlaneEquation::IsNearerThan	(	const class ON_BezierCurve &	bezcrv,
		double	s0,
		double	s1,
		int	sample_count,
		double	endpoint_tolerance,
		double	interior_tolerance,
		double *	smin,
		double *	smax
	)		const

Description: Test points on a bezier curve to see if they are near the plane. Parameters: bezcrv - [in] s0 - [in] s1 - [in] the interval from s0 to s1 is tested (s0 < s1) sample_count - [in] number of interior points to test.
Numbers like 1, 3, 7, 15, ... work best. endpoint_tolerance - [in] If >= 0, then the end points are tested to see if the distance from the endpoints is <= endpoint_tolerance. interior_tolerance - [in] (>=0 and >=endpoint_tolerance) This tolerance is used to test the interior sample points. smin - [put] If not nullptr, *smin = bezier parameter of nearest test point. smax - [put] If not nullptr, *smax = bezier parameter of farthest test point. If false is returned, this is the parameter of the test point that failed. Returns: True if all the tested points passed the tolerance test. False if at least one tested point failed the tolerance test. (The test terminates when the first failure is encountered.)

◆ IsParallelTo()

int ON_PlaneEquation::IsParallelTo	(	const ON_PlaneEquation &	other,
		double	angle_tolerance = `ON_DEFAULT_ANGLE_TOLERANCE`
	)		const

Returns 1: this and other vectors are parallel -1: this and other vectors are anti-parallel 0: this and other vectors are not parallel or at least one of the vectors is zero

Parameters

other	other plane equation
angle_tolerance	optional angle tolerance (radians)

◆ IsSet()

bool ON_PlaneEquation::IsSet ( ) const

Description: returns true if x, y, z, d are valid, finite doubles and at least one of x, y or z is not zero.

◆ IsUnitized()

bool ON_PlaneEquation::IsUnitized ( ) const

Description: returns true if x, y, z, d are valid, finite doubles and x^2 + y^2 + z^2 = 1.

◆ IsValid()

bool ON_PlaneEquation::IsValid ( ) const

Description: returns true if x, y, z, d are valid, finite doubles. Remarks: this function will return true if x, y and z are all zero. See Also: ON_PlaneEquation::IsSet().

◆ MaximumAbsoluteValueAt()

double ON_PlaneEquation::MaximumAbsoluteValueAt	(	bool	bRational,
		int	point_count,
		int	point_stride,
		const double *	points,
		double	stop_value
	)		const

Description: Get the maximum absolute value of the plane equation on a set of 3d points. Parameters: bRational - [in] False if the points are euclidean (x,y,z) True if the points are homogeneous rational (x,y,z,w) (x/w,y/w,z/w) is used to evaluate the value. point_count - [in] point_stride - [in] i-th point's x coordinate = points[i*point_stride] points - [in] coordinates of points stop_value - [in] If stop_value >= 0.0, then the evaluation stops if an absolute value > stop_value is found. If stop_value < 0.0 or stop_value is invalid, then stop_value is ignored. Returns: Maximum value of the plane equation on the point list. If the input is not valid, then ON_UNSET_VALUE is returned.

◆ MaximumCoefficient()

double ON_PlaneEquation::MaximumCoefficient ( ) const

◆ MaximumValueAt() [1/4]

double ON_PlaneEquation::MaximumValueAt	(	bool	bRational,
		int	point_count,
		int	point_stride,
		const double *	points,
		double	stop_value
	)		const

Description: Get the maximum value of the plane equation on a set of 3d points. Parameters: bRational - [in] False if the points are euclidean (x,y,z) True if the points are homogeneous rational (x,y,z,w) (x/w,y/w,z/w) is used to evaluate the value. point_count - [in] point_stride - [in] i-th point's x coordinate = points[i*point_stride] points - [in] coordinates of points stop_value - [in] If stop_value is valid and not ON_UNSET_VALUE, then the evaluation stops if a value > stop_value is found. If stop_value = ON_UNSET_VALUE, then stop_value is ignored. Returns: Maximum value of the plane equation on the point list. If the input is not valid, then ON_UNSET_VALUE is returned.

◆ MaximumValueAt() [2/4]

double ON_PlaneEquation::MaximumValueAt ( const class ON_CurveLeafBox & crvleafbox ) const

Description: Get the maximum value of the plane equation on a bounding box. Parameters: crvleafbox - [in] Returns: Maximum value of the plane equation on the curve leaf box.

◆ MaximumValueAt() [3/4]

double ON_PlaneEquation::MaximumValueAt ( const class ON_SurfaceLeafBox & srfleafbox ) const

Description: Get the maximum value of the plane equation on a bounding box. Parameters: bbox - [in] Returns: Maximum value of the plane equation on the bounding box.

◆ MaximumValueAt() [4/4]

double ON_PlaneEquation::MaximumValueAt ( const ON_BoundingBox & bbox ) const

Description: Get the maximum value of the plane equation on a bounding box. Parameters: bbox - [in] Returns: Maximum value of the plane equation on the bounding box.

