#include <opennurbs_bezier.h>

Public Member Functions
	ON_BezierCurve ()

	ON_BezierCurve (int dim, bool bIsRational, int order)
	Creates a bezier with cv memory allocated. More...

	ON_BezierCurve (const ON_BezierCurve &)

	ON_BezierCurve (const ON_PolynomialCurve &)

	ON_BezierCurve (const ON_2dPointArray &)

	ON_BezierCurve (const ON_3dPointArray &)

	ON_BezierCurve (const ON_4dPointArray &)

	~ON_BezierCurve ()

ON_BoundingBox	BoundingBox () const
	Gets bounding box. More...

bool	ChangeDimension (int desired_dimension)
	Change dimension of bezier. More...

bool	ChangeWeights (int i0, double w0, int i1, double w1)
	Use a combination of scaling and reparameterization to set two rational Bezier weights to specified values. More...

const ON_4dPoint	ControlPoint (int cv_index) const

double	ControlPolygonLength () const
	returns the length of the control polygon More...

bool	Create (int dim, bool bIsRational, int order)
	Creates a bezier with cv memory allocated. More...

ON_3dVector	CurvatureAt (double t) const
	Evaluate the curvature vector at a parameter. More...

double *	CV (int cv_index) const
	Expert user function to get a pointer to control vertex memory. If you are not an expert user, please use ON_BezierCurve::GetCV( ON_3dPoint& ) or ON_BezierCurve::GetCV( ON_4dPoint& ). More...

int	CVCount () const

int	CVSize () const

ON::point_style	CVStyle () const
	Returns the style of control vertices in the m_cv array. More...

int	Degree () const

ON_3dVector	DerivativeAt (double t) const
	Evaluate first derivative at a parameter. More...

void	Destroy ()
	Deallocates m_cv memory. More...

int	Dimension () const

ON_Interval	Domain () const

void	Dump (ON_TextLog &) const

void	EmergencyDestroy ()

bool	Ev1Der (double t, ON_3dPoint &point, ON_3dVector &first_derivative) const
	Evaluate first derivative at a parameter with error checking. More...

bool	Ev2Der (double t, ON_3dPoint &point, ON_3dVector &first_derivative, ON_3dVector &second_derivative) const
	Evaluate second derivative at a parameter with error checking. More...

bool	Evaluate (double t, int der_count, int v_stride, double *v) const
	Evaluate a bezier. More...

bool	EvCurvature (double t, ON_3dPoint &point, ON_3dVector &tangent, ON_3dVector &kappa) const
	Evaluate unit tangent and curvature at a parameter with error checking. More...

bool	EvPoint (double t, ON_3dPoint &point) const
	Evaluate point at a parameter with error checking. More...

bool	EvTangent (double t, ON_3dPoint &point, ON_3dVector &tangent) const
	Evaluate unit tangent at a parameter with error checking. More...

bool	GetBBox (double box_min, double box_max, bool bGrowBox=false) const
	Gets bounding box. More...

bool	GetBoundingBox (ON_BoundingBox &bbox, int bGrowBox=false) const
	Gets bounding box. More...

bool	GetCV (int cv_index, ON::point_style pointstyle, double *cv) const
	Get location of a control vertex. More...

bool	GetCV (int cv_index, ON_3dPoint &point) const
	Get location of a control vertex. More...

bool	GetCV (int cv_index, ON_4dPoint &point) const
	Get value of a control vertex. More...

int	GetNurbForm (ON_NurbsCurve &nurbs_curve) const
	Get ON_NurbsCurve form of a bezier. More...

bool	GetTightBoundingBox (ON_BoundingBox &tight_bbox, bool bGrowBox=false, const ON_Xform *xform=nullptr) const
	Get tight bounding box of the bezier. More...

bool	IncreaseDegree (int desired_degree)
	Increase degree of bezier. More...

bool	IsRational () const

bool	IsValid () const

bool	Loft (const ON_3dPointArray &points)
	Loft a bezier curve through a list of points. More...

bool	Loft (int pt_dim, int pt_count, int pt_stride, const double pt, int t_stride, const double t)
	Loft a bezier curve through a list of points. More...

bool	MakeNonRational ()
	Make beizer not rational by setting all control vertices to their euclidean locations and setting m_is_rat to false. More...

bool	MakeRational ()
	Make beizer rational. More...

