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GeometricObjects Interface CATCurve

Usage: an implementation of this interface is supplied and you must use it as is. You should not reimplement it.

interface CATCurve

Interface representing the base class for all curves.
Each point of a curve is identified by a global parameter CATCrvParam. A curve portion is defined by CATCrvLimits. Curve parameterization
The geometric modeler optimal behavior requires arc length parameterized (or nearly arc length parameterized) curves. Standard operators generate arc length parameterized curves and complete properly when their input data are arc length parameterized curves. Non-standard curves (foreign curves) should be created as arc length parameterized curves.
Retrieving the CATCrvParam of a 3D point located on a curve
To retrieve the curve parameter associated with a 3D point, use a geometric projection operator. Retrieving the point and derivatives from a CATCrvParam
Multiple evaluations can be performed in one way by defining a CATCrvCommand object, evaluating through the Eval method and retrieving the results with a CATCrvEvalResult object. Example:

 CATCrvEvalLocal EvalResult;
 CATCrvParam Parameter ;
 Curve->GetStartLimit(Parameter) ;
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalPoint                , EvalResult) ; // Evaluate point
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalFirstDerivative      , EvalResult) ; // Evaluate first  derivative
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalSecondDerivative     , EvalResult) ; // Evaluate second derivative
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalThirdDerivative      , EvalResult) ; // Evaluate third  derivative
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalUpToFirstDerivative  , EvalResult) ; // Evaluate all    derivatives up to first  derivative 
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalUpToSecondDerivative , EvalResult) ; // Evaluate all    derivatives up to second derivative 
 Curve->Eval(Parameter, CATCrvEvalCommand::EvalUpToThirdDerivative  , EvalResult) ; // Evaluate all    derivatives up to third  derivative

The first and last arc number can be retrieved with the GetMaxLimits method.

Method Index

o CreateParam(double&): Sets a global parameter on this CATCurve.
o CreateParam(double,CATCrvParam&): Sets a global parameter on this CATCurve.
o CreateParam(double&,CATLONG32&): Sets a global parameter on a CATCurve from a local parameter and an arc number.
o CreateParam(double,CATLONG32,CATCrvParam&): Sets a global parameter on a CATCurve from a local parameter and an arc number.
o Eval(CATCrvParam&,CATCrvEvalCommand&,CATCrvEvalLocal&): Evaluates this CATCurve and its derivatives associated with this CATCrvParam.
o Eval(CATCrvLimits&,CATLONG32,CATCrvEvalCommand&,CATCrvEvalResult&): Evaluates this CATCurve and its derivatives inside a domain.
o Eval(CATCrvParam&,CATCrvEvalCommand&,CATMathPoint*,CATMathVector*,CATMathVector*,CATMathVector*): Evaluates this CATCurve and its derivatives associated with this CATCrvParam.
o EvalFirstDeriv(CATCrvParam&): Evaluates this CATCurve by computing a first derivative from a CATCrvParam.
o EvalPoint(CATCrvParam&): Evaluates this CATCurve by computing a CATMathPoint from a CATCrvParam.
o EvalSecondDeriv(CATCrvParam&): Evaluates this CATCurve by computing a second derivative from a CATCrvParam.
o EvalThirdDeriv(CATCrvParam&): Evaluates this CATCurve by computing a third derivative from a CATCrvParam.
o GetBox(CATCrvLimits&,CATMathBox&): Computes the bounding box of this CATCurve trimmed by given Limits.
o GetEndLimit(): Returns the high current limitation of this CATCurve.
o GetEndLimit(CATCrvParam&): Returns the high current limitation of this CATCurve.
o GetEquation(CATLONG32,CATMathFunctionX*&,CATMathFunctionX*&,CATMathFunctionX*&): Retrieves the mathematical equation associated with an arc of this CATCurve.
o GetGeometricRep(CATCrvLimits&,short&): Returns a pointer to the geometric representation of this CATCurve.
o GetGlobalEquation(CATMathFunctionX*&,CATMathFunctionX*&,CATMathFunctionX*&): Retrieves the mathematical equation associated with this CATCurve.
o GetInternalBoundingBox(CATLONG32,CATMathBox&): Retrieves the bounding box including an arc of this CATCurve.
o GetInternalLimits(CATLONG32,CATCrvLimits&): Returns the limitations of an arc of this CATCurve.
o GetInternalMaxBoundingBox(CATLONG32,CATMathBox&): Retrieves the maximum bounding box including an arc of this CATCurve.
o GetInternalMaxLimits(CATLONG32,CATCrvLimits&): Returns the limitations of an arc of this CATCurve.
o GetKnotVector(): Returns the knot vector associated with this CATCurve.
o GetLimits(): Returns the limitations of this CATCurve.
o GetLimits(CATCrvLimits&): Returns the current limits of this CATCurve.
o GetMathCurve(): Returns a pointer to the mathematical representation of this CATCurve.
o GetMaxLimits(): Returns the maximum limitations of this CATCurve.
o GetMaxLimits(CATCrvLimits&): Returns the maximum limitations of this CATCurve.
o GetParam(CATMathPoint&,CATCrvParam&): Retrieves the CATCrvParam on this CATCurve corresponding to a given CATMathPoint.
o GetParam(CATMathPoint&,CATCrvParam&,CATCrvLimits&): Retrieves the CATCrvParam on this CATCurve corresponding to a CATMathPoint inside limitations.
o GetStartLimit(): Returns the low current limitation of this CATCurve.
o GetStartLimit(CATCrvParam&): Returns the low current limitation of this CATCurve.
o HasMathCurve(): Tests whether this CATCurve has a mathematical representation.
o IsClosed(): Tests whether this CATCurve is periodic.
o IsConfused(CATMathTransformation&,CATCurve*,CATMathTransformation1D*): Tests whether this CATCurve is confused with another curve.
o IsContaining(CATCurve*): Tests whether this CATCurve is containing another one.
o IsInvariant(CATMathTransformation&,CATMathTransformation1D*): Tests whether this CATCurve is invariant.
o Lock(): Locks the equations of this CATCurve before read them.
o SetLimits(CATCrvLimits&): Modifies the limitations of this CATCurve.
o Unlock(): Unlocks the equations of this CATCurve after read them.