◆ MinimumValueAt() [1/4]

double ON_PlaneEquation::MinimumValueAt	(	bool	bRational,
		int	point_count,
		int	point_stride,
		const double *	points,
		double	stop_value
	)		const

Description: Get the minimum value of the plane equation on a set of 3d points. Parameters: bRational - [in] False if the points are euclidean (x,y,z) True if the points are homogeneous rational (x,y,z,w) (x/w,y/w,z/w) is used to evaluate the value. point_count - [in] point_stride - [in] i-th point's x coordinate = points[i*point_stride] points - [in] coordinates of points stop_value - [in] If stop_value is valid and not ON_UNSET_VALUE, then the evaluation stops if a value < stop_value is found. If stop_value = ON_UNSET_VALUE, then stop_value is ignored. Returns: Maximum value of the plane equation on the point list. If the input is not valid, then ON_UNSET_VALUE is returned.

◆ MinimumValueAt() [2/4]

double ON_PlaneEquation::MinimumValueAt ( const class ON_CurveLeafBox & crvleafbox ) const

Description: Get the minimum value of the plane equation on a bounding box. Parameters: crvleafbox - [in] Returns: Minimum value of the plane equation on the curve leaf box.

◆ MinimumValueAt() [3/4]

double ON_PlaneEquation::MinimumValueAt ( const class ON_SurfaceLeafBox & srfleafbox ) const

Description: Get the minimum value of the plane equation on a bounding box. Parameters: bbox - [in] Returns: Minimum value of the plane equation on the bounding box.

◆ MinimumValueAt() [4/4]

double ON_PlaneEquation::MinimumValueAt ( const ON_BoundingBox & bbox ) const

Description: Get the minimum value of the plane equation on a bounding box. Parameters: bbox - [in] Returns: Minimum value of the plane equation on the bounding box.

◆ NegatedPlaneEquation()

ON_PlaneEquation ON_PlaneEquation::NegatedPlaneEquation ( ) const

Returns: The plane equation whose coefficient values are the negative of the coefficient values in this, provided the coefficient value is valid. Any invalid coefficient values are copied.

◆ operator!=()

bool ON_PlaneEquation::operator!= ( const ON_PlaneEquation & ) const

◆ operator==()

bool ON_PlaneEquation::operator== ( const ON_PlaneEquation & ) const

◆ operator[]() [1/4]

double& ON_PlaneEquation::operator[] ( int )

index operators mimic double[4] behavior Return null refs or ON_UNSET_VALUE for out-of-range indices

◆ operator[]() [2/4]

double ON_PlaneEquation::operator[] ( int ) const

◆ operator[]() [3/4]

double& ON_PlaneEquation::operator[] ( unsigned int )

◆ operator[]() [4/4]

double ON_PlaneEquation::operator[] ( unsigned int ) const

◆ Set()

static void ON_PlaneEquation::Set	(	ON_PlaneEquation &	plane_equation,
		double	x,
		double	y,
		double	z,
		double	d
	)

static

◆ Transform()

bool ON_PlaneEquation::Transform ( const ON_Xform & xform )

Description: Transform the plane equation so that, if e0 is the initial equation, e1 is transformed equation and P is a point, then e0.ValueAt(P) = e1.ValueAt(xform*P). Parameters: xform - [in] Invertable transformation. Returns: True if the plane equation was successfully transformed. False if xform is not invertable or the equation is not valid. Remarks: This function has to invert xform. If you have apply the same transformation to a bunch of planes, then it will be more efficient to calculate xform's inverse transpose and apply the resulting transformation to the equation's coefficients as if they were 4d point coordinates.

◆ UnitizedPlaneEquation()

ON_PlaneEquation ON_PlaneEquation::UnitizedPlaneEquation ( ) const

Returns: The plane equation whose first three coefficient values are a unit vector.

◆ UnitNormal()

ON_3dVector ON_PlaneEquation::UnitNormal ( ) const

Returns: Unitized direction or zero vector if not set.

◆ ValueAt() [1/6]

double ON_PlaneEquation::ValueAt	(	double	x,
		double	y,
		double	z
	)		const

◆ ValueAt() [2/6]

double* ON_PlaneEquation::ValueAt	(	int	Pcount,
		const ON_3dPoint *	P,
		double *	value,
		double	value_range[2]
	)		const

◆ ValueAt() [3/6]

double* ON_PlaneEquation::ValueAt	(	int	Pcount,
		const ON_3fPoint *	P,
		double *	value,
		double	value_range[2]
	)		const

Description: Evaluate the plane at a list of point values. Parameters: Pcount - [in] number of points P - [in] points value - [in] If not null, value[] must be an array of length at least Pcount. The values will be stored in this array. If null, the an array will be allocated with onmalloc() and returned. value_range - [out] If not null, the range of values will be returned here. Returns: An array of Pcount values. If the input parameter value was null, then the array is allocated on the heap using onmalloc() and the caller is responsible for calling onfree() when finished. If the input is not valid, null is returned.

