#include <opennurbs_circle.h>

Inheritance diagram for ON_Circle:

Public Member Functions
	ON_Circle ()=default

	ON_Circle (const ON_2dPoint &P, const ON_2dPoint &Q, const ON_2dPoint &R)

	ON_Circle (const ON_3dPoint &center, double radius)

	ON_Circle (const ON_3dPoint &P, const ON_3dPoint &Q, const ON_3dPoint &R)

	ON_Circle (const ON_Circle &)=default

	ON_Circle (const ON_Plane &plane, const ON_3dPoint &center, double radius)

	ON_Circle (const ON_Plane &plane, double radius)

	~ON_Circle ()=default

ON_BoundingBox	BoundingBox () const

const ON_3dPoint &	Center () const

double	Circumference () const

ON_3dPoint	ClosestPointTo (const ON_3dPoint &point) const
	returns point on circle that is closest to given point More...

bool	ClosestPointTo (const ON_3dPoint &point, double *t) const
	returns parameters of point on circle that is closest to given point More...

bool	Create (const ON_2dPoint &P, const ON_2dPoint &Q, const ON_2dPoint &R)

bool	Create (const ON_2dPoint &P, const ON_2dVector &tangent_at_P, const ON_2dPoint &Q)

bool	Create (const ON_3dPoint &center, double radius)

bool	Create (const ON_3dPoint &P, const ON_3dPoint &Q, const ON_3dPoint &R)

bool	Create (const ON_3dPoint &P, const ON_3dVector &tangent_at_P, const ON_3dPoint &Q)

bool	Create (const ON_Plane &plane, const ON_3dPoint &center, double radius)

bool	Create (const ON_Plane &plane, double radius)

ON_3dVector	DerivativeAt (int, double) const

double	Diameter () const

double	EquationAt (const ON_2dPoint &plane_point) const
	evaluate circle's implicit equation in plane More...

int	GetNurbForm (ON_NurbsCurve &nurbs_curve) const

bool	GetNurbFormParameterFromRadian (double circle_radians_parameter, double *nurbs_parameter) const

bool	GetRadianFromNurbFormParameter (double nurbs_parameter, double *circle_radians_parameter) const

bool	GetTightBoundingBox (ON_BoundingBox &tight_bbox, bool bGrowBox=false, const ON_Xform *xform=nullptr) const

ON_2dVector	GradientAt (const ON_2dPoint &plane_point) const

bool	IsInPlane (const ON_Plane &, double=ON_ZERO_TOLERANCE) const
	bool UpdatePoints(); ///< sets m_point[] to have valid points More...

bool	IsValid () const
	A Valid circle has m_radius>0 and m_plane.IsValid(). More...

double	MaximumCoordinate () const
	///< absolute value of maximum coordinate More...

const ON_3dVector &	Normal () const

ON_Circle &	operator= (const ON_Circle &)=default

const ON_Plane &	Plane () const
	plane containing circle More...

ON_3dPoint	PointAt (double) const

double	Radius () const

bool	Reverse ()

bool	Rotate (double angle_in_radians, const ON_3dVector &axis_of_rotation)

bool	Rotate (double angle_in_radians, const ON_3dVector &axis_of_rotation, const ON_3dPoint &center_of_rotation)

bool	Rotate (double sin_angle, double cos_angle, const ON_3dVector &axis_of_rotation)
	rotate circle about its center More...

bool	Rotate (double sin_angle, double cos_angle, const ON_3dVector &axis_of_rotation, const ON_3dPoint &center_of_rotation)
	rotate circle about a point and axis More...

ON_3dVector	TangentAt (double) const

bool	Transform (const ON_Xform &)

bool	Translate (const ON_3dVector &delta)

Public Attributes
ON_Plane	plane = ON_Plane::World_xy

double	radius = 1.0

Static Public Attributes
static const ON_Circle	UnitCircle
	unit circle in the xy plane More...

static const ON_Circle	UnsetCircle
	invalid circle with ON_Plane::Unset and ON_UNSET_VALUE radius; More...

Detailed Description

Description: ON_Circle is a circle in 3d. The circle is represented by a radius and an orthonormal frame of the plane containing the circle, with origin at the center.

