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. More...

#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
	Get point on plane that is closest to a given point. More...

bool	Create (ON_3dPoint P, ON_3dVector N)
	Sets (x,y,z) to a unitized N and then sets d = -(xP.x + yP.y + z*P.z). More...

ON_3dVector	Direction () const

double	DirectionLength () 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
	Test points on a bezier curve to see if they are near the plane. More...

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

bool	IsSet () const
	returns true if x, y, z, d are valid, finite doubles and at least one of x, y or z is not zero. More...

bool	IsValid () const
	returns true if x, y, z, d are valid, finite doubles. More...

double	MaximumAbsoluteValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const
	Get the maximum absolute value of the plane equation on a set of 3d points. More...

double	MaximumCoefficient () const

double	MaximumValueAt (const ON_BoundingBox &bbox) const
	Get the maximum value of the plane equation on a bounding box. More...

double	MaximumValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const
	Get the maximum value of the plane equation on a set of 3d points. More...

double	MinimumValueAt (const ON_BoundingBox &bbox) const
	Get the minimum value of the plane equation on a bounding box. More...

double	MinimumValueAt (bool bRational, int point_count, int point_stride, const double *points, double stop_value) const
	Get the minimum value of the plane equation on a set of 3d points. More...

ON_PlaneEquation	NegatedPlaneEquation () const

bool	operator!= (const ON_PlaneEquation &) const

bool	operator== (const ON_PlaneEquation &) const

double &	operator[] (int)

double &	operator[] (unsigned int)

double	operator[] (int) const

double	operator[] (unsigned int) const

bool	Transform (const ON_Xform &xform)
	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). More...

ON_PlaneEquation	UnitizedPlaneEquation () const

ON_3dVector	UnitNormal () const

double	ValueAt (ON_3dPoint P) const
	Evaluate the plane at a point. More...

double	ValueAt (ON_4dPoint P) const

double	ValueAt (ON_3dVector P) const

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

double *	ValueAt (int Pcount, const ON_3fPoint P, double value, double value_range[2]) const
	Evaluate the plane at a list of point values. More...

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

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

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

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

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

ON_Interval	ValueRange (const class ON_3dPointListRef &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

double	ZeroTolerance () const
	This function calculates and evalutes points that would be exactly on the plane if double precision aritmetic were mathematically perfect and returns the largest value of the evaluations. More...

Static Public Member Functions
static void	Set (ON_PlaneEquation &plane_equation, double x, double y, double z, double d)

Public Attributes
double	d

double	x

double	y

double	z

Static Public Attributes
static const ON_PlaneEquation	UnsetPlaneEquation

static const ON_PlaneEquation	ZeroPlaneEquation

Detailed 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

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
	)

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.

◆ Direction()

ON_3dVector ON_PlaneEquation::Direction ( ) const

Returns: Direction (x,y,z)

◆ DirectionLength()

double ON_PlaneEquation::DirectionLength ( ) 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

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

◆ IsSet()

bool ON_PlaneEquation::IsSet ( ) const

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

◆ IsValid()

bool ON_PlaneEquation::IsValid ( ) const

returns true if x, y, z, d are valid, finite doubles.

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

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 homogenous 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 evaulation 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() [1/2]

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

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() [2/2]

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

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 homogenous 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 evaulation 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() [1/2]

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

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() [2/2]

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

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 homogenous 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 evaulation 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.

◆ NegatedPlaneEquation()

ON_PlaneEquation ON_PlaneEquation::NegatedPlaneEquation ( ) const

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

◆ operator[]() [2/4]

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

◆ operator[]() [3/4]

double ON_PlaneEquation::operator[] ( int ) const

◆ 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 )

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.

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 resultingt 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 ( ON_3dPoint P ) const

Evaluate the plane at a point.

Parameters

P [in]

Returns: x*P.x + y*P.y + z*P.z + d;

◆ ValueAt() [2/6]

double ON_PlaneEquation::ValueAt ( ON_4dPoint P ) const

◆ ValueAt() [3/6]

double ON_PlaneEquation::ValueAt ( ON_3dVector P ) const

◆ ValueAt() [4/6]

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

◆ ValueAt() [5/6]

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

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() [6/6]

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

◆ ValueRange() [1/7]

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() [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	(	size_t	point_list_count,
		const ON_3fPoint *	point_list
	)		const

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

◆ ValueRange() [4/7]

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

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

◆ ValueRange() [5/7]

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

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

◆ ValueRange() [6/7]

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() [7/7]

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

◆ ZeroTolerance()

double ON_PlaneEquation::ZeroTolerance ( ) const

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

Member Data Documentation

◆ d

double ON_PlaneEquation::d

◆ UnsetPlaneEquation

const ON_PlaneEquation ON_PlaneEquation::UnsetPlaneEquation

static

◆ x

double ON_PlaneEquation::x

◆ y

double ON_PlaneEquation::y

◆ z

double ON_PlaneEquation::z

◆ ZeroPlaneEquation

const ON_PlaneEquation ON_PlaneEquation::ZeroPlaneEquation

static

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()

◆ Direction()

◆ DirectionLength()

◆ IsNearerThan()

◆ IsParallelTo()

◆ IsSet()

◆ IsValid()

◆ MaximumAbsoluteValueAt()

◆ MaximumCoefficient()

◆ MaximumValueAt() [1/2]

◆ MaximumValueAt() [2/2]

◆ MinimumValueAt() [1/2]

◆ MinimumValueAt() [2/2]

◆ 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

◆ UnsetPlaneEquation

◆ x

◆ y

◆ z

◆ ZeroPlaneEquation