.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
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.TH interpolate 4rheolef "rheolef-7.0" "rheolef-7.0" "rheolef-7.0"
.\" label: /*Class:interpolate
.SH NAME
\fBinterpolate\fP - Lagrange interpolation of a function
.\" skip: @findex  interpolate
.\" skip: @clindex space
.\" skip: @clindex field
.PP
.SH DESCRIPTION

 The function \fBinterpolation\fP implements the
 Lagrange interpolation of a function or a class-function.
.SH SYNOPSIS

 template <class Function>
 field interpolate (const space& Xh, const Function& f);
.SH EXAMPLE

 The following code compute the Lagrange interpolation
 \fBpi_h_u\fP of u(x).
.\" begin_example
.Sp
.nf
  Float u(const point& x);
  ...
  geo omega("square");
  space Xh (omega, "P1");
  field pi_h_u = interpolate (Xh, u);
.Sp
.fi
.\" end_example
.SH ADVANCED EXAMPLE

It is possible the replace the function \fBu\fP
by a variable of the \fBfield\fP type that represents
a picewise polynomial function: this invocation allows
the reinterpolation of a field on another mesh or with
another approximation.
.\" begin_example
.Sp
.nf
  geo omega2 ("square2");
  space X2h (omega2, "P1");
  field uh2 = interpolate (X2h, pi_h_u);
.Sp
.fi
.\" end_example
.\" END
.SH COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>.
This is free software: you are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by law.