Abstract base class for parametric curves. More...

#include <Curve.h>

Inherits SFCGAL::GeometryImpl< Derived, Base >.

Inherited by SFCGAL::GeometryImpl< NURBSCurve, Curve >.

Public Types
enum	Continuity : std::uint8_t { Continuity::C0, Continuity::C1, Continuity::C2, Continuity::G1, Continuity::G2 }
	Curve continuity types. More...

using	FT = Kernel::FT
	Floating-point type for curve calculations. More...

using	Parameter = FT
	Parameter type for curve parameterization. More...

Public Member Functions
	Curve ()
	Default constructor. More...

	Curve (const Curve &other)
	Copy constructor. More...

auto	operator= (const Curve &other) -> Curve &
	Assignment operator. More...

	~Curve () override
	Virtual destructor. More...

auto	dimension () const -> int override
	Return the topological dimension of this geometry. More...

auto	coordinateDimension () const -> int override
	Return the coordinate dimension of the curve. More...

virtual auto	evaluate (Parameter parameter) const -> Point=0
	Evaluate the curve at parameter value. More...

virtual auto	derivative (Parameter parameter, unsigned int order=1) const -> Point=0
	Compute the derivative of the curve at parameter value. More...

virtual auto	tangent (Parameter parameter) const -> Point=0
	Compute the tangent unit vector at parameter value. More...

virtual auto	normal (Parameter parameter) const -> Point=0
	Compute the normal vector at parameter value (for planar curves) More...

virtual auto	binormal (Parameter parameter) const -> Point=0
	Compute the binormal vector at parameter value (for 3D curves) More...

virtual auto	curvature (Parameter parameter) const -> FT=0
	Compute the curvature at parameter value. More...

virtual auto	torsion (Parameter parameter) const -> FT=0
	Compute the torsion at parameter value (for 3D curves) More...

virtual auto	frenetFrame (Parameter parameter) const -> std::tuple< Point, Point, Point >=0
	Get the Frenet-Serret frame at parameter value. More...

virtual auto	toLineString (unsigned int numSegments=32) const -> std::unique_ptr< LineString >=0
	Convert curve to a LineString approximation. More...

virtual auto	toLineStringAdaptive (FT tolerance=FT(1e-3), unsigned int minSegments=8, unsigned int maxSegments=256) const -> std::unique_ptr< LineString >=0
	Convert curve to LineString with adaptive sampling. More...

virtual auto	parameterBounds () const -> std::pair< Parameter, Parameter >=0
	Get the parameter bounds of the curve. More...

virtual auto	isPeriodic () const -> bool=0
	Check if the curve is periodic. More...

virtual auto	isPlanar (std::vector< FT > *plane=nullptr) const -> bool=0
	Check if the curve is planar. More...

virtual auto	isLinear () const -> bool=0
	Check if the curve is linear (straight line) More...

virtual auto	degree () const -> unsigned int=0
	Get the degree of the curve. More...

virtual auto	length (Parameter from=Parameter(-1), Parameter to=Parameter(-1), FT tolerance=FT(1e-6)) const -> FT=0
	Get the curve length. More...

virtual auto	parameterAtLength (FT arcLength, FT tolerance=FT(1e-6)) const -> Parameter=0
	Find parameter value at given arc length from start. More...

virtual auto	reparameterizeByArcLength () const -> std::unique_ptr< Curve >=0
	Reparameterize curve by arc length. More...

virtual auto	split (Parameter parameter) const -> std::pair< std::unique_ptr< Curve >, std::unique_ptr< Curve >>=0
	Split curve at parameter value. More...

virtual auto	subcurve (Parameter from, Parameter to) const -> std::unique_ptr< Curve >=0
	Extract subcurve between two parameters. More...

virtual auto	reverse () const -> std::unique_ptr< Curve >=0
	Reverse the curve direction. More...

virtual auto	join (const Curve &other, Continuity continuity=Continuity::C0, FT tolerance=FT(1e-6)) const -> std::unique_ptr< Curve >=0
	Join with another curve. More...

