aerosandbox.modeling.splines ============================ .. py:module:: aerosandbox.modeling.splines Submodules ---------- .. toctree:: :maxdepth: 1 /autoapi/aerosandbox/modeling/splines/bezier/index /autoapi/aerosandbox/modeling/splines/hermite/index Attributes ---------- .. autoapisummary:: aerosandbox.modeling.splines.x Functions --------- .. autoapisummary:: aerosandbox.modeling.splines.quadratic_bezier_patch_from_tangents aerosandbox.modeling.splines.linear_hermite_patch aerosandbox.modeling.splines.cubic_hermite_patch aerosandbox.modeling.splines.cosine_hermite_patch Package Contents ---------------- .. py:function:: quadratic_bezier_patch_from_tangents(t, x_a, x_b, y_a, y_b, dydx_a, dydx_b) 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. :param t: :param x_a: The x-coordinate of the first endpoint. :param x_b: The x-coordinate of the second endpoint. :param y_a: The y-coordinate of the first endpoint. :param y_b: The y-coordinate of the second endpoint. :param dydx_a: The derivative of y with respect to x at the first endpoint. :param dydx_b: 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. :rtype: 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 >>> ) .. py:function:: linear_hermite_patch(x, x_a, x_b, f_a, f_b) Computes the linear Hermite polynomial patch that passes through the given endpoints f_a and f_b. :param x: Scalar or array of values at which to evaluate the patch. :param x_a: The x-coordinate of the first endpoint. :param x_b: The x-coordinate of the second endpoint. :param f_a: The function value at the first endpoint. :param f_b: The function value at the second endpoint. :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array. .. py:function:: cubic_hermite_patch(x, x_a, x_b, f_a, f_b, dfdx_a, dfdx_b, extrapolation = 'continue') Computes the cubic Hermite polynomial patch that passes through the given endpoints and endpoint derivatives. :param x: Scalar or array of values at which to evaluate the patch. :param x_a: The x-coordinate of the first endpoint. :param x_b: The x-coordinate of the second endpoint. :param f_a: The function value at the first endpoint. :param f_b: The function value at the second endpoint. :param dfdx_a: The derivative of the function with respect to x at the first endpoint. :param dfdx_b: The derivative of the function with respect to x at the second endpoint. :param extrapolation: A string indicating how to handle extrapolation outside of the domain [x_a, x_b]. Valid values are "continue", which continues the patch beyond the endpoints, and "clip", which clips the patch at the endpoints. Default is "continue". :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array. .. py:function:: cosine_hermite_patch(x, x_a, x_b, f_a, f_b, dfdx_a, dfdx_b, extrapolation = 'continue') Computes a Hermite patch (i.e., values + derivatives at endpoints) that uses a cosine function to blend between linear segments. The end result is conceptually similar to a cubic Hermite patch, but computation is faster and the patch is $C^\infty$-continuous. :param x: Scalar or array of values at which to evaluate the patch. :param x_a: The x-coordinate of the first endpoint. :param x_b: The x-coordinate of the second endpoint. :param f_a: The function value at the first endpoint. :param f_b: The function value at the second endpoint. :param dfdx_a: The derivative of the function with respect to x at the first endpoint. :param dfdx_b: The derivative of the function with respect to x at the second endpoint. :param extrapolation: A string indicating how to handle extrapolation outside of the domain [x_a, x_b]. Valid values are "continue", which continues the patch beyond the endpoints, and "linear", which extends the patch linearly at the endpoints. Default is "continue". :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array. .. py:data:: x