◆ ValueAt() [4/6]

double ON_PlaneEquation::ValueAt ( ON_3dPoint P ) const

Description: Evaluate the plane at a point. Parameters: P - [in] Returns: x*P.x + y*P.y + z*P.z + d;

◆ ValueAt() [5/6]

double ON_PlaneEquation::ValueAt ( ON_3dVector P ) const

◆ ValueAt() [6/6]

double ON_PlaneEquation::ValueAt ( ON_4dPoint P ) const

◆ ValueRange() [1/7]

ON_Interval ON_PlaneEquation::ValueRange ( const class ON_3dPointListRef & point_list ) const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ValueRange() [2/7]

ON_Interval ON_PlaneEquation::ValueRange ( const ON_SimpleArray< ON_3dPoint > & point_list ) const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ValueRange() [3/7]

ON_Interval ON_PlaneEquation::ValueRange ( const ON_SimpleArray< ON_3fPoint > & point_list ) const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ValueRange() [4/7]

ON_Interval ON_PlaneEquation::ValueRange	(	size_t	point_index_count,
		const unsigned int *	point_index_list,
		const class ON_3dPointListRef &	point_list
	)		const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ValueRange() [5/7]

ON_Interval ON_PlaneEquation::ValueRange	(	size_t	point_index_count,
		size_t	point_index_stride,
		const unsigned int *	point_index_list,
		const class ON_3dPointListRef &	point_list
	)		const

◆ ValueRange() [6/7]

ON_Interval ON_PlaneEquation::ValueRange	(	size_t	point_list_count,
		const ON_3dPoint *	point_list
	)		const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ValueRange() [7/7]

ON_Interval ON_PlaneEquation::ValueRange	(	size_t	point_list_count,
		const ON_3fPoint *	point_list
	)		const

Returns: ON_Interval::EmptyInterval if input is not valid.

◆ ZeroTolerance()

double ON_PlaneEquation::ZeroTolerance ( ) const

Description: This function calculates and evaluates points that would be exactly on the plane if double precision arithmetic were mathematically perfect and returns the largest value of the evaluations.

Member Data Documentation

◆ d

double ON_PlaneEquation::d

4th coefficient of the plane equation.

◆ NanPlaneEquation

const ON_PlaneEquation ON_PlaneEquation::NanPlaneEquation

static

(ON_DBL_QNAN,ON_DBL_QNAN,ON_DBL_QNAN,ON_DBL_QNAN)

◆ UnsetPlaneEquation

const ON_PlaneEquation ON_PlaneEquation::UnsetPlaneEquation

static

(ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE,ON_UNSET_VALUE)

C++ defaults for construction, destruction, copies, and operator= work fine.

◆ WorldXY

const ON_PlaneEquation ON_PlaneEquation::WorldXY

static

(0,0,1,0)

◆ WorldYZ

const ON_PlaneEquation ON_PlaneEquation::WorldYZ

static

(1,0,0,0)

◆ WorldZX

const ON_PlaneEquation ON_PlaneEquation::WorldZX

static

(0,1,0,0)

◆ x

double ON_PlaneEquation::x

◆ y

double ON_PlaneEquation::y

◆ z

double ON_PlaneEquation::z

◆ ZeroPlaneEquation

const ON_PlaneEquation ON_PlaneEquation::ZeroPlaneEquation

static

(0.0,0.0,0.0,0.0)

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ON_PlaneEquation() [1/2]

◆ ON_PlaneEquation() [2/2]

Member Function Documentation

◆ ClosestPointTo()

◆ Create()

◆ CreateFromPointAndNormal()

◆ CreateFromThreePoints()

◆ Direction()

◆ DirectionLength()

◆ Dump()

◆ IsNearerThan()

◆ IsParallelTo()

◆ IsSet()

◆ IsUnitized()

◆ IsValid()

◆ MaximumAbsoluteValueAt()

◆ MaximumCoefficient()

◆ MaximumValueAt() [1/4]

◆ MaximumValueAt() [2/4]

◆ MaximumValueAt() [3/4]

◆ MaximumValueAt() [4/4]

◆ MinimumValueAt() [1/4]

◆ MinimumValueAt() [2/4]

◆ MinimumValueAt() [3/4]

◆ MinimumValueAt() [4/4]

◆ NegatedPlaneEquation()

◆ operator!=()

◆ operator==()

◆ operator[]() [1/4]

◆ operator[]() [2/4]

◆ operator[]() [3/4]

◆ operator[]() [4/4]

◆ Set()

◆ Transform()

◆ UnitizedPlaneEquation()

◆ UnitNormal()

◆ ValueAt() [1/6]

◆ ValueAt() [2/6]

◆ ValueAt() [3/6]

◆ ValueAt() [4/6]

◆ ValueAt() [5/6]

◆ ValueAt() [6/6]

◆ ValueRange() [1/7]

◆ ValueRange() [2/7]

◆ ValueRange() [3/7]

◆ ValueRange() [4/7]

◆ ValueRange() [5/7]

◆ ValueRange() [6/7]

◆ ValueRange() [7/7]

◆ ZeroTolerance()

Member Data Documentation

◆ d

◆ NanPlaneEquation

◆ UnsetPlaneEquation

◆ WorldXY

◆ WorldYZ

◆ WorldZX

◆ x

◆ y

◆ z

◆ ZeroPlaneEquation