virtual auto	closestPoint (const Point &point, Parameter *parameter=nullptr) const -> Point=0
	Project point onto curve. More...

virtual auto	numControlPoints () const -> size_t
	Get number of control points. More...

virtual auto	isRational () const -> bool
	Check if curve uses non-uniform rational weights. More...

virtual auto	weight (size_t index) const -> FT
	Return the rational weight of the curve's control point at the given index. More...

virtual auto	controlPointN (size_t index) const -> const Point &
	Return a read-only reference to the control point at the given index. More...

virtual auto	controlPointN (size_t index) -> Point &
	Return a modifiable reference to the control point at the given index. More...

auto	startPoint () const -> Point
	Get the start point of the curve. More...

auto	endPoint () const -> Point
	Get the end point of the curve. More...

auto	midPoint () const -> Point
	Get the midpoint of the curve. More...

auto	isValidParameter (const Parameter &parameter) const -> bool
	Check if a parameter value is within curve bounds. More...

auto	normalizeParameter (const Parameter &parameter) const -> FT
	Normalize parameter to [0,1] range. More...

auto	denormalizeParameter (const FT &normalizedParameter) const -> Parameter
	Denormalize parameter from [0,1] to actual range. More...

Detailed Description

Abstract base class for parametric curves.

This class provides a common interface for parametric curves. All curves are represented as NURBS (Non-Uniform Rational B-Splines) which can degenerate to B-splines (uniform weights) or Bezier curves.

Since: 2.3.0

Member Typedef Documentation

using SFCGAL::Curve::FT = Kernel::FT

Floating-point type for curve calculations.

using SFCGAL::Curve::Parameter = FT

Parameter type for curve parameterization.

Member Enumeration Documentation

enum SFCGAL::Curve::Continuity : std::uint8_t

strong

Curve continuity types.

Enumerator
C0	Position continuity (sharp corners allowed)
C1	Tangent continuity.
C2	Curvature continuity.
G1	Geometric tangent continuity.
G2	Geometric curvature continuity.

Constructor & Destructor Documentation

SFCGAL::Curve::Curve ( )

default

Default constructor.

SFCGAL::Curve::Curve ( const Curve & other )

default

Copy constructor.

Parameters

other Curve to copy from

SFCGAL::Curve::~Curve ( )

overridedefault

Virtual destructor.

Member Function Documentation

virtual auto SFCGAL::Curve::binormal ( Parameter parameter ) const -> Point

pure virtual

Compute the binormal vector at parameter value (for 3D curves)

Parameters

parameter Parameter value

Returns: Binormal vector (tangent × normal)

virtual auto SFCGAL::Curve::closestPoint	(	const Point &	point,
		Parameter *	parameter = `nullptr`
	)		const -> Point

pure virtual

Project point onto curve.

Parameters

point	Point to project
parameter	Output parameter at closest point

Returns: Closest point on curve

virtual auto SFCGAL::Curve::controlPointN ( size_t index ) const -> const Point &

inlinevirtual

Return a read-only reference to the control point at the given index.

This method is part of the NURBS-specific interface. The base implementation always throws an Exception to indicate the operation is not supported for curve types that do not expose control points.

Parameters

index Index of the control point.

Returns: Const reference to the control point at index.

Exceptions

Exception if the curve type does not support control points or if index is out of range for implementations that override this method.

virtual auto SFCGAL::Curve::controlPointN ( size_t index ) -> Point &

inlinevirtual

Return a modifiable reference to the control point at the given index.

Concrete NURBS-style curve implementations should override this to provide writable access to their control points. The base implementation throws an Exception indicating the operation is not supported for this curve type.

Parameters

index Zero-based control point index.

Returns: Reference to the control point that can be modified.

Exceptions

Exception If the curve type does not support control point access or if index is out of range.

auto SFCGAL::Curve::coordinateDimension ( ) const -> int

inlineoverride

Return the coordinate dimension of the curve.

Computes 2 for non-3D curves or 3 for 3D curves, and adds 1 if the curve is measured.

