splinebox.spline_curves.

Spline#

class splinebox.spline_curves.Spline(M, basis_function, closed=False, control_points=None, padding_function=<function padding_function>, integration_segment_size=0.1)#

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()).
integration_segment_sizefloat: A positive float number in (0, 1]. Default is 0.1. For details see splinebox.spline_curves.Spline.arc_length().

Attributes:

M
basis_function: The basis function \(\Phi\) of the spline (1).
closed
control_points: The control points \(c[k]\) as defined in equation (1).
half_support
integration_segment_size: Size of the segments for the Gauss-Legendre quadrature.
knots: The knots \(n[k]\) of this spline as defined in equation (3).
ndim: The dimensionality of the space the spline lives in, i.e.
pad

Methods

`__call__`(t[, derivative])	Evalute the spline or one of its derivatives at parameter value(s) t.
`arc_length`([stop, start])	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`([atol, ...])	This energy can be used to enforce equal spacing of the knots.
`distance`(points[, 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.
`fit`(points[, boundary_condition])	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, shift])	Compute a moving frame (local orthonormal coordinate system) along the spline.
`normal`(t[, frame, initial_vector, shift])	Returns the normal vector(s) for 2D and 3D 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.

Raises:

RuntimeError: If M is too small for the specified basis function. M must be at least as large as the support of the basis function.

Examples

Create a new spline object…

>>> spline = splinebox.Spline(M=5, basis_function=splinebox.B3(), closed=False)

Set the control points of the spline. Note that the control points have to be padded for open splines. Here we need to specify 7 3D points instead of 5.

>>> spline.control_points = np.random.rand(7, 3)

Alternatively, we can specify knots instead of control points.

>>> spline.knots = np.array([[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]])

Define a set of parameter value where we want to evaluate the spline

>>> t = np.linspace(0, 5, 11)
>>> t
array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. ])

Evaluate the spline.

>>> spline(t)
array([[1.   , 1.   ],
       [1.413, 1.413],
       [2.   , 2.   ],
       [2.529, 2.529],
       [3.   , 3.   ],
       [3.471, 3.471],
       [4.   , 4.   ],
       [4.587, 4.587],
       [5.   , 5.   ],
       [4.947, 4.947],
       [4.115, 4.115]])