o CATSolutionDiagnostic: The diagnosis of evaluation.

Methods

o CreateParam

public virtual CreateParam( const iGlobalParam)

Sets a global parameter on this CATCurve. This API can lead to bad performances when it is used intensively.

The CATCurve::CreateParam signature which returns a void (see above) should be preferred over the present signature.

Parameters:

iGlobalParam: The value of the global parameter.

Returns:

ioParam The corresponding parameter on this, valuated with iGlobalParam.

o CreateParam

public virtual CreateParam(	const	`iGlobalParam`,
		`ioParam`)

Sets a global parameter on this CATCurve.

Parameters:

iGlobalParam: The value of the global parameter.
ioParam: The corresponding parameter on this, valuated with iGlobalParam.

o CreateParam

public virtual CreateParam(	const	`iLocal`,
	const	`iArc`)

Sets a global parameter on a CATCurve from a local parameter and an arc number. This API can lead to bad performances when it is used intensively.

The CATCurve::CreateParam signature which returns a void (see above) should be preferred over the present signature.

Parameters:

iLocal: The value of the local parameter.
iArc: The arc number.

Returns:

The corresponding parameter on this, valuated with iGlobalParam.

o CreateParam

public virtual CreateParam(	const	`iLocal`,
	const	`iArc`,
		`ioParam`)

Sets a global parameter on a CATCurve from a local parameter and an arc number.

Parameters:

iLocal: The value of the local parameter.
iArc: The arc number.
ioParam: The corresponding parameter on this, valuated with iGlobalParam.

o Eval

public virtual Eval(	const	`iPoint`,
	const	`iCommand`,
		`ioResult`)

Evaluates this CATCurve and its derivatives associated with this CATCrvParam.

Parameters:

iPoint: The parameter of the point to evaluate.
iCommand: The type of evaluation.
ioResult.: The object containing the results.

o Eval

public virtual Eval(	const	`iDomainToEvaluate`,
	const	`iNbOfPoints`,
	const	`iCommand`,
		`ioResult`)

Evaluates this CATCurve and its derivatives inside a domain.

