#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...

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 Is_Valid() circle has positive radius and an Is_ Valid() 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 centr 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 paramaterization.
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.GetNurbsForm( 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::GetNurbFormParameterFromRadian

◆ 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.GetNurbsForm( 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 arc's tight bounding box. xform -[in] (default=nullptr) If not nullptr, the tight bounding box of the transformed arc is calculated. The arc 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

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