aerocaps.geom.curves.BezierCurve2D#

class BezierCurve2D(control_points: List[Point2D], name: str = 'BezierCurve2D', construction: bool = False)[source]#

Bases: PCurve2D

Two-dimensional Bézier curve class

__init__(control_points: List[Point2D], name: str = 'BezierCurve2D', construction: bool = False)[source]#

Creates a two-dimensional Bézier curve objects from a list of control points

Parameters:

  • control_points (List[Point2D] or numpy.ndarray) – Control points for the Bézier curve

  • name (str) – Name of the geometric object. May be re-assigned a unique name when added to a GeometryContainer. Default: ‘BezierCurve2D’

  • construction (bool) – Whether this is a geometry used only for construction of other geometries. If True, this geometry will not be exported or plotted. Default: False

Methods

compute_t_corresponding_to_x(x_seek[, t0])

Computes the \(t\)-value corresponding to a given \(x\)-value

compute_t_corresponding_to_y(y_seek[, t0])

Computes the \(t\)-value corresponding to a given \(y\)-value

convert_to_3d([plane])

Converts the 2-D Bézier curve to a 3-D Bézier curve by mapping it onto a principal plane.

d2cdt2(t)

Evaluates the second derivative of the curve with respect to \(t\)

dcdt(t)

Evaluates the first derivative of the curve with respect to \(t\)

elevate_degree()

Elevates the degree of the Bézier curve.

evaluate(t)

Evaluates the line at one or more \(t\)-values

evaluate_pcurvedata(t)

Evaluates a verbose set of parametric curve data as a class based on an input parameter value or vector

evaluate_point2d(t)

Evaluates the line at one or more \(t\)-values and returns a single point object or list of point objects

get_control_point_array([unit])

Gets an array representation of the control points

split(t_split)

Splits the curve into two curves at a given \(t\)-value by applying the de-Casteljau algorithm

transform(**transformation_kwargs)

Creates a transformed copy of the curve by transforming each of the control points

Attributes

degree

Curve degree
compute_t_corresponding_to_x(x_seek: float, t0: float = 0.5) → float[source]#

Computes the \(t\)-value corresponding to a given \(x\)-value

Parameters:

  • x_seek (float) – \(x\)-value

  • t0 (float) – Initial guess for the output \(t\)-value. Default: 0.5

Returns:

\(t\)-value corresponding to x_seek

Return type:

float

compute_t_corresponding_to_y(y_seek: float, t0: float = 0.5) → float[source]#

Computes the \(t\)-value corresponding to a given \(y\)-value

Parameters:

  • y_seek (float) – \(y\)-value

  • t0 (float) – Initial guess for the output \(t\)-value. Default: 0.5

Returns:

\(t\)-value corresponding to y_seek

Return type:

float

convert_to_3d(plane: str = 'XY') → BezierCurve3D[source]#

Converts the 2-D Bézier curve to a 3-D Bézier curve by mapping it onto a principal plane. This is done by inserting a column of zeros.

Parameters:

plane (str) – Principal plane, one of ‘XY’, ‘YZ’, or ‘XZ’

Returns:

Planar 3-D Bézier curve

Return type:

BezierCurve3D

d2cdt2(t: float) → ndarray[source]#

Evaluates the second derivative of the curve with respect to \(t\)

Parameters:

t (float or int or numpy.ndarray) – Either a single \(t\)-value, a number of evenly spaced \(t\)-values between 0 and 1, or a 1-D array of \(t\)-values

Returns:

If \(t\) is a float, the output is a 1-D array containing two elements: the \(x\)- and \(y\)-components of the second derivative. Otherwise, the output is a 2-D array of size \(\text{len}(t) \times 2\)

Return type:

numpy.ndarray

dcdt(t: float) → ndarray[source]#

Evaluates the first derivative of the curve with respect to \(t\)

Parameters:

t (float or int or numpy.ndarray) – Either a single \(t\)-value, a number of evenly spaced \(t\)-values between 0 and 1, or a 1-D array of \(t\)-values

Returns:

If \(t\) is a float, the output is a 1-D array containing two elements: the \(x\)- and \(y\)-components of the first derivative. Otherwise, the output is a 2-D array of size \(\text{len}(t) \times 2\)

Return type:

numpy.ndarray

property degree: int#

Curve degree

elevate_degree() → BezierCurve2D[source]#

Elevates the degree of the Bézier curve. See algorithm source here.

Returns:

A new Bézier curve with identical shape to the current one but with one additional control point.

Return type:

BezierCurve2D

evaluate(t: float) → ndarray[source]#

Evaluates the line at one or more \(t\)-values

Parameters:

t (float or int or numpy.ndarray) – Either a single \(t\)-value, a number of evenly spaced \(t\)-values between 0 and 1, or a 1-D array of \(t\)-values

Returns:

If t is a float, the output is a 1-D array with two elements: the values of \(x\) and \(y\). Otherwise, the output is an array of size \(\text{len}(t) \times 2\)

Return type:

numpy.ndarray

evaluate_pcurvedata(t: float) → PCurveData2D[source]#

Evaluates a verbose set of parametric curve data as a class based on an input parameter value or vector

Parameters:

t (float or int or numpy.ndarray) – Either a single \(t\)-value, a number of evenly spaced \(t\)-values between 0 and 1, or a 1-D array of \(t\)-values

Returns:

Parametric curve information, including derivative and curvature data

Return type:

PCurveData2D

evaluate_point2d(t: float) → Point2D[source]#

Evaluates the line at one or more \(t\)-values and returns a single point object or list of point objects

Parameters:

t (float or int or numpy.ndarray) – Either a single \(t\)-value, a number of evenly spaced \(t\)-values between 0 and 1, or a 1-D array of \(t\)-values

Returns:

If t is a float, the output is a single point object. Otherwise, the output is a list of point objects

Return type:

Point2D or List[Point2D]

get_control_point_array(unit: str = 'm') → ndarray[source]#

Gets an array representation of the control points

Parameters:

unit (str) – Physical length unit used to determine the output array. Default: "m"

Returns:

Array of size \((n+1)\times 2\) where \(n\) is the curve degree

Return type:

numpy.ndarray

split(t_split: float)[source]#

Splits the curve into two curves at a given \(t\)-value by applying the de-Casteljau algorithm

Parameters:

t_split (float) – \(t\)-value at which to split the curve

Returns:

Two new curves split at the input \(t\)-value

Return type:

Bezier2D, Bezier2D

transform(**transformation_kwargs) → BezierCurve2D[source]#

Creates a transformed copy of the curve by transforming each of the control points

Parameters:

transformation_kwargs – Keyword arguments passed to Transformation2D

Returns:

Transformed curve

Return type:

BezierCurve2D