An IsValid() circle has positive radius and an IsValid() plane defining the frame.

The circle is parameterized by radians from 0 to 2 Pi given by t -> center + cos(t)*radius*xaxis + sin(t)*radius*yaxis
where center, xaxis and yaxis define the orthonormal frame of the circle's plane.

Constructor & Destructor Documentation

◆ ON_Circle() [1/7]

ON_Circle::ON_Circle ( )

default

◆ ~ON_Circle()

ON_Circle::~ON_Circle ( )

default

◆ ON_Circle() [2/7]

ON_Circle::ON_Circle ( const ON_Circle & )

default

◆ ON_Circle() [3/7]

ON_Circle::ON_Circle	(	const ON_Plane &	plane,
		double	radius
	)

Creates a circle in the plane with center at plane.origin.

◆ ON_Circle() [4/7]

ON_Circle::ON_Circle	(	const ON_3dPoint &	center,
		double	radius
	)

Creates a circle parallel to the world XY plane with given center and radius

◆ ON_Circle() [5/7]

ON_Circle::ON_Circle	(	const ON_Plane &	plane,
		const ON_3dPoint &	center,
		double	radius
	)

Creates a circle parallel to the plane with given center and radius.

◆ ON_Circle() [6/7]

ON_Circle::ON_Circle	(	const ON_2dPoint &	P,
		const ON_2dPoint &	Q,
		const ON_2dPoint &	R
	)

Create a circle through three 2d points. The start/end of the circle is at point P.

Parameters

P	circle through 3 2d points

◆ ON_Circle() [7/7]

ON_Circle::ON_Circle	(	const ON_3dPoint &	P,
		const ON_3dPoint &	Q,
		const ON_3dPoint &	R
	)

Create a circle through three 3d points. The start/end of the circle is at point P.

Member Function Documentation

◆ BoundingBox()

ON_BoundingBox ON_Circle::BoundingBox ( ) const

◆ Center()

const ON_3dPoint& ON_Circle::Center ( ) const

◆ Circumference()

double ON_Circle::Circumference ( ) const

◆ ClosestPointTo() [1/2]

ON_3dPoint ON_Circle::ClosestPointTo ( const ON_3dPoint & point ) const

returns point on circle that is closest to given point

◆ ClosestPointTo() [2/2]

bool ON_Circle::ClosestPointTo	(	const ON_3dPoint &	point,
		double *	t
	)		const

returns parameters of point on circle that is closest to given point

◆ Create() [1/7]

bool ON_Circle::Create	(	const ON_2dPoint &	P,
		const ON_2dPoint &	Q,
		const ON_2dPoint &	R
	)

Create a circle through three 2d points. The start/end of the circle is at point P.

Parameters

P	circle through 3 2d points

◆ Create() [2/7]

bool ON_Circle::Create	(	const ON_2dPoint &	P,
		const ON_2dVector &	tangent_at_P,
		const ON_2dPoint &	Q
	)

Create a circle from two 2d points and a tangent at the first point. The start/end of the circle is at point P.

◆ Create() [3/7]

bool ON_Circle::Create	(	const ON_3dPoint &	center,
		double	radius
	)

Creates a circle parallel to the world XY plane with given center and radius

◆ Create() [4/7]

bool ON_Circle::Create	(	const ON_3dPoint &	P,
		const ON_3dPoint &	Q,
		const ON_3dPoint &	R
	)

Create a circle through three 3d points. The start/end of the circle is at point P.

◆ Create() [5/7]

bool ON_Circle::Create	(	const ON_3dPoint &	P,
		const ON_3dVector &	tangent_at_P,
		const ON_3dPoint &	Q
	)

Create a circle from two 3d points and a tangent at the first point. The start/end of the circle is at point P.

◆ Create() [6/7]

bool ON_Circle::Create	(	const ON_Plane &	plane,
		const ON_3dPoint &	center,
		double	radius
	)

Creates a circle parallel to the plane with given center and radius.

◆ Create() [7/7]

bool ON_Circle::Create	(	const ON_Plane &	plane,
		double	radius
	)

Creates a circle in the plane with center at plane.origin.