ON_BezierCurve &	operator= (const ON_BezierCurve &)

ON_BezierCurve &	operator= (const ON_PolynomialCurve &)

ON_BezierCurve &	operator= (const ON_2dPointArray &)

ON_BezierCurve &	operator= (const ON_3dPointArray &)

ON_BezierCurve &	operator= (const ON_4dPointArray &)

int	Order () const

ON_3dPoint	PointAt (double t) const
	Evaluate point at a parameter. More...

bool	Reparameterize (double c)
	Use a linear fractional tranformation for [0,1] to reparameterize the bezier. The locus of the curve is not changed, but the parameterization is changed. More...

bool	Reparametrize (double)
	misspelled function name is obsolete More...

bool	ReserveCVCapacity (int desired_cv_capacity)
	Tools for managing CV and knot memory. More...

bool	Reverse ()
	Reverses bezier by reversing the order of the control points. More...

bool	Rotate (double sin_angle, double cos_angle, const ON_3dVector &rotation_axis, const ON_3dPoint &rotation_center)
	Rotates the bezier curve about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule). More...

bool	Rotate (double rotation_angle, const ON_3dVector &rotation_axis, const ON_3dPoint &rotation_center)
	Rotates the bezier curve about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule). More...

bool	Scale (double scale_factor)
	Scales the bezier curve by the specified facotor. The scale is centered at the origin. More...

bool	ScaleConrolPoints (int i, double w)
	Scale a rational Bezier's control vertices to set a weight to a specified value. More...

bool	SetCV (int cv_index, ON::point_style pointstyle, const double *cv)
	Set control vertex More...

bool	SetCV (int cv_index, const ON_3dPoint &point)
	Set location of a control vertex. More...

bool	SetCV (int cv_index, const ON_4dPoint &point)
	Set value of a control vertex. More...

bool	SetWeight (int cv_index, double weight)
	Set weight of a control vertex. More...

bool	Split (double t, ON_BezierCurve &left_side, ON_BezierCurve &right_side) const
	Split() divides the Bezier curve at the specified parameter. The parameter must satisfy 0 < t < 1. You may pass *this as one of the curves to be returned. More...

ON_3dVector	TangentAt (double t) const
	Evaluate unit tangent vector at a parameter. More...

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

bool	Translate (const ON_3dVector &translation_vector)
	Translates the bezier curve along the specified vector. More...

bool	Trim (const ON_Interval &interval)
	Trims (or extends) the bezier so the bezier so that the result starts bezier(interval[0]) and ends at bezier(interval[1]) (Evaluation performed on input bezier.) More...

double	Weight (int cv_index) const

bool	ZeroCVs ()
	Zeros control vertices and, if rational, sets weights to 1. More...

Public Attributes
double *	m_cv
	The i-th cv begins at cv[i*m_cv_stride]. More...

int	m_cv_capacity

int	m_cv_stride
	Number of doubles per cv ( >= ((m_is_rat)?m_dim+1:m_dim) ) More...

int	m_dim
	Implementation. More...

int	m_is_rat
	1 if bezier is rational, 0 if bezier is not rational More...

int	m_order
	order = degree+1 More...

Constructor & Destructor Documentation

◆ ON_BezierCurve() [1/7]

ON_BezierCurve::ON_BezierCurve ( )

◆ ON_BezierCurve() [2/7]

ON_BezierCurve::ON_BezierCurve	(	int	dim,
		bool	bIsRational,
		int	order
	)

Creates a bezier with cv memory allocated.

Parameters

dim	[in] (>0) dimension of bezier curve
bIsRational	[in] true for a rational bezier
order	[in] (>=2) order (=degree+1) of bezier curve

◆ ~ON_BezierCurve()

ON_BezierCurve::~ON_BezierCurve ( )

◆ ON_BezierCurve() [3/7]

ON_BezierCurve::ON_BezierCurve ( const ON_BezierCurve & )

◆ ON_BezierCurve() [4/7]

ON_BezierCurve::ON_BezierCurve ( const ON_PolynomialCurve & )

◆ ON_BezierCurve() [5/7]

ON_BezierCurve::ON_BezierCurve ( const ON_2dPointArray & )

◆ ON_BezierCurve() [6/7]

ON_BezierCurve::ON_BezierCurve ( const ON_3dPointArray & )

◆ ON_BezierCurve() [7/7]

ON_BezierCurve::ON_BezierCurve ( const ON_4dPointArray & )

Member Function Documentation

◆ BoundingBox()

ON_BoundingBox ON_BezierCurve::BoundingBox ( ) const

Gets bounding box.

