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/************************************************************************/
/* */
/* vspline - a set of generic tools for creation and evaluation */
/* of uniform b-splines */
/* */
/* Copyright 2017 - 2023 by Kay F. Jahnke */
/* */
/* Permission is hereby granted, free of charge, to any person */
/* obtaining a copy of this software and associated documentation */
/* files (the "Software"), to deal in the Software without */
/* restriction, including without limitation the rights to use, */
/* copy, modify, merge, publish, distribute, sublicense, and/or */
/* sell copies of the Software, and to permit persons to whom the */
/* Software is furnished to do so, subject to the following */
/* conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the */
/* Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
/* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
/* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT */
/* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, */
/* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING */
/* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR */
/* OTHER DEALINGS IN THE SOFTWARE. */
/* */
/************************************************************************/
/// basis_sample.cc - access to the b-spline basis functions
/// Calculate a set of equally-spaced samples of a b-spline basis function
/// This program takes four parameters on the command line:
/// - the spline's degree
/// - x0, the location of the initial sample
/// - step, the distance from one sample to the next
/// - normalize - if not zero, result will be normalized
/// These values are fed to 'sample_basis' (see below), which starts by
/// calculating the initial sample and then goes 'both ways' to add more
/// samples. The (optionally normalized) samples are echoed to std::cout.
/// example: basis_sample 3 .05 .25 1
/// vspline offers access to the b-spline basis functions via a helper
/// object 'basis_functor'. A good part of the calculation of the basis
/// function's value can be done beforehand and only depends on the
/// degree of the basis function. The basis_functor object performs
/// these calculations once when it's created, subsequent evaluations
/// are relatively fast and rely on the initially generated state.
/// For this example, we use long double values - this example is
/// not about speed, but rather about providing precise values.
/// The basis_functor object can also evaluate vectorized data,
/// but in this example we'll only use it's scalar form.
#include <deque>
#include <vector>
#include <iostream>
#include <iomanip>
#include <vspline/vspline.h>
/// 'sample_basis' returns a vector of samples of the basis function
/// if we have the basis function b(x), it returns these values:
/// bf ( x - x0 + step * k ) for all k E N,
/// wherever they are greater than zero. So for X0 = 0 and step = 1,
/// we get the ordinary unit-spaced sampling of the basis function,
/// with x0 != 0 and step == 1 a set of weights as it might be
/// applied to a set of coefficients to evaluate a b-spline, and
/// with step != 1, we get a set of values which follow the shape
/// of the basis function with more or less sample points than the
/// 'normal' unit-spaced sampling. What's surprising is that these
/// non-unit-step samplings (when multiplied with the step width)
/// also are (often very) close to a partition of unity.
typedef vspline::basis_functor < long double > bf_type ;
std::vector<long double> sample_basis ( bf_type bfunc ,
long double x0 ,
long double step ,
bool normalize = false )
{
auto y = bfunc ( x0 ) ;
auto sum = y ;
assert ( y > 0 ) ;
std::deque<long double> accu ;
accu.push_back ( y ) ;
for ( int k = 1 ; ; k++ )
{
y = bfunc ( x0 - k * step ) ;
if ( y <= 0 )
break ;
accu.push_front ( y ) ;
sum += y ;
}
for ( int k = 1 ; ; k++ )
{
y = bfunc ( x0 + k * step ) ;
if ( y <= 0 )
break ;
accu.push_back ( y ) ;
sum += y ;
}
size_t sz = accu.size() ;
std::vector < long double > result ( sz ) ;
if ( normalize )
{
for ( size_t i = 0 ; i < sz ; i++ )
result[i] = accu[i] / sum ;
}
else
{
for ( size_t i = 0 ; i < sz ; i++ )
result[i] = accu[i] ;
}
return result ;
}
int main ( int argc, char * argv[] )
{
if ( argc != 5 )
{
std::cerr
<< "use: basis_sample degree(int) x0(float) step(float) normalize(0/1)"
<< std::endl ;
exit ( -1 ) ;
}
int degree = std::atoi ( argv[1] ) ;
auto bfunc = bf_type ( degree ) ;
auto x0 = std::atof ( argv[2] ) ;
auto step = std::atof ( argv[3] ) ;
bool normalize = std::atoi ( argv[4] ) ;
auto sample = sample_basis ( bfunc , x0 , step , normalize ) ;
std::cout << std::fixed << std::showpoint
<< std::setprecision
(std::numeric_limits<long double>::max_digits10) ;
for ( auto & e : sample )
std::cout << e << std::endl ;
}
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