buffalo_wings.airfoil.SplineCurve

class buffalo_wings.airfoil.SplineCurve(*, curve)

Bases: Curve

Bezier-backed spline curve runtime for open section geometry.

Notes

This runtime is intentionally backend-neutral in name while the first supported schema slice stores Bezier control points directly.

Methods

arc_length(u_s, u_e)	Calculate the arc-length distance between two points on surface.
arc_length_breakpoints()	Return the breakpoint locations in arc-length coordinates.
breakpoint_parameter_limits(*, index)	Return parameter limits for one breakpoint.
breakpoints()	Return the native endpoint breakpoints for the open curve.
k(u)	Calculate the curvature at parameter location.
normal(u)	Calculate the unit normal at parameter location.
tangent(u)	Calculate the unit tangent at parameter location.
u_from_s(s)	Calculate the parametric value for arc-length provided.
xy_from_s(s)	Return curve coordinates at arc-length locations.
xy_from_u(u)	Evaluate open-curve coordinates at native parameter values.
xy_s(s)	Calculate first derivatives at arc-length location.
xy_s_breakpoint(*, index)	Return both sides of first derivatives at a breakpoint.
xy_ss(s)	Calculate second derivatives at arc-length location.
xy_ss_breakpoint(*, index)	Return one-sided second derivatives at a breakpoint.
xy_u(u)	Evaluate first derivatives at native parameter values.
xy_u_breakpoint(*, index)	Return both sides of first derivatives at one breakpoint.
xy_uu(u)	Evaluate second derivatives at native parameter values.
xy_uu_breakpoint(*, index)	Return one-sided second derivatives at one breakpoint.

Attributes

curve	Return the underlying Bezier curve representation.
length	Return the total curve length.

property curve: BezierCurve2D

Return the underlying Bezier curve representation.

xy_from_u(u)

Evaluate open-curve coordinates at native parameter values.

Return type:

tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’), TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’)]

xy_u(u)

Evaluate first derivatives at native parameter values.

Return type:

tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’), TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’)]

xy_uu(u)

Evaluate second derivatives at native parameter values.

Return type:

tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’), TypeAliasForwardRef(‘buffalo_core.typing.FloatArray’)]

breakpoints()

Return the native endpoint breakpoints for the open curve.

Return type:

list[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]

arc_length(u_s, u_e)

Calculate the arc-length distance between two points on surface.

Parameters:

• u_s (buffalo_core.typing.FloatScalar) – Start point of distance calculation.

• u_e (buffalo_core.typing.FloatInput) – End point of distance calculation.

Returns:

Distance from start point to end point.

Return type:

buffalo_core.typing.FloatArray

arc_length_breakpoints()

Return the breakpoint locations in arc-length coordinates.

Returns:

Arc-length coordinates measured from the minimum native parameter.

Return type:

list[FloatScalar]

Notes

These values include the two curve endpoints as boundary markers. Interior breakpoints correspond to the native-parameter interior breakpoints returned by breakpoints().

breakpoint_parameter_limits(*, index)

Return parameter limits for one breakpoint.

Notes

Endpoint breakpoints return the exact boundary parameter. Interior breakpoints return nearby one-sided parameters chosen within the neighboring breakpoint interval for the current generic breakpoint-side implementation. These limits exist to support the sampled fallback in the generic *_breakpoint methods and should not be treated as the primary source of truth when a subclass can provide exact one-sided values directly.

Return type:

tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]

k(u)

Calculate the curvature at parameter location.

Parameters:

u (buffalo_core.typing.FloatInput) – Parameter for desired locations.

Returns:

Curvature of surface matching the normalized shape of u.

Return type:

buffalo_core.typing.FloatArray

property length: buffalo_core.typing.FloatScalar

Return the total curve length.

Returns:

Arc length measured from the minimum to maximum native parameter.

Return type:

buffalo_core.typing.FloatScalar

normal(u)

Calculate the unit normal at parameter location.

Parameters:

u (buffalo_core.typing.FloatInput) – Parameter for desired locations.

Returns:

Tuple (n_x, n_y) of float64 arrays matching the normalized shape of u.

Return type:

tuple[FloatArray, FloatArray]

tangent(u)

Calculate the unit tangent at parameter location.