Returns: Axis aligned bounding box.

◆ ChangeDimension()

bool ON_BezierCurve::ChangeDimension ( int desired_dimension )

Change dimension of bezier.

Parameters

desired_dimension [in]

Returns: true if successful. false if desired_dimension < 1

◆ ChangeWeights()

bool ON_BezierCurve::ChangeWeights	(	int	i0,
		double	w0,
		int	i1,
		double	w1
	)

Use a combination of scaling and reparameterization to set two rational Bezier weights to specified values.

Parameters

i0	[in] control point index (0 <= i0 < order, i0 != i1)
w0	[in] Desired weight for i0-th control point
i1	[in] control point index (0 <= i1 < order, i0 != i1)
w1	[in] Desired weight for i1-th control point

Returns: True if successful. The returned bezier has the same locus but probably has a different parameterization.

The i0-th cv will have weight w0 and the i1-rst cv will have weight w1. If v0 and v1 are the cv's input weights, then v0, v1, w0 and w1 must all be nonzero, and w0*v0 and w1*v1 must have the same sign.

The equations

    s * r^i0 = w0/v0
    s * r^i1 = w1/v1

determine the scaling and reparameterization necessary to change v0,v1 to w0,w1.

If the input Bezier has control vertices

    (B_0, ..., B_d),

then the output Bezier has control vertices

    (s*B_0, ... s*r^i * B_i, ..., s*r^d * B_d).

See also: ON_Bezier::Reparameterize, ON_Bezier::ScaleConrolPoints

◆ ControlPoint()

const ON_4dPoint ON_BezierCurve::ControlPoint ( int cv_index ) const

Parameters

cv_index [in] zero based control point index

Returns: Control point as an ON_4dPoint.

If cv_index or the bezier is not valid, then ON_4dPoint::Nan is returned. If dim < 3, unused coordinates are zero. If dim >= 4, the first three coordinates are returned. If is_rat is false, the weight is 1.

◆ ControlPolygonLength()

double ON_BezierCurve::ControlPolygonLength ( ) const

returns the length of the control polygon

◆ Create()

bool ON_BezierCurve::Create	(	int	dim,
		bool	bIsRational,
		int	order
	)

Creates a bezier with cv memory allocated.

Parameters

dim	[in] (>0) dimension of bezier curve
bIsRational	[in] true for a rational bezier
order	[in] (>=2) order (=degree+1) of bezier curve

Returns: true if successful.

◆ CurvatureAt()

ON_3dVector ON_BezierCurve::CurvatureAt ( double t ) const

Evaluate the curvature vector at a parameter.

Parameters

t	[in] evaluation parameter

Returns: curvature vector of the curve at the parameter t.

No error handling.

See also: ON_Curve::EvCurvature

◆ CV()

double* ON_BezierCurve::CV ( int cv_index ) const

Expert user function to get a pointer to control vertex memory. If you are not an expert user, please use ON_BezierCurve::GetCV( ON_3dPoint& ) or ON_BezierCurve::GetCV( ON_4dPoint& ).

Parameters

cv_index [in] (0 <= cv_index < m_order)

Returns: Pointer to control vertex.

If the Bezier curve is rational, the format of the returned array is a homogeneos rational point with length m_dim+1. If the Bezier curve is not rational, the format of the returned array is a nonrational euclidean point with length m_dim. See Also ON_BezierCurve::CVStyle ON_BezierCurve::GetCV ON_BezierCurve::Weight

◆ CVCount()

int ON_BezierCurve::CVCount ( ) const

Returns: Number of control vertices in the bezier. This is always the same as the order of the bezier.

