buffalo_wings.airfoil.PolylineCurve

class buffalo_wings.airfoil.PolylineCurve(*, points)

Bases: Curve

Piecewise-linear open-curve runtime for authored section geometry.

Notes

The native parameter u is the normalized cumulative arc-length fraction along the polyline, so every segment occupies a parameter span proportional to its physical length.

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 normalized arc-fraction breakpoints along the polyline.
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 polyline coordinates by arc-fraction interpolation.
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)	Return the piecewise-constant derivative on each segment.
xy_u_breakpoint(*, index)	Return both sides of first derivatives at one breakpoint.
xy_uu(u)	Return zero second derivatives away from breakpoints.
xy_uu_breakpoint(*, index)	Return one-sided second derivatives at one breakpoint.

Attributes

length	Return the total curve length.
points	Return the stored polyline vertices as an (n, 2) array.

property points: buffalo_core.typing.FloatArray

Return the stored polyline vertices as an (n, 2) array.

xy_from_u(u)

Evaluate polyline coordinates by arc-fraction interpolation.

Return type:

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

xy_u(u)

Return the piecewise-constant derivative on each segment.

Return type:

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

xy_uu(u)

Return zero second derivatives away from breakpoints.

Return type:

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

breakpoints()

Return normalized arc-fraction breakpoints along the polyline.

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.