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RhinoMathIntegrate Method (FuncObject, Int32, Double, Double, Object, Curve, Double, Double, Double)

Calculates the definite integral of a smooth (C-infinity) function of one variable using a Rhomberg integration technique and returns returns Integral(f(t)*|curve'(t)|*dt). The C-infinity requirement is used by the Rhomberg algorithm when estimating error bounds and convergence. If you choose to pass a C2 function, you are likely to converge while getting less accurate results and incorrect error bound estimates. Using a C0 or C1 fucntion will often return nonsense.

Namespace:  Rhino
Assembly:  RhinoCommon (in RhinoCommon.dll)
Syntax
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public static double Integrate(
	Func<Object, int, double, double> integrandFunction,
	Object context,
	Curve curve,
	double relativeTolerance,
	double absoluteTolerance,
	out double errorBound
)

Parameters

integrandFunction
Type: SystemFuncObject, Int32, Double, Double
The integrand function is double f(ON__UINT_PTR context, int limit_direction, double t) and returns the value of the integrand at t. The limit_direction parameter will be -1, 0, or +1 and specifies which limit direction should be used in the evaluation. If limit_direction = 1, then the integrand may not be C-infinity at t and should be evaluated using the limit from above. If limit_direction = -1, then the integrand may not be C-infinity at t and should be evaluated using the limit from below. If limit_direction = 0, then the integrand is C-infinity at t and may and evaluation from above and below will return the same answer.
context
Type: SystemObject
First parameter passed into the integrand function.
curve
Type: Rhino.GeometryCurve
The integration is performed over the C-infinity spans of the curve and |curve'(t)| is automatically included in the integrand. The integrand must be C-infinity on the intesection each curve span with the interval (limits[0],limits[1]). The curve may have any dimension.
relativeTolerance
Type: SystemDouble
Desired relative tolerance. If I = mathematical value and N = numerical integration value, then the algorithm will terminate when |I - N| <= relative_tolerance*|I|. For example, if you want to know the answer with 5 digits of accuracy, then pass 1e-5.
absoluteTolerance
Type: SystemDouble
Desired absolute tolerance. If I = mathematical value and N = numerical integration value, then the algorithm will terminate when |I - N| <= absolute_tolerance.
errorBound
Type: SystemDouble
If error_bound is not nullptr, then the returned value is upper bound on the error in the calculation. If I = mathematical value and N = returned value, then |I - N| <= *error_bound;

Return Value

Type: Double
If the calulation succeeds, then the numerical integral is returned. Otherwise ON_DBL_QNAN is returned.
See Also