◆ CVSize()

int ON_BezierCurve::CVSize ( ) const

Returns: Number of doubles per control vertex. (= IsRational() ? Dim()+1 : Dim())

◆ CVStyle()

ON::point_style ON_BezierCurve::CVStyle ( ) const

Returns the style of control vertices in the m_cv array.

Returns: table ON::not_rational m_is_rat is false ON::homogeneous_rational m_is_rat is true

◆ Degree()

int ON_BezierCurve::Degree ( ) const

Returns: Degree of the bezier. (degree=order-1)

◆ DerivativeAt()

ON_3dVector ON_BezierCurve::DerivativeAt ( double t ) const

Evaluate first derivative at a parameter.

Parameters

t	[in] evaluation parameter

Returns: First derivative of the curve at the parameter t.

No error handling.

See also: ON_Curve::Ev1Der

◆ Destroy()

void ON_BezierCurve::Destroy ( )

Deallocates m_cv memory.

◆ Dimension()

int ON_BezierCurve::Dimension ( ) const

Returns: Dimension of bezier.

◆ Domain()

ON_Interval ON_BezierCurve::Domain ( ) const

Returns: Domain of bezier (always [0,1]).

◆ Dump()

void ON_BezierCurve::Dump ( ON_TextLog & ) const

◆ EmergencyDestroy()

void ON_BezierCurve::EmergencyDestroy ( )

◆ Ev1Der()

bool ON_BezierCurve::Ev1Der	(	double	t,
		ON_3dPoint &	point,
		ON_3dVector &	first_derivative
	)		const

Evaluate first derivative at a parameter with error checking.

Parameters

t	[in] evaluation parameter
point	[out] value of curve at t
first_derivative	[out] value of first derivative at t

Returns: false if unable to evaluate.

◆ Ev2Der()

bool ON_BezierCurve::Ev2Der	(	double	t,
		ON_3dPoint &	point,
		ON_3dVector &	first_derivative,
		ON_3dVector &	second_derivative
	)		const

Evaluate second derivative at a parameter with error checking.

Parameters

t	[in] evaluation parameter
point	[out] value of curve at t
first_derivative	[out] value of first derivative at t
second_derivative	[out] value of second derivative at t

Returns: false if unable to evaluate.

◆ Evaluate()

bool ON_BezierCurve::Evaluate	(	double	t,
		int	der_count,
		int	v_stride,
		double *	v
	)		const

Evaluate a bezier.

Parameters

t	[in] evaluation parameter (usually 0 <= t <= 1)
der_count	[in] (>=0) number of derivatives to evaluate
v_stride	[in] (>=m_dim) stride to use for the v[] array
v	[out] array of length (der_count+1)v_stride bez(t) is returned in (v[0],...,v[m_dim-1]), bez'(t) is retuned in (v[v_stride],...,v[v_stride+m_dim-1]), bez"(t) is retuned in (v[2v_stride],...,v[2*v_stride+m_dim-1]), etc.

Returns: true if successful

◆ EvCurvature()

bool ON_BezierCurve::EvCurvature	(	double	t,
		ON_3dPoint &	point,
		ON_3dVector &	tangent,
		ON_3dVector &	kappa
	)		const

Evaluate unit tangent and curvature at a parameter with error checking.

Parameters

t	[in] evaluation parameter
point	[out] value of curve at t
tangent	[out] value of unit tangent
kappa	[out] value of curvature vector

Returns: false if unable to evaluate.

◆ EvPoint()

bool ON_BezierCurve::EvPoint	(	double	t,
		ON_3dPoint &	point
	)		const

Evaluate point at a parameter with error checking.

Parameters

t	[in] evaluation parameter
point	[out] value of curve at t

Returns: false if unable to evaluate.

◆ EvTangent()

bool ON_BezierCurve::EvTangent	(	double	t,
		ON_3dPoint &	point,
		ON_3dVector &	tangent
	)		const

Evaluate unit tangent at a parameter with error checking.

Parameters

t	[in] evaluation parameter
point	[out] value of curve at t
tangent	[out] value of unit tangent

Returns: false if unable to evaluate.

See also: ON_Curve::TangentAt, ON_Curve::Ev1Der

◆ GetBBox()

bool ON_BezierCurve::GetBBox	(	double *	box_min,
		double *	box_max,
		bool	bGrowBox = `false`
	)		const

Gets bounding box.

