aerosandbox.modeling.splines.bezier#

Module Contents#

Functions#

quadratic_bezier_patch_from_tangents(t, x_a, x_b, y_a, ...)

Computes sampled points in 2D space from a quadratic Bezier spline defined by endpoints and end-tangents.
aerosandbox.modeling.splines.bezier.quadratic_bezier_patch_from_tangents(t, x_a, x_b, y_a, y_b, dydx_a, dydx_b)[source]#

Computes sampled points in 2D space from a quadratic Bezier spline defined by endpoints and end-tangents.

Note: due to the inherent nature of a quadratic Bezier curve, curvature will be strictly one-sided - in other words, this will not make “S”-shaped curves. This means that you should be aware that bad values of dydx at either endpoint might cause this curvature to flip, which would result in the curve “going backwards” at one endpoint.

Also, note that, in general, points will not be spaced evenly in x, y, or arc length s.

Parameters:

  • t (Union[float, aerosandbox.numpy.ndarray]) –

  • x_a (float) – The x-coordinate of the first endpoint.

  • x_b (float) – The x-coordinate of the second endpoint.

  • y_a (float) – The y-coordinate of the first endpoint.

  • y_b (float) – The y-coordinate of the second endpoint.

  • dydx_a (float) – The derivative of y with respect to x at the first endpoint.

  • dydx_b (float) – The derivative of y with respect to x at the second endpoint.

Returns:

A scalar or numpy array of scalars representing the x-coordinates of the sampled points. y: A scalar or numpy array of scalars representing the y-coordinates of the sampled points.

Return type:

x

Usage:
>>> x_a, x_b = 0, 10
>>> y_a, y_b = 0, 5
>>> dydx_a, dydx_b = 0.5, -0.5
>>>
>>> t = np.linspace(0, 1, 50)
>>> x, y = quadratic_bezier_patch_from_tangents(
>>>     t=t,
>>>     x_a=x_a,
>>>     x_b=x_b,
>>>     y_a=y_a,
>>>     y_b=y_b,
>>>     dydx_a=dydx_a,
>>>     dydx_b=dydx_b
>>> )