# Approximation¶

Methods for approximating functions in spline spaces.

pyiga.approx.interpolate(kvs, f, geo=None, nodes=None)

Perform interpolation in a spline space.

Returns the coefficients for the interpolant of the function f in the tensor product B-spline basis kvs.

By default, f is assumed to be defined in the parameter domain. If a geometry is passed in geo, interpolation is instead done in physical coordinates.

nodes should be a tensor grid (i.e., a sequence of one-dimensional arrays) in the parameter domain specifying the interpolation nodes. If not specified, the Gréville abscissae are used.

pyiga.approx.project_L2(kvs, f, f_physical=False, geo=None)

Perform $$L_2$$-projection into a spline space.

Returns the coefficients for the $$L_2$$-projection of the function f into the tensor product B-spline basis kvs. Optionally, a geometry transform geo can be specified to compute the projection in a physical domain.

By default, f is assumed to be defined in the parameter domain. If it is given in physical coordinates, pass f_physical=True. This requires geo to be specified.

This function also supports projection into a hierarchical spline space by passing a HSpace object in place of kvs.