Returns: Coordinate dimension (2 or 3, plus 1 when measured).

virtual auto SFCGAL::Curve::curvature ( Parameter parameter ) const -> FT

pure virtual

Compute the curvature at parameter value.

Parameters

parameter Parameter value

Returns: Curvature value (1/radius of curvature)

virtual auto SFCGAL::Curve::degree ( ) const -> unsigned int

pure virtual

Get the degree of the curve.

Returns: Polynomial degree

auto SFCGAL::Curve::denormalizeParameter ( const FT & normalizedParameter ) const -> Parameter

Denormalize parameter from [0,1] to actual range.

Parameters

normalizedParameter Parameter in [0,1]

Returns: Actual parameter value

virtual auto SFCGAL::Curve::derivative	(	Parameter	parameter,
		unsigned int	order = `1`
	)		const -> Point

pure virtual

Compute the derivative of the curve at parameter value.

Parameters

parameter	Parameter value
order	Derivative order (1 for first derivative, 2 for second, etc.)

Returns: Vector representing the derivative at parameter

auto SFCGAL::Curve::dimension ( ) const -> int

inlineoverride

Return the topological dimension of this geometry.

For Curve objects this is always 1.

Returns: The integer dimension (always 1 for curves).

auto SFCGAL::Curve::endPoint ( ) const -> Point

Get the end point of the curve.

Returns: Last point of the curve

virtual auto SFCGAL::Curve::evaluate ( Parameter parameter ) const -> Point

pure virtual

Evaluate the curve at parameter value.

Parameters

parameter Parameter value (usually in [tMin, tMax])

Returns: Point on the curve at parameter

Exceptions

Exception if parameter is outside valid range

virtual auto SFCGAL::Curve::frenetFrame ( Parameter parameter ) const -> std::tuple< Point, Point, Point >

pure virtual

Get the Frenet-Serret frame at parameter value.

Parameters

parameter Parameter value

Returns: Tuple of (tangent, normal, binormal) vectors

virtual auto SFCGAL::Curve::isLinear ( ) const -> bool

pure virtual

Check if the curve is linear (straight line)

Returns: true if curve is a straight line segment

virtual auto SFCGAL::Curve::isPeriodic ( ) const -> bool

pure virtual

Check if the curve is periodic.

Returns: true if curve has periodic parameterization

virtual auto SFCGAL::Curve::isPlanar ( std::vector< FT > * plane = nullptr ) const -> bool

pure virtual

Check if the curve is planar.

Parameters

plane Output parameter for the plane equation if planar

Returns: true if curve lies in a plane

virtual auto SFCGAL::Curve::isRational ( ) const -> bool

inlinevirtual

Check if curve uses non-uniform rational weights.

Returns: false for non-NURBS curves, true if NURBS with varying weights

Exceptions

Exception if not implemented for curve type

auto SFCGAL::Curve::isValidParameter ( const Parameter & parameter ) const -> bool

Check if a parameter value is within curve bounds.

Parameters

parameter Parameter to check

Returns: true if parameter is valid for this curve

virtual auto SFCGAL::Curve::join	(	const Curve &	other,
		Continuity	continuity = `Continuity::C0`,
		FT	tolerance = `FT(1e-6)`
	)		const -> std::unique_ptr< Curve >

pure virtual

Join with another curve.

Parameters

other	Curve to join with
continuity	Desired continuity at join
tolerance	Tolerance for join

Returns: Joined curve or nullptr if join impossible

virtual auto SFCGAL::Curve::length	(	Parameter	from = `Parameter(-1)`,
		Parameter	to = `Parameter(-1)`,
		FT	tolerance = `FT(1e-6)`
	)		const -> FT

pure virtual

Get the curve length.

Parameters

from	Start parameter (default: curve start)
to	End parameter (default: curve end)
tolerance	Integration tolerance

Returns: Arc length between parameters

auto SFCGAL::Curve::midPoint ( ) const -> Point

Get the midpoint of the curve.

