buffalo_wings.airfoil.Curve

class buffalo_wings.airfoil.Curve[source]

Bases: ABC

Base class for 1-d curves.

Curves can be interrogated based on their natural parameterization, using the parameter, t.

__init__()

Methods

`__init__`()
`arc_length`(t_s, t_e)	Calculate the arc-length distance between two points on surface.
`joints`()	Return the locations of any joints/discontinuities in the curve.
`k`(t)	Calculate the curvature at parameter location.
`normal`(t)	Calculate the unit normal at parameter location.
`tangent`(t)	Calculate the unit tangent at parameter location.
`xy`(t)	Calculate the coordinates of geometry at parameter location.
`xy_t`(t)	Calculate rates of change of the coordinates at parameter location.
`xy_tt`(t)	Calculate second derivative of the coordinates at parameter location.

abstractmethod xy(t)[source]

Calculate the coordinates of geometry at parameter location.

Parameters:

t (numpy.ndarray) – Parameter for desired locations.

Returns:

numpy.ndarray – X-coordinate of point.
numpy.ndarray – Y-coordinate of point.

Return type:

tuple[ndarray[tuple[int, …], dtype[float64]], ndarray[tuple[int, …], dtype[float64]]]

abstractmethod xy_t(t)[source]

Calculate rates of change of the coordinates at parameter location.

Parameters:

t (numpy.ndarray) – Parameter for desired locations.

Returns:

numpy.ndarray – Parametric rate of change of the x-coordinate of point.
numpy.ndarray – Parametric rate of change of the y-coordinate of point.

Return type:

tuple[ndarray[tuple[int, …], dtype[float64]], ndarray[tuple[int, …], dtype[float64]]]

abstractmethod xy_tt(t)[source]

Calculate second derivative of the coordinates at parameter location.

Parameters:

t (numpy.ndarray) – Parameter for desired locations.

Returns:

numpy.ndarray – Parametric second derivative of the x-coordinate of point.
numpy.ndarray – Parametric second derivative of the y-coordinate of point.

Return type:

tuple[ndarray[tuple[int, …], dtype[float64]], ndarray[tuple[int, …], dtype[float64]]]

normal(t)[source]

Calculate the unit normal at parameter location.

Parameters:: t (numpy.ndarray) – Parameter for desired locations.
Returns:: Unit normal at point.
Return type:: numpy.ndarray, numpy.ndarray

tangent(t)[source]

Calculate the unit tangent at parameter location.

Parameters:: t (numpy.ndarray) – Parameter for desired locations.
Returns:: Unit tangent at point.
Return type:: numpy.ndarray, numpy.ndarray

k(t)[source]

Calculate the curvature at parameter location.

Parameters:: t (numpy.ndarray) – Parameter for desired locations.
Returns:: Curvature of surface at point.
Return type:: numpy.ndarray

arc_length(t_s, t_e)[source]

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

Parameters:

t_s (float) – Start point of distance calculation.
t_e (numpy.ndarray) – End point of distance calculation.

Returns:

Distance from start point to end point.

Return type:

numpy.ndarray

abstractmethod joints()[source]

Return the locations of any joints/discontinuities in the curve.

The resulting list needs to contain any parametric locations where some non-standard discontinuity (slope, curvature, etc.) occurs as well as the end points for the curve (if they exist).

Returns:: Parametric coordinates of any discontinuities.
Return type:: List[float]