openswmm::fv::secgeom::detail Namespace Reference

Functions
double	circTheta (double r, double y)
	Evaluate the central angle of a circular water segment.
double	circArea (double r, double y)
	Evaluate the exact wetted area of a circular segment.
double	circWidth (double r, double y)
	Evaluate the exact circular free-surface chord width.
double	circPerim (double r, double y)
	Evaluate the exact submerged circular arc length.
template<class F>
double	simpsonStep (F &f, double a, double b, double fa, double fm, double fb, double whole, double eps, int depth)
	Recursively refine a cached Simpson panel to an absolute error target.
template<class F>
double	integrate (F f, double a, double b, double eps=1.0e-12, int depth=40)
	Integrate a scalar function with adaptive Simpson quadrature.
double	ellipsePerim (double ax, double by, double y)
	Integrate the submerged arc of a mathematical ellipse.

Function Documentation

circArea()

double openswmm::fv::secgeom::detail::circArea ( double r, double y )

inline

Evaluate the exact wetted area of a circular segment.

Uses the exact segment formula between invert and crown, without a lookup table.

Parameters

[in]	r	Positive circle radius in ft.
[in]	y	Finite water depth from the invert in ft.

Returns

Area in ft2; zero at/below the invert and full pi*r*r at/above the crown.

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circPerim()

double openswmm::fv::secgeom::detail::circPerim ( double r, double y )

inline

Evaluate the exact submerged circular arc length.

The chord/free surface is excluded from wetted perimeter.

Parameters

[in]	r	Positive circle radius in ft.
[in]	y	Finite water depth from the invert in ft.

Returns

Wetted perimeter in ft; zero at/below the invert and full circumference at/above the crown.

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circTheta()

double openswmm::fv::secgeom::detail::circTheta ( double r, double y )

inline

Evaluate the central angle of a circular water segment.

Clamps 1-y/r to [-1,1]; positive finite radius is required and NaN is not diagnosed.

Parameters

[in]	r	Positive circle radius in ft.
[in]	y	Finite water depth from the invert in ft.

Returns

Angle in radians in [0,2*pi].

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circWidth()

double openswmm::fv::secgeom::detail::circWidth ( double r, double y )

inline

Evaluate the exact circular free-surface chord width.

Uses 2*sqrt(y*(2*r-y)) only in the wet sub-crown interval.

Parameters

[in]	r	Positive circle radius in ft.
[in]	y	Finite water depth from the invert in ft.

Returns

Width in ft; zero at/below the invert or at/above the crown.

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ellipsePerim()

double openswmm::fv::secgeom::detail::ellipsePerim ( double ax, double by, double y )

inline

Integrate the submerged arc of a mathematical ellipse.

Uses adaptive angular quadrature with absolute target 1e-12*(ax+by). This mathematical ellipse helper is not the table-defined SWMM HORIZ_ELLIPSE/VERT_ELLIPSE profile evaluator.

Parameters

[in]	ax	Positive horizontal semi-axis in ft.
[in]	by	Positive vertical semi-axis in ft.
[in]	y	Finite depth from the bottom in ft; <=0 returns zero and depths above 2*by saturate.

Returns

Both wetted side arcs in ft, excluding the free-surface chord.

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integrate()

template<class F>

double openswmm::fv::secgeom::detail::integrate	(	F	f,
		double	a,
		double	b,
		double	eps = 1.0e-12,
		int	depth = 40 )

Integrate a scalar function with adaptive Simpson quadrature.

No heap workspace is used by the quadrature itself. Callable copy/evaluation exceptions propagate; numerical error bounds are not certified for singular or nonfinite integrands.

Parameters

[in]	f	Integrand copied for this call and invoked synchronously; no callable is retained.
[in]	a	Lower finite integration coordinate.
[in]	b	Upper finite coordinate; b<=a returns zero without evaluating f.
[in]	eps	Positive absolute integral error target; defaults to 1e-12.
[in]	depth	Maximum recursive refinement depth; default 40. Exhaustion accepts the latest corrected estimate.

Returns

Estimated integral in integrand-units times coordinate-units; no error/status object.

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simpsonStep()

template<class F>

double openswmm::fv::secgeom::detail::simpsonStep	(	F &	f,
		double	a,
		double	b,
		double	fa,
		double	fm,
		double	fb,
		double	whole,
		double	eps,
		int	depth )

Recursively refine a cached Simpson panel to an absolute error target.

Samples two quarter points per call; stops when abs(delta)<=15*eps or the depth budget is exhausted. No convergence status or nonfinite check is returned. Recursion uses stack storage, and integrand exceptions propagate.

Parameters

[in,out]	f	Synchronous scalar integrand callable, borrowed by reference; its own side effects/exceptions are permitted.
[in]	a	Lower finite integration coordinate.
[in]	b	Upper finite coordinate, greater than a.
[in]	fa	Cached f(a).
[in]	fm	Cached f((a+b)/2).
[in]	fb	Cached f(b).
[in]	whole	Simpson estimate over [a,b], in integral units.
[in]	eps	Positive absolute error target in integral units; halved on each recursive child.
[in]	depth	Remaining subdivision depth; <=0 accepts the next refined estimate regardless of error.

Returns

Sum of refined Simpson panels plus delta/15 correction.

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