Returns: Point at middle parameter value

virtual auto SFCGAL::Curve::normal ( Parameter parameter ) const -> Point

pure virtual

Compute the normal vector at parameter value (for planar curves)

Parameters

parameter Parameter value

Returns: Normal vector perpendicular to tangent

auto SFCGAL::Curve::normalizeParameter ( const Parameter & parameter ) const -> FT

Normalize parameter to [0,1] range.

Parameters

parameter Raw parameter value

Returns: Normalized parameter in [0,1]

virtual auto SFCGAL::Curve::numControlPoints ( ) const -> size_t

inlinevirtual

Get number of control points.

Returns: Control point count

Exceptions

Exception if not implemented for curve type

auto SFCGAL::Curve::operator= ( const Curve & other ) -> Curve &

default

Assignment operator.

Parameters

other Curve to assign from

Returns: Reference to this curve

virtual auto SFCGAL::Curve::parameterAtLength	(	FT	arcLength,
		FT	tolerance = `FT(1e-6)`
	)		const -> Parameter

pure virtual

Find parameter value at given arc length from start.

Parameters

arcLength	Target arc length from curve start
tolerance	Tolerance for root finding

Returns: Parameter value at specified arc length

virtual auto SFCGAL::Curve::parameterBounds ( ) const -> std::pair< Parameter, Parameter >

pure virtual

Get the parameter bounds of the curve.

Returns: Pair containing (minParameter, maxParameter)

virtual auto SFCGAL::Curve::reparameterizeByArcLength ( ) const -> std::unique_ptr< Curve >

pure virtual

Reparameterize curve by arc length.

Returns: New curve parameterized by arc length [0, totalLength]

virtual auto SFCGAL::Curve::reverse ( ) const -> std::unique_ptr< Curve >

pure virtual

Reverse the curve direction.

Returns: Reversed curve

virtual auto SFCGAL::Curve::split ( Parameter parameter ) const -> std::pair< std::unique_ptr< Curve >, std::unique_ptr< Curve >>

pure virtual

Split curve at parameter value.

Parameters

parameter Split location

Returns: Pair of curves (before split, after split)

auto SFCGAL::Curve::startPoint ( ) const -> Point

Get the start point of the curve.

Returns: First point of the curve

virtual auto SFCGAL::Curve::subcurve	(	Parameter	from,
		Parameter	to
	)		const -> std::unique_ptr< Curve >

pure virtual

Extract subcurve between two parameters.

Parameters

from	Start parameter
to	End parameter

Returns: Subcurve between parameters

virtual auto SFCGAL::Curve::tangent ( Parameter parameter ) const -> Point

pure virtual

Compute the tangent unit vector at parameter value.

Parameters

parameter Parameter value

Returns: Normalized tangent vector

virtual auto SFCGAL::Curve::toLineString ( unsigned int numSegments = 32 ) const -> std::unique_ptr< LineString >

pure virtual

Convert curve to a LineString approximation.

Parameters

numSegments Number of line segments to use

Returns: LineString approximating the curve

virtual auto SFCGAL::Curve::toLineStringAdaptive	(	FT	tolerance = `FT(1e-3)`,
		unsigned int	minSegments = `8`,
		unsigned int	maxSegments = `256`
	)		const -> std::unique_ptr< LineString >

pure virtual

Convert curve to LineString with adaptive sampling.

Parameters

tolerance	Maximum deviation from actual curve
minSegments	Minimum number of segments
maxSegments	Maximum number of segments

Returns: Adaptively sampled LineString

virtual auto SFCGAL::Curve::torsion ( Parameter parameter ) const -> FT

pure virtual

Compute the torsion at parameter value (for 3D curves)

Parameters

parameter Parameter value

Returns: Torsion value (measure of curve twisting)

virtual auto SFCGAL::Curve::weight ( size_t index ) const -> FT

inlinevirtual

Return the rational weight of the curve's control point at the given index.

Default implementation throws an Exception indicating that weight access is not supported for this curve type; concrete NURBS-derived classes must override to provide valid weights.

Parameters

index Index of the control point weight.

Returns: Weight value associated with the control point.

Exceptions

Exception if this curve type does not support weights or if the index is out of range.

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation