A nurbs curve value. More...

#include <NurbsCurve.h>

Inheritance diagram for maquina::NurbsCurve:

Public Types
enum	Mode { Open = 0, Closed = 1, Periodic = 2 }
	The surface curves mode. More...

Public Types inherited from maquina::Shape
enum	Topology { constant =0, vertex, face, face_varying }
	The different attribute topologies. More...

Public Member Functions
Access
const BufferConstFloat	read_knots () const
	Return the readable curve knots. More...

BufferFloat	write_knots ()
	Return the writable curve knots. More...

const BufferConstFloat	read_weights () const
	Return the readable control points weights. More...

BufferFloat	write_weights ()
	Return the writable control points weights. More...

int	degree () const
	Return the curve degree. More...

Mode	mode () const
	Return the curve degree. More...

int	span () const
	Return the number of span. More...

Imath::V2f	range () const
	Return the curve parameter visible range. More...

Evaluation
Imath::V3f	evaluate (float u) const
	Evaluate the curve at a u coordinate. More...

Imath::V3d	evaluate (double u) const
	Evaluate the curve at a u coordinate in double precision. More...

Imath::V3f	evaluate_dp (float u) const
	Evaluate the curve position derivatives at a u coordinate. More...

void	derivatives (float u, int n, std::vector< Imath::V3f > &derivatives) const
	Evaluate the n first derivatives. More...

float	length (float start, float end, float error=0.001f) const
	Compute the curve length between the start and end u parameters. More...

float	param_from_length (float length, bool relative=false, float error=0.001f, int max_try=100) const
	Compute the parameter for the given arc length. More...

float	closest (const Imath::V3f &p, Imath::V3f *r=nullptr, float error=0.001f, int max_try=10, const gsl::span< const Imath::V3f > &cache={}) const
	Compute the curve closest point to p. More...

Modifications
void	resample (const gsl::span< const float > &knots, int degree)
	Resample a curve. More...

void	set_range (const Imath::V2f &range)
	Remap the curve knots between new_min and float new_max. More...

void	reverse ()
	Reverse the control point order. More...

bool	split (float u, NurbsCurve &lower, NurbsCurve &upper) const
	Split the curve along the u parameter. More...

Public Member Functions inherited from maquina::Points
	Points ()
	Create an empty. More...

	Points (const Value &v)
	Cast a Value in Points. More...

BufferV3f	write_points ()
	Return the points buffer. More...

const BufferConstV3f	read_points () const
	Return the points buffer. More...

size_t	point_count () const
	Return the number of points. More...

Imath::Box3f	bounding_box () const
	Compute the object points bounding box. More...

void	compute_vertex_normals (BufferV3f &result) const
	Compute and return the vertex normals. More...

Public Member Functions inherited from maquina::Shape
	Shape ()

	Shape (const Value &v)
	Cast a Value object in Shape. More...

bool	has_attribute (const char *attribute_name, Topology topology) const
	Test if the shape has this attribute. More...

template<typename T >
T	write_attribute (const char *attribute_name, Topology topology)
	Get a write access to an attribute. More...

const Value	read_attribute (const char *attribute_name, Topology topology) const
	Get a read access to an attribute. More...

bool	set_attribute (const char *name, Topology topology, const Value &value)
	Set an attribute. More...

bool	remove_attribute (const char *name, Topology topology)
	Remove an attribute. More...

void	finalize ()
	Finalize the shape after deformation. More...

size_t	topology_size (Topology topology) const
	Get the number of faces, edges or vertices. More...

Attributes	read_attributes () const
	Return a read-only attribute iteration. More...

Public Member Functions inherited from maquina::Value
	Value ()

	Value (Value &&other)=default

	Value (const Value &other)=default

Value &	operator= (Value &&other)=default

Value &	operator= (const Value &other)=default

virtual	~Value ()=default

Value	duplicate () const
	Duplicate the value. More...

bool	as_bool () const
	Returns the value as a bool. More...

int	as_int () const
	Returns the value as an integer. More...

float	as_float () const
	Returns the value as a float. More...

double	as_double () const
	Returns the value as a double. More...

const std::string &	as_string () const
	Returns the value as a string. More...

std::wstring	as_wstring () const
	Returns the value as a wstring. More...

Imath::V2f	as_V2f () const
	Returns the value as a V2f. More...

Imath::V3f	as_V3f () const
	Returns the value as a V3f. More...