Parameters

box_min	[out] minimum corner of axis aligned bounding box The box_min[] array must have size m_dim.
box_max	[out] maximum corner of axis aligned bounding box The box_max[] array must have size m_dim.
bGrowBox	[in] if true, input box_min/box_max must be set to valid bounding box corners and this box is enlarged to be the union of the input box and the bezier's bounding box.

Returns: true if successful.

◆ GetBoundingBox()

bool ON_BezierCurve::GetBoundingBox	(	ON_BoundingBox &	bbox,
		int	bGrowBox = `false`
	)		const

Gets bounding box.

Parameters

bbox	[out] axis aligned bounding box returned here.
bGrowBox	[in] if true, input bbox must be a valid bounding box and this box is enlarged to be the union of the input box and the bezier's bounding box.

Returns: true if successful.

◆ GetCV() [1/3]

bool ON_BezierCurve::GetCV	(	int	cv_index,
		ON::point_style	pointstyle,
		double *	cv
	)		const

Get location of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
pointstyle	[in] specifes what kind of values to get ON::not_rational cv[] is an array of length m_dim that defines a euclidean (world coordinate) point ON::homogeneous_rational cv[] is an array of length (m_dim+1) that defines a rational homogeneous point. ON::euclidean_rational cv[] is an array of length (m_dim+1). The first m_dim values define the euclidean (world coordinate) location of the point. cv[m_dim] is the weight ON::intrinsic_point_style If m_is_rat is true, cv[] has ON::homogeneous_rational point style. If m_is_rat is false, cv[] has ON::not_rational point style.
cv	[out] array with control vertex value.

Returns: true if successful. false if cv_index is invalid.

◆ GetCV() [2/3]

bool ON_BezierCurve::GetCV	(	int	cv_index,
		ON_3dPoint &	point
	)		const

Get location of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
point	[out] Location of control vertex. If the bezier is rational, the euclidean location is returned.

Returns: true if successful.

◆ GetCV() [3/3]

bool ON_BezierCurve::GetCV	(	int	cv_index,
		ON_4dPoint &	point
	)		const

Get value of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
point	[out] Homogenous value of control vertex. If the bezier is not rational, the weight is 1.

Returns: true if successful.

◆ GetNurbForm()

int ON_BezierCurve::GetNurbForm ( ON_NurbsCurve & nurbs_curve ) const

Get ON_NurbsCurve form of a bezier.

Parameters

nurbs_curve [out] NURBS curve form of a bezier. The domain is [0,1].

Returns: 0 = failure 1 = success

◆ GetTightBoundingBox()

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

Get tight bounding box of the bezier.

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 tight bounding box of the bezier curve.
xform	[in] (default=nullptr) If not nullptr, the tight bounding box of the transformed bezier is calculated. The bezier curve is not modified.

Returns: True if the returned tight_bbox is set to a valid bounding box.

◆ IncreaseDegree()

bool ON_BezierCurve::IncreaseDegree ( int desired_degree )

Increase degree of bezier.

Parameters

desired_degree [in]

Returns: true if successful. false if desired_degree < current degree.

◆ IsRational()

bool ON_BezierCurve::IsRational ( ) const

Returns: true if bezier is rational.

◆ IsValid()

bool ON_BezierCurve::IsValid ( ) const

◆ Loft() [1/2]

bool ON_BezierCurve::Loft ( const ON_3dPointArray & points )

Loft a bezier curve through a list of points.

Parameters

points [in] an array of 2 or more points to interpolate

Returns: true if successful

The result has order = points.Count() and the loft uses the uniform parameterizaton curve( i/(points.Count()-1) ) = points[i].

◆ Loft() [2/2]

bool ON_BezierCurve::Loft	(	int	pt_dim,
		int	pt_count,
		int	pt_stride,
		const double *	pt,
		int	t_stride,
		const double *	t
	)

Loft a bezier curve through a list of points.

Parameters

pt_dim	[in] dimension of points to interpolate
pt_count	[in] number of points (>=2)
pt_stride	[in] (>=pt_dim) pt[] array stride
pt	[in] array of points
t_stride	[in] (>=1) t[] array stride
t	[in] strictly increasing array of interpolation parameters

Returns: true if successful

The result has order = points.Count() and the loft uses the parameterizaton curve( t[i] ) = points[i].