Parameters:

iDomainToEvaluate: The limits inside which the domain is to be evaluated.
iNbOfPoints: The number of equally spaced points of iDomainToEvaluate.
iCommand: The type of evaluation.
ioResult.: The object containing the results.

o Eval

public virtual Eval(	const	`iParam`,
	const	`iCommand`,
		`iPoint`,
		`iFirstDeriv`	`= NULL`,
		`iSecondDeriv`	`= NULL`,
		`iThirdDeriv`	`= NULL` )

Evaluates this CATCurve and its derivatives associated with this CATCrvParam.

Parameters:

iParam: The parameter of the point to evaluate.
iCommand: The type of evaluation. The corresponding output pointer must be allocated.
iPoint: A pointer to the resulting 3D point.
iFirstDeriv: A pointer to the resulting first derivative.
iSecondDeriv: A pointer to the resulting second derivative.
iThirdDeriv: A pointer to the resulting third derivative.

o EvalFirstDeriv

public virtual EvalFirstDeriv( const iParam)

Evaluates this CATCurve by computing a first derivative from a CATCrvParam.

The CATCurve::Eval signature with the CATCrvEvalCommand::EvalFirstDeriv argument should be preferred over CATCurve::EvalFirstDeriv as CATCurve::EvalFirstDeriv can lead to bad performances when it is used intensively.

Parameters:

iParam: The parameter of the vector to evaluate.

Returns:

CATMathVector The CATMathVector which has iParam as its parameter.

o EvalPoint

public virtual EvalPoint( const iParam)

Evaluates this CATCurve by computing a CATMathPoint from a CATCrvParam.

The CATCurve::Eval signature with the CATCrvEvalCommand::EvalPoint argument should be preferred over CATCurve::EvalPoint as CATCurve::EvalPoint can lead to bad performances when it is used intensively.

Parameters:

iParam: The parameter of the point to evaluate.

Returns:

CATMathPoint The CATMathPoint which has iParam as its parameter.

o EvalSecondDeriv

public virtual EvalSecondDeriv( const iParam)

Evaluates this CATCurve by computing a second derivative from a CATCrvParam.

The CATCurve::Eval signature with the CATCrvEvalCommand::EvalSecondDeriv argument should be preferred over CATCurve::EvalSecondDeriv as CATCurve::EvalSecondDeriv can lead to bad performances when it is used intensively.

Parameters:

iParam: The parameter of the vector to evaluate.

Returns:

CATMathVector The CATMathVector which has iParam as its parameter.

o EvalThirdDeriv

public virtual EvalThirdDeriv( const iParam)

Evaluates this CATCurve by computing a third derivative from a CATCrvParam.

The CATCurve::Eval signature with the CATCrvEvalCommand::EvalThirdDeriv argument should be preferred over CATCurve::EvalThirdDeriv as CATCurve::EvalThirdDeriv can lead to bad performances when it is used intensively.

Parameters:

iParam: The parameter of the vector to evaluate.

Returns:

CATMathVector The CATMathVector which has iParam as its parameter.

o GetBox

public virtual GetBox(	const	`iLimits`,
		`ioBox`)

Computes the bounding box of this CATCurve trimmed by given Limits.
This does not take into account the current limitations of the curve.

Parameters:

iLimits: The domain to take into account.
ioBox.: The 3D box.

o GetEndLimit

public virtual GetEndLimit(

)

Returns the high current limitation of this CATCurve. The CATCurve::GetEndLimit signature which returns a void should be preferred over the present API.

Returns:: The end limitation.

o GetEndLimit

public virtual GetEndLimit( ioEndParam)

Returns the high current limitation of this CATCurve.

Parameters:

ioEndParam: The end limitation.

o GetEquation

public virtual GetEquation(	const	`iArc`,
	const	`oFx`,
	const	`oFy`,
	const	`oFz`)

Retrieves the mathematical equation associated with an arc of this CATCurve.
Before retrieving the equations, you must Lock the curve. You can then obtained the equations. When you have finished, you Unlock the curve. The equations are then automatically deleted.