Imath::V4f	as_V4f () const
	Returns the value as a V4f. More...

const Imath::V2d &	as_V2d () const
	Returns the value as a V2d. More...

const Imath::V3d &	as_V3d () const
	Returns the value as a V3d. More...

const Imath::V4d &	as_V4d () const
	Returns the value as a V4d. More...

const Imath::V2i &	as_V2i () const
	Returns the value as a V2i. More...

const Imath::V3i &	as_V3i () const
	Returns the value as a V3i. More...

const Imath::V4i &	as_V4i () const
	Returns the value as a V4i. More...

Imath::M44f	as_M44f () const
	Returns the value as a M44f. More...

const Imath::M44d &	as_M44d () const
	Returns the value as a M44d. More...

const Imath::Box3f &	as_Box3f () const
	Returns the value as a Box3f. More...

const Imath::Color4f &	as_Color4f () const
	Returns the value as a Color4f. More...

Imath::Quatf	as_Quatf () const
	Returns the value as a Quatf. More...

const Imath::Quatd &	as_Quatd () const
	Returns the value as a Quatd. More...

std::shared_ptr< const UserData >	as_user_data () const
	Returns the value as a user data. More...

StringView	type_name () const
	Return the type name of the Value. More...

virtual bool	has_node_delegate () const
	Check if this value can produces a NodeDelegate. More...

virtual std::shared_ptr< NodeDelegate >	node_delegate (const std::shared_ptr< NodeDelegate > &parent, const StringView &name) const

bool	operator== (const Value &o) const
	Compare the two values. More...

bool	operator!= (const Value &o) const

bool	is_instance (const char *value_type_name) const
	Check if this type derives from another value type. More...

	operator bool () const

	Value (bool)
	Create a boolean value. More...

	Value (int)
	Create an integer value. More...

	Value (float)
	Create a float value. More...

	Value (double)
	Create a double value (stored in a float right now) More...

	Value (const char *string)
	Create a string value. More...

	Value (const wchar_t *string)
	Create a string value. More...

	Value (const std::string &string)
	Create a string value. More...

	Value (const std::wstring &string)
	Create a wide string value. More...

	Value (const Imath::V2f &)
	Create a Imath::V2f value. More...

	Value (const Imath::V3f &)
	Create a Imath::V3f value. More...

	Value (const Imath::V4f &)
	Create a Imath::V4f value. More...

	Value (const Imath::V2d &)
	Create a Imath::V2d value. More...

	Value (const Imath::V3d &)
	Create a Imath::V3d value. More...

	Value (const Imath::V4d &)
	Create a Imath::V4d value. More...

	Value (const Imath::V2i &)
	Create a Imath::V2i value. More...

	Value (const Imath::V3i &)
	Create a Imath::V3i value. More...

	Value (const Imath::V4i &)
	Create a Imath::V4i value. More...

	Value (const Imath::Color4f &)
	Create a Imath::Color4f value. More...

	Value (const Imath::M44f &)
	Create a Imath::M44f value. More...

	Value (const Imath::M44d &)
	Create a Imath::M44d value. More...

	Value (const Imath::Box3f &)
	Create a Imath::Box3f value. More...

	Value (const Imath::Quatf &)
	Create a Imath::Quatf value. More...

	Value (const Imath::Quatd &)
	Create a Imath::Quatd value. More...

	Value (const std::shared_ptr< const UserData > &user_data)
	Create a user data value. More...

Static Public Attributes
static const NurbsCurve	default_value
	The default value. More...

Static Public Attributes inherited from maquina::Points
static const Points	default_value
	The default value. More...

Static Public Attributes inherited from maquina::Value
static const Value	default_value
	The default value. More...

Construction
	NurbsCurve ()
	Create an empty curve. More...

	NurbsCurve (const BufferConstV3f &points, const BufferConstFloat &knots, int degree, Mode mode)
	Create a curve. More...

	NurbsCurve (const BufferConstV3f &points, const BufferConstFloat &knots, const BufferConstFloat &weights, int degree, Mode mode)

	NurbsCurve (const Value &v)
	Cast a Value in NurbsCurve. More...

static NurbsCurve	fit_closed (const BufferConstV3f &points, const BufferConstFloat &points_parameter, const BufferConstFloat &knots, int degree)
	Create a closed curve which fits the points. More...

static NurbsCurve	fit_open (const BufferConstV3f &points, const BufferConstFloat &points_parameter, const BufferConstFloat &knots, int degree)
	Create an open curve which fits the points. More...

static NurbsCurve	fit_open2 (const BufferConstV3f &points, const BufferConstFloat &points_parameter, const BufferConstFloat &knots, int degree)
	Create an open curve which fits the points, with constraint first and last control vertices. More...

static NurbsCurve	fit_open (const BufferConstV3f &points, const BufferConstFloat &points_parameter, const BufferConstFloat &knots, const Imath::V3f &d0, const Imath::V3f &dn, int degree)
	Create an open curve which fits the points using starting and ending differentials. More...