◆ MakeNonRational()

bool ON_BezierCurve::MakeNonRational ( )

Make beizer not rational by setting all control vertices to their euclidean locations and setting m_is_rat to false.

See also: ON_Bezier::MakeRational

◆ MakeRational()

bool ON_BezierCurve::MakeRational ( )

Make beizer rational.

Returns: true if successful.

See also: ON_Bezier::MakeNonRational

◆ operator=() [1/5]

ON_BezierCurve& ON_BezierCurve::operator= ( const ON_BezierCurve & )

◆ operator=() [2/5]

ON_BezierCurve& ON_BezierCurve::operator= ( const ON_PolynomialCurve & )

◆ operator=() [3/5]

ON_BezierCurve& ON_BezierCurve::operator= ( const ON_2dPointArray & )

◆ operator=() [4/5]

ON_BezierCurve& ON_BezierCurve::operator= ( const ON_3dPointArray & )

◆ operator=() [5/5]

ON_BezierCurve& ON_BezierCurve::operator= ( const ON_4dPointArray & )

◆ Order()

int ON_BezierCurve::Order ( ) const

Returns: Order of the bezier. (order=degree+1)

◆ PointAt()

ON_3dPoint ON_BezierCurve::PointAt ( double t ) const

Evaluate point at a parameter.

Parameters

t	[in] evaluation parameter

Returns: Point (location of curve at the parameter t).

◆ Reparameterize()

bool ON_BezierCurve::Reparameterize ( double c )

Use a linear fractional tranformation for [0,1] to reparameterize the bezier. The locus of the curve is not changed, but the parameterization is changed.

Parameters

c	[in] reparameterization constant (generally speaking, c should be > 0). If c != 1, then the returned bezier will be rational.

Returns: true if successful.

The reparameterization is performed by composing the input Bezier with the function lambda: [0,1] -> [0,1] given by

    t ->  c*t / ( (c-1)*t + 1 )

Note that lambda(0) = 0, lambda(1) = 1, lambda'(t) > 0, lambda'(0) = c and lambda'(1) = 1/c.

If the input Bezier has control vertices {B_0, ..., B_d}, then the output Bezier has control vertices

    (B_0, ... c^i * B_i, ..., c^d * B_d).

To derive this formula, simply compute the i-th Bernstein polynomial composed with lambda().

The inverse parameterization is given by 1/c. That is, the cumulative effect of the two calls

    Reparameterize(c)
    Reparameterize(1.0/c)

is to leave the bezier unchanged.

See also: ON_Bezier::ScaleConrolPoints

◆ Reparametrize()

bool ON_BezierCurve::Reparametrize ( double )

misspelled function name is obsolete

◆ ReserveCVCapacity()

bool ON_BezierCurve::ReserveCVCapacity ( int desired_cv_capacity )

Tools for managing CV and knot memory.

Make sure m_cv array has a certain length.

Parameters

desired_cv_capacity [in] minimum length of m_cv array.

Returns: true if successful.

◆ Reverse()

bool ON_BezierCurve::Reverse ( )

Reverses bezier by reversing the order of the control points.

◆ Rotate() [1/2]

bool ON_BezierCurve::Rotate	(	double	sin_angle,
		double	cos_angle,
		const ON_3dVector &	rotation_axis,
		const ON_3dPoint &	rotation_center
	)

Rotates the bezier curve about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule).

Parameters

sin_angle	[in] sine of rotation angle
cos_angle	[in] sine of rotation angle
rotation_axis	[in] direction of the axis of rotation
rotation_center	[in] point on the axis of rotation

Returns: true if bezier curve successfully rotated

Uses ON_BezierCurve::Transform() function to calculate the result.

◆ Rotate() [2/2]

bool ON_BezierCurve::Rotate	(	double	rotation_angle,
		const ON_3dVector &	rotation_axis,
		const ON_3dPoint &	rotation_center
	)

Rotates the bezier curve about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule).

