aerocaps.geom.curves.PCurveData2D

class PCurveData2D(t: float, x: float, y: float, xp: float, yp: float, xpp: float, ypp: float, k: float = None, R: float = None)

Bases: object

Data-processing class for 2-D parametric curves

__init__(t: float, x: float, y: float, xp: float, yp: float, xpp: float, ypp: float, k: float = None, R: float = None)

Data-processing class for 2-D parametric curves. Adds convenience methods for plotting, approximating arc length, and computing curvature combs.

Parameters:

• t (float or numpy.ndarray) – \(t\)-value or vector for the curve

• x (float or numpy.ndarray) – Value of the curve in the \(x\)-direction

• y (float or numpy.ndarray) – Value of the curve in the \(y\)-direction

• xp (float or numpy.ndarray) – First derivative \(x\)-component of the curve with respect to \(t\)

• yp (float or numpy.ndarray) – First derivative \(y\)-component of the curve with respect to \(t\)

• xpp (float or numpy.ndarray) – Second derivative \(x\)-component of the curve with respect to \(t\)

• ypp (float or numpy.ndarray) – Second derivative \(y\)-component of the curve with respect to \(t\)

• k (float or v.ndarray) – Curvature of the curve. If not specified, it will be computed. Default: None

• R (float or numpy.ndarray) – Radius of curvature of the curve. If not specified, it will be computed. Default: None

Methods

approximate_arc_length()	Approximates the arc-length of the curve by summing the arc-lengths of each segment of the evaluated polyline
get_curvature_comb(max_comb_length[, interval])	Gets the curvature comb for the curve
plot(ax, **kwargs)	Plots the curve on a matplotlib.pyplot.Axes

approximate_arc_length() → ndarray

Approximates the arc-length of the curve by summing the arc-lengths of each segment of the evaluated polyline

Note

This method will raise an exception if t is a float

Returns:

1-D array with \((\text{len}(t) - 1)\) elements

Return type:

numpy.ndarray

get_curvature_comb(max_comb_length: float, interval: int = 1) -> (<class 'numpy.ndarray'>, <class 'numpy.ndarray'>)

Gets the curvature comb for the curve

Note

This method will raise an exception if t is a float

Parameters:

• max_comb_length (float) – Length of the comb corresponding to the location of maximum unsigned curvature

• interval (int) – Interval between the output combs. If 1, the combs corresponding to every evaluated \(t\)-value will be used. If 2, every other comb will be skipped, etc. The first and last combs are guaranteed to be output as long as len(t) > 1. Default: 1

Returns:

2-D arrays corresponding to the comb heads and comb tails, respectively. Each array has outer dimension dependent on the interval (if interval=1, the length of this dimension will be len(t)) and inner dimension 2

Return type:

numpy.ndarray, numpy.ndarray

plot(ax: Axes, **kwargs)

Plots the curve on a matplotlib.pyplot.Axes

Note

If t is a float, specifying the marker keyword argument may be desirable as a line plot cannot be generated in this case

Parameters:

• ax (plt.Axes) – Axis on which to plot

• kwargs (dict) – Keyword arguments to pass to matplotlib.pyplot.Axes.plot