Parameters:

u (buffalo_core.typing.FloatInput) – Parameter for desired locations.

Returns:

Tuple (t_x, t_y) of float64 arrays matching the normalized shape of u.

Return type:

tuple[FloatArray, FloatArray]

u_from_s(s)

Calculate the parametric value for arc-length provided.

Parameters:

s (buffalo_core.typing.FloatInput) – Arc-length location of point.

Returns:

Parametric value matching the normalized shape of s.

Return type:

buffalo_core.typing.FloatArray

Raises:

ValueError – When arc-length provided lies outside the curve arc-length range.

xy_from_s(s)

Return curve coordinates at arc-length locations.

Parameters:

s (buffalo_core.typing.FloatInput) – Arc length location of point.

Returns:

(x, y) coordinates matching the normalized shape of s.

Return type:

tuple[FloatArray, FloatArray]

xy_s(s)

Calculate first derivatives at arc-length location.

Parameters:

s (buffalo_core.typing.FloatInput) – Arc length location of point.

Returns:

(dx/ds, dy/ds) coordinates matching the normalized shape of s.

Return type:

tuple[FloatArray, FloatArray]

Notes

If s matches one of arc_length_breakpoints() exactly, this method returns the minus-side derivative limit. Subclasses should override xy_s_breakpoint() when exact one-sided breakpoint derivatives are available analytically.

xy_s_breakpoint(*, index)

Return both sides of first derivatives at a breakpoint.

Parameters:

index (int) – Index into arc_length_breakpoints().

Returns:

((x_s_minus, y_s_minus), (x_s_plus, y_s_plus)).

Return type:

CurveBreakpointSides

Notes

Endpoint breakpoints return the same boundary value for both entries. This method is the exact-breakpoint contract that pairs with xy_s(). Subclasses should override it whenever exact one-sided arc-length derivatives are available. The generic implementation evaluates nearby one-sided native- parameter samples and therefore serves only as an approximation fallback.

xy_ss(s)

Calculate second derivatives at arc-length location.

Parameters:

s (buffalo_core.typing.FloatInput) – Arc length location of point.

Returns:

(d^2x/ds^2, d^2y/ds^2) coordinates matching the normalized shape of s.

Return type:

tuple[FloatArray, FloatArray]

Notes

If s matches one of arc_length_breakpoints() exactly, this method returns the minus-side derivative limit. Subclasses should override xy_ss_breakpoint() when exact one-sided breakpoint second derivatives are available analytically.

xy_ss_breakpoint(*, index)

Return one-sided second derivatives at a breakpoint.

Parameters:

index (int) – Index into arc_length_breakpoints().

Returns:

((x_ss_minus, y_ss_minus), (x_ss_plus, y_ss_plus)).

Return type:

CurveBreakpointSides

Notes

Endpoint breakpoints return the same boundary value for both entries. This method is the exact-breakpoint contract that pairs with xy_ss(). Subclasses should override it whenever exact one-sided arc-length second derivatives are available. The generic implementation evaluates nearby one-sided native- parameter samples and therefore serves only as an approximation fallback.

xy_u_breakpoint(*, index)

Return both sides of first derivatives at one breakpoint.

Parameters:

index (int) – Index into breakpoints().

Returns:

((x_u_minus, y_u_minus), (x_u_plus, y_u_plus)).

Return type:

CurveBreakpointSides

Notes

Endpoint breakpoints return the same boundary value for both entries. This method is the exact-breakpoint contract that pairs with xy_u(). Subclasses should override it whenever they can return exact one-sided derivative values. The generic implementation evaluates nearby one-sided parameter samples and therefore serves only as an approximation fallback.

xy_uu_breakpoint(*, index)

Return one-sided second derivatives at one breakpoint.

Parameters:

index (int) – Index into breakpoints().

Returns:

((x_uu_minus, y_uu_minus), (x_uu_plus, y_uu_plus)).

Return type:

CurveBreakpointSides

Notes

Endpoint breakpoints return the same boundary value for both entries. This method is the exact-breakpoint contract that pairs with xy_uu(). Subclasses should override it whenever they can return exact one-sided second-derivative values. The generic implementation evaluates nearby one-sided parameter samples and therefore serves only as an approximation fallback.