The analytic shape formulas — the single definition of each. More...

Functions
OPENSWMM_KERNEL_FN double	rectAofY (double y, double w_max)
	Compute rectangular area as depth times width.

OPENSWMM_KERNEL_FN double	trapezAofY (double y, double y_bot, double s_bot)
	Compute trapezoid area as (bottom width+side slopedepth)depth.

OPENSWMM_KERNEL_FN double	triangAofY (double y, double s_bot)
	Compute triangular area from depth and side slope.

OPENSWMM_KERNEL_FN double	parabAofY (double y, double r_bot)
	Compute parabolic area using its square-root depth relation.

OPENSWMM_KERNEL_FN double	powerfuncAofY (double y, double s_bot, double r_bot)
	Compute power-function section area.

OPENSWMM_KERNEL_FN double	rectClosedRofA (double a, double w_max, double a_full)
	Compute closed rectangular hydraulic radius with near-crown perimeter correction.

OPENSWMM_KERNEL_FN double	rectOpenRofA (double a, double w_max, double s_bot)
	Compute open rectangular radius excluding selected side banks.

OPENSWMM_KERNEL_FN double	trapezRofY (double y, double y_bot, double s_bot, double r_bot)
	Compute trapezoid hydraulic radius from depth.

OPENSWMM_KERNEL_FN double	triangRofY (double y, double s_bot, double r_bot)
	Compute triangular hydraulic radius from its side geometry.

OPENSWMM_KERNEL_FN double	rectClosedWofY (double y_norm, double w_max)
	Apply the closed rectangular crown top-width convention.

OPENSWMM_KERNEL_FN double	trapezWofY (double y, double y_bot, double s_bot)
	Compute trapezoid top width from depth.

OPENSWMM_KERNEL_FN double	triangWofY (double y, double s_bot)
	Compute triangular top width from depth.

OPENSWMM_KERNEL_FN double	parabWofY (double y, double r_bot)
	Compute parabolic top width from depth.

OPENSWMM_KERNEL_FN double	powerfuncWofY (double y, double s_bot, double r_bot)
	Compute power-function top width as the area-depth derivative.

Detailed Description

The analytic shape formulas — the single definition of each.

These are the shapes whose geometry is a closed-form expression rather than a table lookup. They live outside XsectEval because they need no tables at all, which lets the two consumers that are shaped differently share them:

XsectEval's per-element methods (host DW scalar fallbacks, FV, device), which unpack an XSectParams; and
xsect_batch's SoA loops (XSectBatch.cpp), which DWSolver's computeLinkGeometry STEP B/D runs on and which read parallel arrays.

Both call the same function on the same operands, so the two paths cannot drift — which is the point (plan §5.1, Phase 4b). Each body is legacy xsect.c verbatim, including operand order and the guards: multiplication is not associative in IEEE-754, so y*y*sBot and sBot*y*y are different computations and only the first is legacy's.

The y/a guards are legacy's own (xsect_getRofA's a <= 0 early return for the rect family, trapez_getRofY's y == 0). STEP A floors every conduit depth at FUDGE before STEP B/D sees it, so on the DW path they are unreachable either way; they are here so the shared body is complete rather than context-dependent.

Function Documentation

◆ parabAofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::parabAofY	(	double	y,
		double	r_bot )

Compute parabolic area using its square-root depth relation.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	r_bot	Positive inverse sqrt(parabola coefficient), units sqrt(ft).

Returns: (4/3)*r_bot*y*sqrt(y), ft2.

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◆ parabWofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::parabWofY	(	double	y,
		double	r_bot )

Compute parabolic top width from depth.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	r_bot	Positive inverse sqrt(parabola coefficient), sqrt(ft).

Returns: 2*r_bot*sqrt(y), ft.

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◆ powerfuncAofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::powerfuncAofY	(	double	y,
		double	s_bot,
		double	r_bot )

Compute power-function section area.

No finite/power-domain checks.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	s_bot	Positive depth exponent (inverse authoring exponent), dimensionless.
[in]	r_bot	Positive area coefficient, units ft^(1-s_bot).

Returns: r_bot*y^(s_bot+1), ft2.

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◆ powerfuncWofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::powerfuncWofY	(	double	y,
		double	s_bot,
		double	r_bot )

Compute power-function top width as the area-depth derivative.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	s_bot	Positive depth exponent, dimensionless.
[in]	r_bot	Positive coefficient with units ft^(1-s_bot).

