Base class for 3D curves. More...

Inheritance diagram for cadex.Geom.Curve:

Public Member Functions
	Curve (global::System.IntPtr cPtr, bool cMemoryOwn)

cadex.Geom.CurveType	Type ()

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

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

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

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

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

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

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

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

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

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

void	Transform (cadex.Geom.Transformation theTransformation)
	Applies transformation matrix to this object.

cadex.Geom.Curve	Transformed (cadex.Geom.Transformation theTransformation)
	Returns a copy this object after applying transformation.

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

void	D1 (double theParameter, cadex.Geom.Point theValue, cadex.Geom.Vector theD1)

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

bool	DN (double theParameter, uint theDerivativeOrder, cadex.Geom.Point theValue, cadex.Collections.VectorList theD)

void	Mirror (cadex.Geom.Point thePoint)

void	Mirror (cadex.Geom.Axis1d theAxis)

void	Mirror (cadex.Geom.Axis3d theAxis)

cadex.Geom.Curve	Mirrored (cadex.Geom.Point theRef)

cadex.Geom.Curve	Mirrored (cadex.Geom.Axis1d theAxis)

cadex.Geom.Curve	Mirrored (cadex.Geom.Axis3d theAxis)

void	Rotate (cadex.Geom.Axis1d theAxis, double theAngle)

cadex.Geom.Curve	Rotated (cadex.Geom.Axis1d theAxis, double theAngle)

void	Translate (cadex.Geom.Vector theVector)

cadex.Geom.Curve	Translated (cadex.Geom.Vector theVector)

void	Scale (cadex.Geom.Point thePoint, double theScale)

cadex.Geom.Curve	Scaled (cadex.Geom.Point thePoint, double theScale)

Public Member Functions inherited from cadex.Geom.Geometry
	Geometry (global::System.IntPtr cPtr, bool cMemoryOwn)

Public Member Functions inherited from cadex.BaseObject
	BaseObject (global::System.IntPtr cPtr, bool cMemoryOwn)

void	Dispose ()

bool	IsNull ()

ulong	Id ()
	Return unique identifier of public object.

bool	IsEqual (cadex.BaseObject theObj)

override int	GetHashCode ()

override bool	Equals (System.Object o)

Static Public Member Functions
static new bool	CompareType (cadex.BaseObject theObject)

static cadex.Geom.Curve	Cast (cadex.Geom.Geometry theBase)

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

static cadex.Geom.Geometry	Cast (cadex.BaseObject theBase)

Protected Member Functions
override void	Dispose (bool disposing)

Protected Member Functions inherited from cadex.Geom.Geometry
override void	Dispose (bool disposing)

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.cs:28

cadex.Geom.Point

Defines a 3D point.

Definition Point.cs:17

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.

Examples: exploring/brep_geometry/Program.cs, exploring/brep_geometry/main.cxx, exploring/brep_topology/Program.cs, and exploring/brep_topology/main.cxx.

Member Function Documentation

◆ D0()

void cadex.Geom.Curve.D0	(	double	theParameter,
		cadex.Geom.Point	theValue )

inline

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.

◆ D2()

void cadex.Geom.Curve.D2	(	double	theParameter,
		cadex.Geom.Point	theValue,
		cadex.Geom.Vector	theD1,
		cadex.Geom.Vector	theD2 )

inline

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

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

◆ Dispose()

override void cadex.Geom.Curve.Dispose ( bool disposing )

inlineprotectedvirtual

Reimplemented from cadex.BaseObject.

◆ DN()

bool cadex.Geom.Curve.DN	(	double	theParameter,
		uint	theDerivativeOrder,
		cadex.Geom.Point	theValue,
		cadex.Collections.VectorList	theD )

inline

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	(	out double	theUMin,
		out double	theUMax )

inline

Returns a definition domain.

See also: UMin(), UMax().

◆ Transform()

void cadex.Geom.Curve.Transform ( cadex.Geom.Transformation theTransformation )

inline

Applies transformation matrix to this object.

Results depends on the actual curve type.

See also: Transformed().

◆ Transformed()

cadex.Geom.Curve cadex.Geom.Curve.Transformed ( cadex.Geom.Transformation theTransformation )

inline

Returns a copy this object after applying transformation.

The contents of this object is not modified.

See also: Transform().

◆ Type()

cadex.Geom.CurveType cadex.Geom.Curve.Type ( )

inline

Returns a curve type.

Examples: exploring/brep_geometry/Program.cs, exploring/brep_geometry/main.cxx, exploring/brep_topology/Program.cs, and exploring/brep_topology/main.cxx.

◆ UMax()

double cadex.Geom.Curve.UMax ( )

inline

Returns a maximum parameter of a definition domain.

See also: UMin(), Domain().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ UMin()

double cadex.Geom.Curve.UMin ( )

inline

Returns a minimum parameter of a definition domain.

See also: UMax(), Domain().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Value()

cadex.Geom.Point cadex.Geom.Curve.Value ( double theParameter )

inline

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

Detailed Description

Types

Parametric Definition

Evaluation

Continuity

Transformation

Member Function Documentation

◆ D0()

◆ D2()

◆ Dispose()

◆ DN()

◆ Domain()

◆ Transform()

◆ Transformed()

◆ Type()

◆ UMax()

◆ UMin()

◆ Value()