Parameters:

iArc: The arc number.
oFx: A pointer to the equation of the first coordinate X=oFx(w).
oFy: A pointer to the equation of the second coordinate Y=oFy(w).
oFz: A pointer to the equation of the third coordinate Z=oFy(w).

o GetGeometricRep

public virtual GetGeometricRep(		`ioRepLimits`,
		`ioRepOrientation`)

Returns a pointer to the geometric representation of this CATCurve.

Parameters:

ioRepLimits

The limitations of the returned curve.

ioRepOrientation

The relative orientation of the returned curve.
Legal values::

1: If the returned curve has the same orientation
-1: If the returned curve has the opposite orientation.

Returns:

The canonical underlying geometry.
This is usefull for CATEdgeCurves suc as CATSimCurves in order to access the underlying canonical geometry (such as CATCircle, CATLine,...). Returns this otherwise.

o GetGlobalEquation

public virtual GetGlobalEquation(	const	`oFx`,
	const	`oFy`,
	const	`oFz`)

Retrieves the mathematical equation associated with this CATCurve.
Before retrieving the equations, you must Lock the curve. You can then obtained the equations. When you have finished, you Unlock the curve. The equations are then automatically deleted.

Parameters:

oFx: A pointer to the equation of the first coordinate X=oFx(w).
oFy: A pointer to the equation of the second coordinate Y=oFy(w).
oFz: A pointer to the equation of the third coordinate Z=oFy(w).

o GetInternalBoundingBox

public virtual GetInternalBoundingBox(	const	`iArc`,
		`ioBox`)

Retrieves the bounding box including an arc of this CATCurve.
This takes into account the current limitations of the curve.

Parameters:

iArc: The arc number.
ioBox.: The 3D box.

o GetInternalLimits

public virtual GetInternalLimits(	const	`iArc`,
		`ioInternalMaxLimits`)

Returns the limitations of an arc of this CATCurve.
This takes into account the current limitations of the curve.

Parameters:

iArc: The arc number.
ioInternalMaxLimits: The corresponding limitations.

o GetInternalMaxBoundingBox

public virtual GetInternalMaxBoundingBox(	const	`iArc`,
		`ioBox`)

Retrieves the maximum bounding box including an arc of this CATCurve.
This does not take into account the current limitations of the curve.

Parameters:

iArc: The arc number.
ioBox.: The 3D box.

o GetInternalMaxLimits

public virtual GetInternalMaxLimits(	const	`iArc`,
		`ioInternalMaxLimits`)

Returns the limitations of an arc of this CATCurve.
This does not take into account the current limitations of the curve.

Parameters:

iArc: The arc number.
ioInternalMaxLimits: The corresponding limitations.

o GetKnotVector

public virtual GetKnotVector(

)

Returns the knot vector associated with this CATCurve.

Returns:: The knot vector.

o GetLimits

public virtual GetLimits(

)

Returns the limitations of this CATCurve. The CATCurve::GetLimits signature which returns a void should be preferred over the present API.

Returns:: The current limitations.

o GetLimits

public virtual GetLimits( ioCurrentLimits)

Returns the current limits of this CATCurve.

Parameters:

ioCurrentLimits: The current limits.

o GetMathCurve

public virtual GetMathCurve(

)

Returns a pointer to the mathematical representation of this CATCurve. The life cycle of the returned CATMathCurve must be managed by the calling application.

 CATMathCurve * pMathCurve = hCurve->GetMathCurve();
 if (pMathCurve)
   {
     ...
     delete pMathCurve; pMathCurve=NULL;
	 }

Returns:: The mathematical curve associated with this. If the mathematical representation does not exist, the method returns a NULL pointer.

o GetMaxLimits

public virtual GetMaxLimits(

)

Returns the maximum limitations of this CATCurve. The CATCurve::GetMaxLimits signature which returns a void should be preferred over the present API.

Returns:: The current limitations.

o GetMaxLimits

public virtual GetMaxLimits( ioMaxLimits)

Returns the maximum limitations of this CATCurve.
This does not take into account the current limitations of the curve. This maximum limits can be the creation limits or the limits that are obtained by extrapolation, depending on the types of geometric objects.