Returns: (s_bot+1)*r_bot*y^s_bot, ft.

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◆ rectAofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::rectAofY	(	double	y,
		double	w_max )

Compute rectangular area as depth times width.

No clamp to full depth.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	w_max	Positive section width in ft.

Returns: Wetted area ft2.

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◆ rectClosedRofA()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::rectClosedRofA	(	double	a,
		double	w_max,
		double	a_full )

Compute closed rectangular hydraulic radius with near-crown perimeter correction.

Above RECT_ALFMAX full-area fraction, adds a linearly increasing crown width to wetted perimeter.

Parameters

[in]	a	Finite nonnegative wetted area in ft2; caller supplies valid initialized geometry.
[in]	w_max	Positive section width in ft.
[in]	a_full	Positive full section area ft2.

Returns: Radius ft,0 when a<=0.

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◆ rectClosedWofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::rectClosedWofY	(	double	y_norm,
		double	w_max )

Apply the closed rectangular crown top-width convention.

Does not clamp negative/overfull normalized depths.

Parameters

[in]	y_norm	Normalized depth y/y_full; exact1 denotes crown.
[in]	w_max	Positive section width in ft.

Returns: 0 exactly at y_norm=1, otherwise w_max ft.

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◆ rectOpenRofA()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::rectOpenRofA	(	double	a,
		double	w_max,
		double	s_bot )

Compute open rectangular radius excluding selected side banks.

Perimeter is width+(2-s_bot)*depth.

Parameters

[in]	a	Finite nonnegative wetted area in ft2; caller supplies valid initialized geometry.
[in]	w_max	Positive section width in ft.
[in]	s_bot	Number of excluded wetted banks, convention0,1 or2; caller validates.

Returns: Radius ft,0 when a<=0.

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◆ trapezAofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::trapezAofY	(	double	y,
		double	y_bot,
		double	s_bot )

Compute trapezoid area as (bottom width+side slope*depth)*depth.

No full-depth clamp.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	y_bot	Nonnegative bottom width ft, with valid positive section dimensions.
[in]	s_bot	Average horizontal/vertical side slope, dimensionless.

Returns: Area ft2.

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◆ trapezRofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::trapezRofY	(	double	y,
		double	y_bot,
		double	s_bot,
		double	r_bot )

Compute trapezoid hydraulic radius from depth.

No nonzero-denominator validation.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	y_bot	Bottom width ft.
[in]	s_bot	Average horizontal/vertical side slope.
[in]	r_bot	Positive sum of sloped side lengths per unit depth, dimensionless.

Returns: Area/(y_bot+y*r_bot), ft;0 exactly at y=0.

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◆ trapezWofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::trapezWofY	(	double	y,
		double	y_bot,
		double	s_bot )

Compute trapezoid top width from depth.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	y_bot	Nonnegative bottom width ft.
[in]	s_bot	Average horizontal/vertical side slope.

Returns: y_bot+2*y*s_bot, ft.

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◆ triangAofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::triangAofY	(	double	y,
		double	s_bot )

Compute triangular area from depth and side slope.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	s_bot	Positive horizontal/vertical side slope, dimensionless.

Returns: y*y*s_bot in ft2.

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◆ triangRofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::triangRofY	(	double	y,
		double	s_bot,
		double	r_bot )

Compute triangular hydraulic radius from its side geometry.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	s_bot	Positive horizontal/vertical side slope.
[in]	r_bot	Positive side-length/depth factor sqrt(1+s_bot*s_bot).

Returns: y*s_bot/(2*r_bot), ft.

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◆ triangWofY()

OPENSWMM_KERNEL_FN double openswmm::xsect::shape::triangWofY	(	double	y,
		double	s_bot )

Compute triangular top width from depth.

Parameters

[in]	y	Finite nonnegative water depth in ft; caller keeps input within the intended geometric branch.
[in]	s_bot	Positive horizontal/vertical side slope.

Returns: 2*s_bot*y, ft.

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Functions

Detailed Description

Function Documentation

◆ parabAofY()

◆ parabWofY()

◆ powerfuncAofY()

◆ powerfuncWofY()

◆ rectAofY()

◆ rectClosedRofA()

◆ rectClosedWofY()

◆ rectOpenRofA()

◆ trapezAofY()

◆ trapezRofY()

◆ trapezWofY()

◆ triangAofY()

◆ triangRofY()

◆ triangWofY()