Base class for 3D curves. More...

#include <cadex/Geom/Curve.hxx>

Inheritance diagram for cadex::Geom::Curve:

Public Member Functions
	Curve ()
	Constructor.

CurveType	Type () const

Geom::Continuity	Continuity () const
	Returns a continuity type of the curve.

Point	Value (double theParameter) const
	Evaluates a point on the curve.

Direction	Normal (double theParameter) const
	Returns the normal direction theNormal of parameter theParam.

double	Curvature (double theParameter) const
	Returns the curvature value of parameter theParam.

bool	IsPeriodic () const
	Returns true if the curve is periodic.

double	UMin () const
	Returns a minimum parameter of a definition domain.

double	UMax () const
	Returns a maximum parameter of a definition domain.

void	Domain (double &theUMin, double &theUMax) const
	Returns a definition domain.

bool	IsTrimmed () const
	Returns whether curve is trimmed or not.

void	SetTrim (double theFirst, double theLast)
	Trims curve with [theFirst, theLast] section.

void	Transform (const Transformation &theTransformation)
	Applies transformation matrix to this object.

Curve	Transformed (const Transformation &theTransformation) const
	Returns a copy this object after applying transformation.

void	D0 (double theParameter, Point &theValue) const
	Returns the point theValue of parameter theParam.

void	D1 (double theParameter, Point &theValue, Vector &theD1) const
	Returns the point theValue of parameter theParam and the first derivative theD1.

void	D2 (double theParameter, Point &theValue, Vector &theD1, Vector &theD2) const
	Returns the point theValue of parameter theParam, the first theD1 and second theD2 derivatives.

bool	DN (double theParameter, size_t theDerivativeOrder, Geom::Point &theValue, std::vector< Geom::Vector > &theD) const

void	Mirror (const Point &thePoint)

void	Mirror (const Axis1d &theAxis)

void	Mirror (const Axis3d &theAxis)

Curve	Mirrored (const Point &theRef) const

Curve	Mirrored (const Axis1d &theAxis) const

Curve	Mirrored (const Axis3d &theAxis) const

void	Rotate (const Axis1d &theAxis, double theAngle)

Curve	Rotated (const Axis1d &theAxis, double theAngle) const

void	Translate (const Vector &theVector)

Curve	Translated (const Vector &theVector) const

void	Scale (const Point &thePoint, double theScale)

Curve	Scaled (const Point &thePoint, double theScale) const

Public Member Functions inherited from cadex::BaseObject
size_t	Id () const
	Return unique identifier of public object.

internal::BaseObjectImpl *	Impl () const

bool	IsNull () const

	operator bool () const

template<typename T >
bool	IsOfType () const

template<typename T >
T *	Impl () const
	Reserved for internal use.

Static Public Member Functions
static bool	CompareType (const BaseObject &theObject)

Static Public Member Functions inherited from cadex::Geom::Geometry
static bool	CompareType (const BaseObject &theObject)

Protected Member Functions
	Curve (const ImplType &theImpl)

Protected Member Functions inherited from cadex::Geom::Geometry
	Geometry (const ImplType &theImpl)

Protected Member Functions inherited from cadex::BaseObject
	BaseObject (const ImplType &theImpl)

Additional Inherited Members
Public Types inherited from cadex::BaseObject
typedef std::shared_ptr< internal::BaseObjectImpl >	ImplType

Detailed Description

Base class for 3D curves.

3D curves are used to represent curves in 3D space. Each non-degenerated edge must refer to a 3D curve.

Types

Refer to Curve Types for the list of supported curve types. Type() returns a curve type as enumeration value which can be used to downcast to a respective subclass type, for instance:

Curve aCurve = ...;
if (aCurve.Type() == Geom::CurveType::Circle) {
    const Circle& aCircle = static_cast<const Circle&> (aCurve);
    double aRadius = aCircle.Radius();
    ...
}

Parametric Definition

Curve is defined using parametric definition as \(\mathbf{C}(t)\) where \(\mathbf{C}\) is a 3D radius-vector \((x,y,z)^\top\) and \(t\) is a parameter from a definition range \([a, b]\).

UMin() and UMax(), and Domain() return parametric definition range. Parametric range can be bounded (e.g. \([0, 2\pi]\) for a circle) or unbounded (e.g. \((-\infty, +\infty)\) for a line).