◆ DerivativeAt()

ON_3dVector ON_Circle::DerivativeAt	(	int	,
		double
	)		const

◆ Diameter()

double ON_Circle::Diameter ( ) const

◆ EquationAt()

double ON_Circle::EquationAt ( const ON_2dPoint & plane_point ) const

evaluate circle's implicit equation in plane

◆ GetNurbForm()

int ON_Circle::GetNurbForm ( ON_NurbsCurve & nurbs_curve ) const

Description: Get a four span rational degree 2 NURBS circle representation of the circle. Returns: 2 for success, 0 for failure Remarks: Note that the parameterization of NURBS curve does not match circle's transcendental parameterization. Use ON_Circle::GetRadianFromNurbFormParameter() and ON_Circle::GetParameterFromRadian() to convert between the NURBS curve parameter and the transcendental parameter.

◆ GetNurbFormParameterFromRadian()

bool ON_Circle::GetNurbFormParameterFromRadian	(	double	circle_radians_parameter,
		double *	nurbs_parameter
	)		const

Description: Convert a circle radians parameter to a NURBS curve circle parameter. Parameters: circle_radians_parameter - [in] 0.0 to 2.0*ON_PI nurbs_parameter - [out] Example:

    ON_Circle circle = ...;
    double circle_t = 1.2345; ///< some number in interval (0,2.0*ON_PI).
    double nurbs_t;
    circle.GetNurbFormParameterFromRadian( circle_t, &nurbs_t );

    ON_NurbsCurve nurbs_curve;
    circle.GetNurbForm( nurbs_curve );
    circle_pt = circle.PointAt(circle_t);
    nurbs_pt = nurbs_curve.PointAt(nurbs_t);

/ circle_pt and nurbs_pt will be the same

Remarks: The NURBS curve parameter is with respect to the NURBS curve created by ON_Circle::GetNurbForm. At radian values of 0.0, 0.5*ON_PI, ON_PI, 1.5*ON_PI, and 2.0*ON_PI, the nurbs parameter and radian parameter are the same. At all other values the nurbs and radian parameter values are different. See Also: ON_Circle::GetRadianFromNurbFormParameter

◆ GetRadianFromNurbFormParameter()

bool ON_Circle::GetRadianFromNurbFormParameter	(	double	nurbs_parameter,
		double *	circle_radians_parameter
	)		const

Description: Convert a NURBS curve circle parameter to a circle radians parameter. Parameters: nurbs_parameter - [in] circle_radians_parameter - [out] Example:

    ON_Circle circle = ...;
    double nurbs_t = 1.2345; ///< some number in interval (0,2.0*ON_PI).
    double circle_t;
    circle.GetRadianFromNurbFormParameter( nurbs_t, &circle_t );

    ON_NurbsCurve nurbs_curve;
    circle.GetNurbForm( nurbs_curve );
    circle_pt = circle.PointAt(circle_t);
    nurbs_pt = nurbs_curve.PointAt(nurbs_t);

/ circle_pt and nurbs_pt will be the same

Remarks: The NURBS curve parameter is with respect to the NURBS curve created by ON_Circle::GetNurbForm. At nurbs parameter values of 0.0, 0.5*ON_PI, ON_PI, 1.5*ON_PI, and 2.0*ON_PI, the nurbs parameter and radian parameter are the same. At all other values the nurbs and radian parameter values are different. See Also: ON_Circle::GetNurbFormParameterFromRadian

◆ GetTightBoundingBox()

bool ON_Circle::GetTightBoundingBox	(	ON_BoundingBox &	tight_bbox,
		bool	bGrowBox = `false`,
		const ON_Xform *	xform = `nullptr`
	)		const

Description: Get tight bounding box. Parameters: tight_bbox - [in/out] tight bounding box bGrowBox -[in] (default=false)
If true and the input tight_bbox is valid, then returned tight_bbox is the union of the input tight_bbox and the circle's tight bounding box. xform -[in] (default=nullptr) If not nullptr, the tight bounding box of the transformed circle is calculated. The circle is not modified. Returns: True if a valid tight_bbox is returned.

◆ GradientAt()

ON_2dVector ON_Circle::GradientAt ( const ON_2dPoint & plane_point ) const

◆ IsInPlane()

bool ON_Circle::IsInPlane	(	const ON_Plane &	,
		double	= `ON_ZERO_TOLERANCE`
	)		const

bool UpdatePoints(); ///< sets m_point[] to have valid points

◆ IsValid()

bool ON_Circle::IsValid ( ) const

A Valid circle has m_radius>0 and m_plane.IsValid().

◆ MaximumCoordinate()

double ON_Circle::MaximumCoordinate ( ) const

///< absolute value of maximum coordinate

◆ Normal()

const ON_3dVector& ON_Circle::Normal ( ) const

◆ operator=()

ON_Circle& ON_Circle::operator= ( const ON_Circle & )

default

◆ Plane()

const ON_Plane& ON_Circle::Plane ( ) const

plane containing circle

◆ PointAt()

ON_3dPoint ON_Circle::PointAt ( double ) const

Circles use trigonometric parameterization t -> center + cos(t)*radius*xaxis + sin(t)*radius*yaxis

◆ Radius()

double ON_Circle::Radius ( ) const

◆ Reverse()

bool ON_Circle::Reverse ( )

◆ Rotate() [1/4]

bool ON_Circle::Rotate	(	double	angle_in_radians,
		const ON_3dVector &	axis_of_rotation
	)

◆ Rotate() [2/4]

bool ON_Circle::Rotate	(	double	angle_in_radians,
		const ON_3dVector &	axis_of_rotation,
		const ON_3dPoint &	center_of_rotation
	)

◆ Rotate() [3/4]

bool ON_Circle::Rotate	(	double	sin_angle,
		double	cos_angle,
		const ON_3dVector &	axis_of_rotation
	)

rotate circle about its center

◆ Rotate() [4/4]

bool ON_Circle::Rotate	(	double	sin_angle,
		double	cos_angle,
		const ON_3dVector &	axis_of_rotation,
		const ON_3dPoint &	center_of_rotation
	)

rotate circle about a point and axis

◆ TangentAt()

ON_3dVector ON_Circle::TangentAt ( double ) const

◆ Transform()

bool ON_Circle::Transform ( const ON_Xform & )

◆ Translate()

bool ON_Circle::Translate ( const ON_3dVector & delta )

Member Data Documentation

◆ plane

ON_Plane ON_Circle::plane = ON_Plane::World_xy

◆ radius

double ON_Circle::radius = 1.0

◆ UnitCircle

const ON_Circle ON_Circle::UnitCircle

static

unit circle in the xy plane

◆ UnsetCircle

const ON_Circle ON_Circle::UnsetCircle

static

invalid circle with ON_Plane::Unset and ON_UNSET_VALUE radius;

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ON_Circle() [1/7]

◆ ~ON_Circle()

◆ ON_Circle() [2/7]

◆ ON_Circle() [3/7]

◆ ON_Circle() [4/7]

◆ ON_Circle() [5/7]

◆ ON_Circle() [6/7]

◆ ON_Circle() [7/7]

Member Function Documentation

◆ BoundingBox()

◆ Center()

◆ Circumference()

◆ ClosestPointTo() [1/2]

◆ ClosestPointTo() [2/2]

◆ Create() [1/7]

◆ Create() [2/7]

◆ Create() [3/7]

◆ Create() [4/7]

◆ Create() [5/7]

◆ Create() [6/7]

◆ Create() [7/7]

◆ DerivativeAt()

◆ Diameter()

◆ EquationAt()

◆ GetNurbForm()

◆ GetNurbFormParameterFromRadian()

◆ GetRadianFromNurbFormParameter()

◆ GetTightBoundingBox()

◆ GradientAt()

◆ IsInPlane()

◆ IsValid()

◆ MaximumCoordinate()

◆ Normal()

◆ operator=()

◆ Plane()

◆ PointAt()

◆ Radius()

◆ Reverse()

◆ Rotate() [1/4]

◆ Rotate() [2/4]

◆ Rotate() [3/4]

◆ Rotate() [4/4]

◆ TangentAt()

◆ Transform()

◆ Translate()

Member Data Documentation

◆ plane

◆ radius

◆ UnitCircle

◆ UnsetCircle