splinepy.spline.Spline

class splinepy.spline.Spline(spline=None, **kwargs)

Bases: SplinepyBase, PySpline

Spline base class. Extends PySpline with documentation.

Generally, all types of splines can be seen as mappings from a \(N_{param}\)-dimensional parametric domain \(\Omega_{param} \subset \mathbb{R}^{N_{param}}\) to a \(N_{phys}\)-dimensional physical domain \(\Omega_{phys} \subset \mathbb{R}^{N_{phys}}\), i.e.,

\[M : \Omega_{param} \to \Omega_{phys}\]

splinepy generally supports different combinations of embeddings, that is different combinations of dimensionalities \(N_{param}\) and \(N_{phys}\), up to dimension 10. The supported spline types differ in the way how the spline function \(M\) is defined. For an overview of the mathematical theories for the different types of supported splines, we refer to the documentation of the classes BSplineBase and BezierBase for a more in-depth discussion of the theory on B-Spline/Bezier families, as well as to their children BSpline, NURBS, Bezier, and RationalBezier for usage examples.

Parameters:

• spline (Spline) – Initialize using another spline. Will SHARE core spline.

• degrees ((para_dim,) array-like) – Keyword only parameter.

• knot_vectors ((para_dim, n) list of array-like) – Keyword only parameter.

• control_points ((m, dim) array-like) – Keyword only parameter.

• weights ((m,) array-like) – Keyword only parameter.

Return type:

None

Methods

Spline.basis(queries[, nthreads])	Returns basis function values on the supports of given queries.
Spline.basis_and_support(queries[, nthreads])	Returns basis function values and their support ids of given queries.
Spline.basis_derivative(queries, orders[, ...])	Returns derivative of basis functions evaluated on the supports of given queries.
Spline.basis_derivative_and_support(queries, ...)	Returns derivative of basis functions and their support ids of given queries.
Spline.clear()	Clears core spline and saved data
Spline.copy([saved_data])	Returns deepcopy of stored data and newly initialized self.
Spline.current_core_properties(self)
Spline.derivative(queries, orders[, nthreads])	Evaluates derivatives of spline.
Spline.elevate_degrees(parametric_dimensions)	Elevate degree.
Spline.evaluate(queries[, nthreads])	Evaluates spline.
Spline.export(fname)	Export spline.
Spline.greville_abscissae([duplicate_tolerance])	Returns greville abscissae.
Spline.jacobian(queries[, nthreads])	Evaluates jacobians on spline.
Spline.mapper(reference)	Retrieve a mapper that can be used to get physical derivatives such as a gradient or hessian in physical space
Spline.proximities(queries[, ...])	Given physical coordinate, finds a parametric coordinate that maps to the nearest physical coordinate.
Spline.reduce_degrees(parametric_dimensions)	Tries to reduce degree.
Spline.sample(resolutions[, nthreads])	Uniformly sample along each parametric dimensions from spline.
Spline.show(**kwargs)	Equivalent to
Spline.showable(**kwargs)	Equivalent to
Spline.support(queries[, nthreads])	Returns basis support ids of given queries.
Spline.todict([tolist])	Return current spline as dict.

Attributes

Spline.check	Returns spline checker.
Spline.control_mesh_resolutions	Returns control mesh resolutions.
Spline.control_point_bounds	Returns bounds of control points.
Spline.control_points	Returns control points.
Spline.cps	Returns control points.
Spline.create	Returns spline creator Can be used to create new splines using geometric relations.
Spline.degrees	Returns Degrees.
Spline.dim	Returns physical dimension.
Spline.ds	Returns Degrees.
Spline.extract	Returns spline extractor.
Spline.has_knot_vectors	Returns True iff spline has knot vectors.
Spline.integrate	Returns spline integrator.
Spline.is_rational	Returns True iff spline is rational.
Spline.knot_multiplicities	Returns knot multiplicities.
Spline.knot_vectors	Returns knot vectors.
Spline.kvs	Returns knot vectors.
Spline.multi_index	Easy control point / weights access using (unraveled) multi index.
Spline.name	Name of the spline provided by cpp side as a str.
Spline.para_dim	Returns parametric dimension.
Spline.parametric_bounds	Returns bounds of parametric_space.
Spline.required_properties	Returns required property of current spline.
Spline.show_options	Show option manager for splines.
Spline.spline_data	Spline data helper for splines.
Spline.unique_knots	Returns unique knots.
Spline.weights	Returns weights.
Spline.whatami	Answers a deep philosophical question of "what am i?"
Spline.ws	Returns weights.