Additional Inherited Members
Static Public Member Functions inherited from maquina::Value
static bool	validate_type_name (const char *type_name)
	Return true if the name is a valid type name. More...

static Value	get_default_value (const char *type_name)
	Return a default value for a given type. More...

Detailed Description

A nurbs curve value.

This object is a standard nurbs curve with no other parameter than a position.

Member Enumeration Documentation

◆ Mode

enum maquina::NurbsCurve::Mode

The surface curves mode.

Enumerator
Open	The curve is open.
Closed	The curve is closed, the first and last vertices should stay the same.
Periodic	The curve is periodic, the N-degree first vertices should be the same as the N-degree last ones.

Constructor & Destructor Documentation

◆ NurbsCurve() [1/4]

maquina::NurbsCurve::NurbsCurve ( )

Create an empty curve.

◆ NurbsCurve() [2/4]

maquina::NurbsCurve::NurbsCurve	(	const BufferConstV3f &	points,
		const BufferConstFloat &	knots,
		int	degree,
		Mode	mode
	)

Create a curve.

◆ NurbsCurve() [3/4]

maquina::NurbsCurve::NurbsCurve	(	const BufferConstV3f &	points,
		const BufferConstFloat &	knots,
		const BufferConstFloat &	weights,
		int	degree,
		Mode	mode
	)

◆ NurbsCurve() [4/4]

maquina::NurbsCurve::NurbsCurve ( const Value & v )

Cast a Value in NurbsCurve.

If v is not a NurbsCurve object, this object will be an empty curve.

Member Function Documentation

◆ closest()

float maquina::NurbsCurve::closest	(	const Imath::V3f &	p,
		Imath::V3f *	r = `nullptr`,
		float	error = `0.001f`,
		int	max_try = `10`,
		const gsl::span< const Imath::V3f > &	cache = `{}`
	)		const

Compute the curve closest point to p.

Returns the curve parameter value of the closest point. To speedup many closest queries on the same curve, it is possible to provide a cache of the subdivided curve. The subdivision must be done from start=knots[degree] to end=knots[knots.size()-degree-1] using a uniform parameter step. The default subdivision step count is 6*(knots.size()-degree*2).

Parameters

p	The position to project on the curve
r	If not null, it is filled with the closest curve position
error	The minimum error in vertex space
max_try	Maximum numbr of try
cache	An optionnal nurbs subdivision cache

◆ degree()

int maquina::NurbsCurve::degree ( ) const

Return the curve degree.

◆ derivatives()

void maquina::NurbsCurve::derivatives	(	float	u,
		int	n,
		std::vector< Imath::V3f > &	derivatives
	)		const

Evaluate the n first derivatives.

derivatives[0] is the position. derivatives[1] is the first derivative. derivatives[degree] is the last derivative.

◆ evaluate() [1/2]

Imath::V3f maquina::NurbsCurve::evaluate ( float u ) const

Evaluate the curve at a u coordinate.

◆ evaluate() [2/2]

Imath::V3d maquina::NurbsCurve::evaluate ( double u ) const

Evaluate the curve at a u coordinate in double precision.

◆ evaluate_dp()

Imath::V3f maquina::NurbsCurve::evaluate_dp ( float u ) const

Evaluate the curve position derivatives at a u coordinate.

Return the dp/du vector which may not be normalized.

◆ fit_closed()

static NurbsCurve maquina::NurbsCurve::fit_closed	(	const BufferConstV3f &	points,
		const BufferConstFloat &	points_parameter,
		const BufferConstFloat &	knots,
		int	degree
	)

static

Create a closed curve which fits the points.

Points must have 'degree' points wrapped around. points are the points to fit with a nurbs curve. points_parameter is the nurbs curve parameter value of the points. knots are the nurbs curve knots. knots.size() must be points.size()+degree+1. degree is the degree of the returned curve.

◆ fit_open() [1/2]

static NurbsCurve maquina::NurbsCurve::fit_open	(	const BufferConstV3f &	points,
		const BufferConstFloat &	points_parameter,
		const BufferConstFloat &	knots,
		int	degree
	)

static

Create an open curve which fits the points.

points are the points to fit with a nurbs curve. points_parameter is the nurbs curve parameter value of the points. knots are the nurbs curve knots. knots.size() must be points.size()+degree+3. degree is the degree of the returned curve.