Parameters

rotation_angle	[in] angle of rotation in radians
rotation_axis	[in] direction of the axis of rotation
rotation_center	[in] point on the axis of rotation

Returns: true if bezier curve successfully rotated

Uses ON_BezierCurve::Transform() function to calculate the result.

◆ Scale()

bool ON_BezierCurve::Scale ( double scale_factor )

Scales the bezier curve by the specified facotor. The scale is centered at the origin.

Parameters

scale_factor [in] scale factor

Returns: true if bezier curve successfully scaled

Uses ON_BezierCurve::Transform() function to calculate the result.

◆ ScaleConrolPoints()

bool ON_BezierCurve::ScaleConrolPoints	(	int	i,
		double	w
	)

Scale a rational Bezier's control vertices to set a weight to a specified value.

Parameters

i	[in] (0 <= i < order)
w	[in] w != 0.0

Returns: True if successful. The i-th control vertex will have weight w.

Each control point is multiplied by w/w0, where w0 is the input value of Weight(i).

See also: ON_Bezier::Reparameterize, ON_Bezier::ChangeWeights

◆ SetCV() [1/3]

bool ON_BezierCurve::SetCV	(	int	cv_index,
		ON::point_style	pointstyle,
		const double *	cv
	)

Set control vertex

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
pointstyle	[in] specifes what kind of values are passed in the cv array. ON::not_rational cv[] is an array of length m_dim that defines a euclidean (world coordinate) point ON::homogeneous_rational cv[] is an array of length (m_dim+1) that defines a rational homogeneous point. ON::euclidean_rational cv[] is an array of length (m_dim+1). The first m_dim values define the euclidean (world coordinate) location of the point. cv[m_dim] is the weight ON::intrinsic_point_style If m_is_rat is true, cv[] has ON::homogeneous_rational point style. If m_is_rat is false, cv[] has ON::not_rational point style.
cv	[in] array with control vertex value.

Returns: true if the point can be set.

◆ SetCV() [2/3]

bool ON_BezierCurve::SetCV	(	int	cv_index,
		const ON_3dPoint &	point
	)

Set location of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
point	[in] control vertex location. If the bezier is rational, the weight will be set to 1.

Returns: true if successful.

See also: ON_BezierCurve::CV, ON_BezierCurve::SetCV,, ON_BezierCurve::SetWeight, ON_BezierCurve::Weight

◆ SetCV() [3/3]

bool ON_BezierCurve::SetCV	(	int	cv_index,
		const ON_4dPoint &	point
	)

Set value of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
point	[in] control vertex value. If the bezier is not rational, the euclidean location of homogenoeous point will be used.

Returns: true if successful.

See also: ON_BezierCurve::CV, ON_BezierCurve::SetCV,, ON_BezierCurve::SetWeight, ON_BezierCurve::Weight

◆ SetWeight()

bool ON_BezierCurve::SetWeight	(	int	cv_index,
		double	weight
	)

Set weight of a control vertex.

Parameters

cv_index	[in] control vertex index (0 <= cv_index < m_order)
weight	[in] weight

Returns: true if the weight can be set. If weight is not 1 and the bezier is not rational, then false is returned. Use ON_BezierCurve::MakeRational to make a bezier curve rational.

See also: ON_BezierCurve::SetCV, ON_BezierCurve::MakeRational,, ON_BezierCurve::IsRational, ON_BezierCurve::Weight

◆ Split()

bool ON_BezierCurve::Split	(	double	t,
		ON_BezierCurve &	left_side,
		ON_BezierCurve &	right_side
	)		const

Split() divides the Bezier curve at the specified parameter. The parameter must satisfy 0 < t < 1. You may pass *this as one of the curves to be returned.

Parameters

t	[in] (0 < t < 1 ) parameter to split at
left_side	[out]
right_side	[out]

     ON_BezierCurve crv = ...;
     ON_BezierCurve right_side;
     crv.Split( 0.5, crv, right_side );
would split crv at the 1/2, put the left side in crv,
and return the right side in right_side.

◆ TangentAt()

ON_3dVector ON_BezierCurve::TangentAt ( double t ) const

Evaluate unit tangent vector at a parameter.

Parameters

t	[in] evaluation parameter

Returns: Unit tangent vector of the curve at the parameter t.

No error handling.