Parameters:

ioMaxLimits: The maximum limits.

o GetParam

public virtual GetParam(	const	`iPoint`,
		`ioParam`)

Retrieves the CATCrvParam on this CATCurve corresponding to a given CATMathPoint.
This transformation is only available on canonical objects such as planes, lines, conics.

Parameters:

iPoint: The CATMathPoint which coordinates are to be transformed as CATCrvParam.
ioParam: The first corresponding CATCrvParam on the curve.

Returns:

The diagnosis of the number of parameters that can be evaluated on this point.

o GetParam

public virtual GetParam(	const	`iPoint`,
		`ioParam`,
	const	`iInside`)

Retrieves the CATCrvParam on this CATCurve corresponding to a CATMathPoint inside limitations.
This transformation is only available on canonical objects such as lines and conics.

Parameters:

iPoint: The CATMathPoint whose coordinates are to be transformed as a CATCrvParam.
ioParam: The first corresponding CATCrvParam on the curve.
iInside: The CATCrvLimits to take into account for trimming the CATCurve.

Returns:

The diagnosis of the number of parameters that can be evaluated on this point.

o GetStartLimit

public virtual GetStartLimit(

)

Returns the low current limitation of this CATCurve. The CATCurve::GetStartLimit signature which returns a void should be preferred over the present API.

Returns:: The start limitation.

o GetStartLimit

public virtual GetStartLimit( ioStartParam)

Returns the low current limitation of this CATCurve.

Parameters:

ioStartParam: The first limitation.

o HasMathCurve

public virtual HasMathCurve(

)

Tests whether this CATCurve has a mathematical representation.

Returns:

The result of the test.
Legal values::

1: If this has a mathematical representation.
0: Otherwise.

o IsClosed

public virtual IsClosed(

)

Tests whether this CATCurve is periodic.
This method does not take into account the current limitations of the curve.

Returns:

The result of the test.
Legal values::

0: If the CATCurve is not periodic.
1: If the CATCurve is periodic.

o IsConfused

public virtual IsConfused(	const	`iTransfo`,
	const	`iTCurve`,
		`oTransfo1D`	`= NULL`)

Tests whether this CATCurve is confused with another curve.
This method does not take into account the current limitations of the curves.

Parameters:

oTransfo1D: The 1D-transformation defining the change of parametrization between the transformation of this and iTCurve. If NULL, this argument is not set.

Returns:

The result of the test.
Legal values::

1: If the transformation of this is geometrically the same as iTCurve.
0: Otherwise.

o IsContaining

public virtual IsContaining( const iOther)

Tests whether this CATCurve is containing another one.

Parameters:

iOther: The oother curve.

Returns:

The diagnosis of the test.

FALSE: if the CATCurve does not contain iOther
TRUE: if the CATCurve contains iOther

o IsInvariant

public virtual IsInvariant(	const	`iTransfo`,
		`oTransfo1D`	`= NULL`)

Tests whether this CATCurve is invariant.
This method does not take into account the current limitations of the curve.

Parameters:

oTransfo1D: The 1D-transformation defining the change of parametrization between this and the transformation of this. If NULL, this argument is not set.

Returns:

The result of the test.
Legal values::

1: If the transformation of this is geometrically the same as this.
0: Otherwise.

o Lock

public virtual Lock(

)

Locks the equations of this CATCurve before read them.

o SetLimits

public virtual SetLimits( const iLimits)

Modifies the limitations of this CATCurve.

Parameters:

iLimits: The new current limitations.

o Unlock

public virtual Unlock(

)

Unlocks the equations of this CATCurve after read them.

Enumerated Types

o CATSolutionDiagnostic

enum CATSolutionDiagnostic {
  NoSolution,
  SingleSolution,
  MultipleSolution,
  InfiniteSolution
}

The diagnosis of evaluation.

Parameters:

NoSolution: No parameter corresponds to this point
SingleSolutionOnly: one parameter corresponds to this point.
MultipleSolutionSeveral: parameters correspond to this point.
InfiniteSolution: Infinitely many parameters correspond

This object is included in the file: CATCurve.h
If needed, your Imakefile.mk should include the module: CATGMGeometricInterfaces

GeometricObjects Interface CATCurve

Method Index

Enumerated Type Index

Methods

Enumerated Types