Spline

class splinebox.spline_curves.Spline(M, basis_function, closed=False, control_points=None, padding_function=<function padding_function>)

Base class for the construction of a spline.

Parameters

Mint

Number of knots.

basis_functionsplinebox.basis_functions.BasisFunction

The basis function used to construct the spline.

closedboolean

Whether or not the spline is closed, i.e. the two ends are connected.

control_pointsnp.array

The control points of the spline. Optional, can be provided later.

padding_functioncallable

A function that accepts an array of knots as the first argument and the padding size as the second argument. It should return a padded array. If None, a padded array has to be supplied when setting the knots. The default is constant padding with the edge values (see splinebox.spline_curves.padding_function()).

Attributes

M
basis_function	The basis function of the spline.
closed
control_points	The control points of this spline, i.e. the c[k] in equation (1).
half_support
knots	The knots of this spline, i.e. the values of the spline at \(t=0,1,...,M\).
pad

Methods

arc_length([stop, start, epsabs, epsrel])	Compute the arc length of the spline between the two parameter values specified.
arc_length_to_parameter(s[, atol])	Convert the arc length s to the coresponding value in parameter space.
copy()	Returns a deep copy of this spline.
curvature(t)	Compute the curvature of the spline at position(s) t.
curvilinear_reparametrization_energy([...])	This energy can be used to enforce equal spacing of the knots.
distance(point[, return_t])	Computes the distance of point from the spline.
draw(x, y)	Computes whether a point is inside or outside a closed spline on a regular grid of points.
dtheta(t)	Helper function for calculating the winding number.
eval(t[, derivative])	eval is deprecated use splinebox.spline_curves.Spline.__call__() instead.
fit(points[, arc_length_parameterization])	Fit the provided points with the spline using least squares.
from_json(path)	Constructs a spline from a json file that was saved using splinebox.spline_curves.Spline.to_json().
is_inside(x, y)	Determines if a point with coordinates x, y is inside the spline.
mesh([radius, step_t, step_angle, ...])	Create a 3D mesh around the spline curve.
moving_frame(t[, method, initial_vector])	Compute a moving frame (local orthonormal coordinate system) along the spline.
normal(t[, frame, initial_vector])	Returns the normal vector for 1D and 2D splines.
rotate(rotation_matrix[, centred])	Rotate the spline with the provided rotation matrix.
scale(scaling_factor)	Enlarge or shrink the spline by the provided factor.
to_json(path[, version])	Saves the spline as a json file.
translate(vector)	Translates the spline by a vector.