pymead.core.ferguson.Ferguson#

class Ferguson(point_sequence: PointSequence, default_nt: int | None = None, name: str | None = None, t_start: float | None = None, t_end: float | None = None, **kwargs)[source]#

Bases: ParametricCurve

__init__(point_sequence: PointSequence, default_nt: int | None = None, name: str | None = None, t_start: float | None = None, t_end: float | None = None, **kwargs)[source]#

Computes the Ferguson curve (see “Multivariable Curve Interpolation” by James Ferguson) through the 4 control points P.

Parameters:

  • point_sequence (PointSequence) – Sequence of points defining the control points for the Ferguson curve. Points 0 and 3 define the starting and ending points for the curve, respectively. Point 1 defines the head of the tangent vector at Point 0 (Point 0 is the tail). Point 2 defines the tail of the tangent vector at Point 3 (point 2 is the head).

  • name (str or None) – Optional name for the curve. Default: None

  • t_start (float or None) – Optional starting parameter vector value for the Bézier curve. Not specifying this value automatically gives a value of 0.0. Default: None

  • t_end (float or None) – Optional ending parameter vector value for the Bézier curve. Not specifying this value automatically gives a value of 1.0. Default: None

Methods

derivative(t, order)

Calculates an arbitrary-order derivative of the Ferguson curve

evaluate([t])

Evaluates the curve using an optionally specified parameter vector.

evaluate_xy([t])

get_control_point_array()

get_dict_rep()

Gets a dictionary representation of the pymead object.

plot([ax, nt, show, save_file])

Plots the airfoil to a matplotlib figure.

point_removal_deletes_curve()

point_sequence()

points()

remove()

remove_point([idx, point])

reverse_point_sequence()

set_point_sequence(point_sequence)

Attributes

derivative(t: ndarray, order: int) → ndarray[source]#

Calculates an arbitrary-order derivative of the Ferguson curve

Parameters:

  • t (np.ndarray) – The parameter vector

  • order (int) – The derivative order. For example, order=2 returns the second derivative.

Returns:

An array of shape=(N,2) where N is the number of evaluated points specified by the \(t\) vector. The columns represent \(C^{(m)}_x(t)\) and \(C^{(m)}_y(t)\), where \(m\) is the derivative order.

Return type:

np.ndarray

evaluate(t: array | None = None, **kwargs)[source]#

Evaluates the curve using an optionally specified parameter vector.

Parameters:

t (np.ndarray or None) – Optional direct specification of the parameter vector for the curve. Not specifying this value gives a linearly spaced parameter vector from t_start or t_end with the default size. Default: None

Returns:

Data class specifying the following information about the Bézier curve:

\[C_x(t), C_y(t), C'_x(t), C'_y(t), C''_x(t), C''_y(t), \kappa(t)\]

where the \(x\) and \(y\) subscripts represent the \(x\) and \(y\) components of the vector-valued functions \(\vec{C}(t)\), \(\vec{C}'(t)\), and \(\vec{C}''(t)\).

Return type:

PCurveData

get_dict_rep()[source]#

Gets a dictionary representation of the pymead object. In general, this dictionary should consist of only the required arguments for object instantiation. For example, the dictionary representation of a point looks something like this: {"x": 0.3, "y": 0.5}. If the argument requires a reference to a PymeadObj rather than a string or float value, the name() method should be the value that is stored. For an example, see the overridden value of this method in pymead.core.airfoil.Airfoil. All subclasses of PymeadObj must implement this method, since it is the way pymead objects are stored in saved instances of a GeometryCollection (.jmea files).

plot(ax: Axes | None = None, nt: int = 100, show: bool = True, save_file: str | None = None, **plt_kwargs)[source]#

Plots the airfoil to a matplotlib figure.

Parameters:

  • ax (plt.Axes or None) – Matplotlib Axes object on which the curve will be plotted. If specified, this method will only. If None, a new figure will be created. Default: None

  • nt (int) – Number of parametric values to evaluate along the curve. Default: 100

  • show (bool) – Whether to immediately show the curve plot. Ignored if ax is not None. Default: True

  • save_file (str or None) – Name of the file to save. If None, the curve image will not be saved to file. Ignored if ax is not None. Default: None

  • plt_kwargs – Additional keyword arguments to pass to matplotlib.pyplot.plot