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/************************************************************************/
/* */
/* vspline - a set of generic tools for creation and evaluation */
/* of uniform b-splines */
/* */
/* Copyright 2015 - 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. */
/* */
/************************************************************************/
/// \file gradient.cc
///
/// \brief evaluating a specific spline, derivatives, precision
///
/// If we create a b-spline over an array containing, at each grid point,
/// the sum of the grid point's coordinates, each 1D row, column, etc will
/// hold a linear gradient with first derivative == 1. If we use NATURAL
/// BCs, evaluating the spline with real coordinates anywhere inside the
/// defined range should produce precisely the sum of the coordinates.
/// This is a good test for both the precision of the evaluation and it's
/// correct functioning, particularly with higher-D arrays.
///
/// compile: clang++ -O3 -DUSE_VC -march=native -std=c++11 -pthread
/// -o gradient gradient.cc -lVc
///
/// (with Vc; use -DUSE_HWY and -lhwy for highway, or -std=c++17 and
/// -DUSE_STDSIMD for the std::simd backend)
///
/// or clang++ -O3 -march=native -std=c++11 -pthread -o gradient gradient.cc
#include <random>
#include <iostream>
#include <vspline/vspline.h>
int main ( int argc , char * argv[] )
{
typedef vspline::bspline < double , 3 > spline_type ;
typedef typename spline_type::shape_type shape_type ;
typedef typename spline_type::view_type view_type ;
typedef typename spline_type::bcv_type bcv_type ;
// let's have a knot point array with nicely odd shape
shape_type core_shape = { 35 , 43 , 19 } ;
// we have to use a longish call to the constructor since we want to pass
// 0.0 to 'tolerance' and it's way down in the argument list, so we have to
// explicitly pass a few arguments which usually take default values before
// we have a chance to pass the tolerance
spline_type bspl ( core_shape , // shape of knot point array
3 , // cubic b-spline
bcv_type ( vspline::NATURAL ) , // natural boundary conditions
0.0 ) ; // no tolerance
// get a view to the bspline's core, to fill it with data
view_type core = bspl.core ;
// create the gradient in each dimension
for ( int d = 0 ; d < bspl.dimension ; d++ )
{
for ( int c = 0 ; c < core_shape[d] ; c++ )
core.bindAt ( d , c ) += c ;
}
// now prefilter the spline. This is more to make sure that the prefilter
// does not do anything wrong - for the given signal, using 'brace()' would
// be sufficient, because the prefilter on a linear gradient should not have
// an effect on the coefficients (due to symmetry)
bspl.prefilter() ;
// set up the evaluator type
typedef vigra::TinyVector < double , 3 > coordinate_type ;
typedef vspline::evaluator < coordinate_type , double > evaluator_type ;
// we also want to verify the derivative along each axis
typedef typename evaluator_type::derivative_spec_type deriv_t ;
deriv_t dsx , dsy , dsz ;
dsx[0] = 1 ; // first derivative along axis 0
dsy[1] = 1 ; // first derivative along axis 1
dsz[2] = 1 ; // first derivative along axis 2
// set up the evaluator for the underived result
evaluator_type ev ( bspl ) ;
// and evaluators for the three first derivatives
evaluator_type ev_dx ( bspl , dsx ) ;
evaluator_type ev_dy ( bspl , dsy ) ;
evaluator_type ev_dz ( bspl , dsz ) ;
// we want to bombard the evaluator with random in-range coordinates
std::random_device rd;
std::mt19937 gen(rd());
// std::mt19937 gen(12345); // fix starting value for reproducibility
coordinate_type c ;
// here comes our test, feed 100 random 3D coordinates and compare the
// evaluator's result with the expected value, which is precisely the
// sum of the coordinate's components. The printout of the derivatives
// is boring: it's always 1. But this assures us that the b-spline is
// perfectly plane, even off the grid points. Towards the surface of the
// volume, the derivative remains at 1.0 because we're using NATURAL
// boundary conditions.
for ( int times = 0 ; times < 100 ; times++ )
{
for ( int d = 0 ; d < bspl.dimension ; d++ )
c[d] = ( core_shape[d] - 1 ) * std::generate_canonical<double, 20>(gen) ;
double result ;
ev.eval ( c , result ) ;
double delta = result - sum ( c ) ;
std::cout << "eval(" << c << ") = " << result
<< " -> delta = " << delta << std::endl ;
ev_dx.eval ( c , result ) ;
std::cout << "dx: " << result ;
ev_dy.eval ( c , result ) ;
std::cout << " dy: " << result ;
ev_dz.eval ( c , result ) ;
std::cout << " dz: " << result << std::endl ;
}
}
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