◆ fit_open() [2/2]

static NurbsCurve maquina::NurbsCurve::fit_open	(	const BufferConstV3f &	points,
		const BufferConstFloat &	points_parameter,
		const BufferConstFloat &	knots,
		const Imath::V3f &	d0,
		const Imath::V3f &	dn,
		int	degree
	)

static

Create an open curve which fits the points using starting and ending differentials.

points are the points to fit with a nurbs curve. points_parameter is the nurbs curve parameter value of the points. knots are the nurbs curve knots. knots.size() must be points.size()+degree+3. d0 is the starting curve differential. dn is the ending curve differential. degree is the degree of the returned curve.

◆ fit_open2()

static NurbsCurve maquina::NurbsCurve::fit_open2	(	const BufferConstV3f &	points,
		const BufferConstFloat &	points_parameter,
		const BufferConstFloat &	knots,
		int	degree
	)

static

Create an open curve which fits the points, with constraint first and last control vertices.

points are the points to fit with a nurbs curve. points_parameter is the nurbs curve parameter value of the points. knots are the nurbs curve knots. knots.size() must be points.size()+degree+3. degree is the degree of the returned curve. The returned curve has n=points.size() control points P, with P1=lerp(P0, P2, 1/3) and Pn-1=lerp(Pn-3, Pn-1, 2/3). points[1] and points[n-2] are ignored.

◆ length()

float maquina::NurbsCurve::length	(	float	start,
		float	end,
		float	error = `0.001f`
	)		const

Compute the curve length between the start and end u parameters.

Parameters

start	The starting u parameter of the arc
end	The ending u parameter of the arc
error	The relative accepted error of the result

◆ mode()

Mode maquina::NurbsCurve::mode ( ) const

Return the curve degree.

◆ param_from_length()

float maquina::NurbsCurve::param_from_length	(	float	length,
		bool	relative = `false`,
		float	error = `0.001f`,
		int	max_try = `100`
	)		const

Compute the parameter for the given arc length.

Parameters

length	The arc length for which we want a parameter
relative	If false length is expressed in the curve's length unit, if true, length is a ratio of the curve's length between [0,1].
error	The relative accepted error of the result
max_try	Maximum try to reach the error

◆ range()

Imath::V2f maquina::NurbsCurve::range ( ) const

Return the curve parameter visible range.

For periodic curves, this is not the same than the first and last knots.

◆ read_knots()

const BufferConstFloat maquina::NurbsCurve::read_knots ( ) const

Return the readable curve knots.

◆ read_weights()

const BufferConstFloat maquina::NurbsCurve::read_weights ( ) const

Return the readable control points weights.

◆ resample()

void maquina::NurbsCurve::resample	(	const gsl::span< const float > &	knots,
		int	degree
	)

Resample a curve.

Modify the curve knots and degree and rebuild the curve in order to keep its shape if possible.

◆ reverse()

void maquina::NurbsCurve::reverse ( )

Reverse the control point order.

◆ set_range()

void maquina::NurbsCurve::set_range ( const Imath::V2f & range )

Remap the curve knots between new_min and float new_max.

This has no effect on the shape of the curve.

◆ span()

int maquina::NurbsCurve::span ( ) const

Return the number of span.

◆ split()

bool maquina::NurbsCurve::split	(	float	u,
		NurbsCurve &	lower,
		NurbsCurve &	upper
	)		const

Split the curve along the u parameter.

Returns false if the split is not possible, else return true and fill the lower and upper curves with the two curve parts.

◆ write_knots()

BufferFloat maquina::NurbsCurve::write_knots ( )

Return the writable curve knots.

◆ write_weights()

BufferFloat maquina::NurbsCurve::write_weights ( )

Return the writable control points weights.

Member Data Documentation

◆ default_value

const NurbsCurve maquina::NurbsCurve::default_value

static

The default value.

The documentation for this class was generated from the following file:

include/Maquina/NurbsCurve.h

Public Types

Public Member Functions

Static Public Attributes

Construction

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ Mode

Constructor & Destructor Documentation

◆ NurbsCurve() [1/4]

◆ NurbsCurve() [2/4]

◆ NurbsCurve() [3/4]

◆ NurbsCurve() [4/4]

Member Function Documentation

◆ closest()

◆ degree()

◆ derivatives()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ evaluate_dp()

◆ fit_closed()

◆ fit_open() [1/2]

◆ fit_open() [2/2]

◆ fit_open2()

◆ length()

◆ mode()

◆ param_from_length()

◆ range()

◆ read_knots()

◆ read_weights()

◆ resample()

◆ reverse()

◆ set_range()

◆ span()

◆ split()

◆ write_knots()

◆ write_weights()

Member Data Documentation

◆ default_value