Evaluation

At any parameter \(t\) within a definition range, the curve can be evaluated as follows:

Value() and D0() return a 3D point;
D1(), D2() and DN() return a derivative of a respective order;
Curvature() returns a curvature;
Normal() returns a normal to the curve (i.e. perpendicular to its first derivative).

The following example demonstrates computation of a point on a line at parameter t=2:

Line aLine = ...;

Point aPoint = aLine.Value (2.);

cadex::Geom::Line

Defines 3D line.

Definition Line.hxx:31

cadex::Geom::Point

Defines a 3D point.

Definition Point.hxx:35

If the curve is periodic (IsPeriodic() returns true) then the curve can be evaluated at any parameter t, otherwise behavior is undefined (e.g. an exception can be thrown or a weird value can be returned).

Continuity

Continuity() returns continuity ( \(C^0\), \(C^1\), \(C^2\), \(C^N\)) of the curve, where \(C^0\) that only the curve itself is continuous, \(C^1\) - that the curve is continuous together with its first derivative, and so on.

Transformation

The curve can be modified using the following operations:

translation (Translate() and Translated());
rotation (Rotate() and Rotated());
mirroring (Mirror() and Mirrored());
scaling (Scale() and Scaled());
arbitrary transformation using 3x4 matrix (Transform() and Transformed()).
Reversed() returns a curve with opposite orientation.

Warning: As the curve data is shared via internal pointer modification of the curve may affect other users of the curve (e.g. an edge referring to it). So you might want to use method returning a modified copy of the curve (such as Transformed()).

See also: Curves, Curve2d, ModelData::Edge, Surface.

Member Function Documentation

◆ D0()

void cadex::Geom::Curve::D0	(	double	theParameter,
		Point &	theValue ) const

Returns the point theValue of parameter theParam.

Throws exception only for the OffsetCurve if it is not possible to compute the current point. For example when the first derivative on the basis curve and the offset direction are parallel.

◆ D1()

void cadex::Geom::Curve::D1	(	double	theParameter,
		Point &	theValue,
		Vector &	theD1 ) const

Returns the point theValue of parameter theParam and the first derivative theD1.

Throws exception if the continuity of the curve is not \(C^1\).

◆ D2()

void cadex::Geom::Curve::D2	(	double	theParameter,
		Point &	theValue,
		Vector &	theD1,
		Vector &	theD2 ) const

Returns the point theValue of parameter theParam, the first theD1 and second theD2 derivatives.

Throws exception if the continuity of the curve is not \(C^2\).

◆ DN()

bool cadex::Geom::Curve::DN	(	double	theParameter,
		size_t	theDerivativeOrder,
		Geom::Point &	theValue,
		std::vector< Geom::Vector > &	theD ) const

Returns true if calculation completed successfully. In this case theD contains values of the derivatives from 0 up to theDerivativeOrder. Otherwise returns false. May throw exception if the continuity of the curve is less than theDerivativeOrder.

Parameters:

theDerivativeOrder must belong to range [0, 3].
theD should have size to store theDerivativeOrder derivatives (i.e. theDerivativeOrder or more).

◆ Domain()

void cadex::Geom::Curve::Domain	(	double &	theUMin,
		double &	theUMax ) const

Returns a definition domain.

See also: UMin(), UMax().

◆ Transform()

void cadex::Geom::Curve::Transform ( const Transformation & theTransformation )

Applies transformation matrix to this object.

Results depends on the actual curve type.

See also: Transformed().

◆ Transformed()

Curve cadex::Geom::Curve::Transformed ( const Transformation & theTransformation ) const

Returns a copy this object after applying transformation.

The contents of this object is not modified.

See also: Transform().

◆ Type()

CurveType cadex::Geom::Curve::Type ( ) const

Returns a curve type.

◆ UMax()

double cadex::Geom::Curve::UMax ( ) const

Returns a maximum parameter of a definition domain.

See also: UMin(), Domain().

◆ UMin()

double cadex::Geom::Curve::UMin ( ) const

Returns a minimum parameter of a definition domain.

See also: UMax(), Domain().

◆ Value()

Point cadex::Geom::Curve::Value ( double theParameter ) const

Evaluates a point on the curve.

theParameter must be within Domain() if the curve is not periodic.

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members