See also: ON_Curve::EvTangent

◆ Transform()

bool ON_BezierCurve::Transform ( const ON_Xform & xform )

Transform the bezier.

Parameters

xform [in] transformation to apply to bezier

Returns: true if successful. false if bezier is invalid and cannot be transformed.

◆ Translate()

bool ON_BezierCurve::Translate ( const ON_3dVector & translation_vector )

Translates the bezier curve along the specified vector.

Parameters

translation_vector [in] translation vector

Returns: true if bezier curve successfully translated

Uses ON_BezierCurve::Transform() function to calculate the result.

◆ Trim()

bool ON_BezierCurve::Trim ( const ON_Interval & interval )

Trims (or extends) the bezier so the bezier so that the result starts bezier(interval[0]) and ends at bezier(interval[1]) (Evaluation performed on input bezier.)

Parameters

interval [in]

An interval of [0,1] leaves the bezier unchanged.  An
interval of [0.5,1] would trim away the left half.  An
interval of [0.0,2.0] would extend the right end.

◆ Weight()

double ON_BezierCurve::Weight ( int cv_index ) const

Parameters

cv_index [in] control vertex index (0<=i<m_order)

Returns: Weight of the i-th control vertex.

◆ ZeroCVs()

bool ON_BezierCurve::ZeroCVs ( )

Zeros control vertices and, if rational, sets weights to 1.

Member Data Documentation

◆ m_cv

double* ON_BezierCurve::m_cv

The i-th cv begins at cv[i*m_cv_stride].

◆ m_cv_capacity

int ON_BezierCurve::m_cv_capacity

◆ m_cv_stride

int ON_BezierCurve::m_cv_stride

Number of doubles per cv ( >= ((m_is_rat)?m_dim+1:m_dim) )

◆ m_dim

int ON_BezierCurve::m_dim

Implementation.

dimension of bezier (>=1)

◆ m_is_rat

int ON_BezierCurve::m_is_rat

1 if bezier is rational, 0 if bezier is not rational

◆ m_order

int ON_BezierCurve::m_order

order = degree+1

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ ON_BezierCurve() [1/7]

◆ ON_BezierCurve() [2/7]

◆ ~ON_BezierCurve()

◆ ON_BezierCurve() [3/7]

◆ ON_BezierCurve() [4/7]

◆ ON_BezierCurve() [5/7]

◆ ON_BezierCurve() [6/7]

◆ ON_BezierCurve() [7/7]

Member Function Documentation

◆ BoundingBox()

◆ ChangeDimension()

◆ ChangeWeights()

◆ ControlPoint()

◆ ControlPolygonLength()

◆ Create()

◆ CurvatureAt()

◆ CV()

◆ CVCount()

◆ CVSize()

◆ CVStyle()

◆ Degree()

◆ DerivativeAt()

◆ Destroy()

◆ Dimension()

◆ Domain()

◆ Dump()

◆ EmergencyDestroy()

◆ Ev1Der()

◆ Ev2Der()

◆ Evaluate()

◆ EvCurvature()

◆ EvPoint()

◆ EvTangent()

◆ GetBBox()

◆ GetBoundingBox()

◆ GetCV() [1/3]

◆ GetCV() [2/3]

◆ GetCV() [3/3]

◆ GetNurbForm()

◆ GetTightBoundingBox()

◆ IncreaseDegree()

◆ IsRational()

◆ IsValid()

◆ Loft() [1/2]

◆ Loft() [2/2]

◆ MakeNonRational()

◆ MakeRational()

◆ operator=() [1/5]

◆ operator=() [2/5]

◆ operator=() [3/5]

◆ operator=() [4/5]

◆ operator=() [5/5]

◆ Order()

◆ PointAt()

◆ Reparameterize()

◆ Reparametrize()

◆ ReserveCVCapacity()

◆ Reverse()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ Scale()

◆ ScaleConrolPoints()

◆ SetCV() [1/3]

◆ SetCV() [2/3]

◆ SetCV() [3/3]

◆ SetWeight()

◆ Split()

◆ TangentAt()

◆ Transform()

◆ Translate()

◆ Trim()

◆ Weight()

◆ ZeroCVs()

Member Data Documentation

◆ m_cv

◆ m_cv_capacity

◆ m_cv_stride