323 lines
10 KiB
C++
323 lines
10 KiB
C++
// ____ ______ __
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// / __ \ / ____// /
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// / /_/ // / / /
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// / ____// /___ / /___ PixInsight Class Library
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// /_/ \____//_____/ PCL 2.4.23
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// ----------------------------------------------------------------------------
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// pcl/AkimaInterpolation.h - Released 2022-03-12T18:59:29Z
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// ----------------------------------------------------------------------------
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// This file is part of the PixInsight Class Library (PCL).
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// PCL is a multiplatform C++ framework for development of PixInsight modules.
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//
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// Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved.
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//
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// Redistribution and use in both source and binary forms, with or without
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// modification, is permitted provided that the following conditions are met:
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//
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// 1. All redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// 2. All redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// 3. Neither the names "PixInsight" and "Pleiades Astrophoto", nor the names
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// of their contributors, may be used to endorse or promote products derived
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// from this software without specific prior written permission. For written
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// permission, please contact info@pixinsight.com.
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//
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// 4. All products derived from this software, in any form whatsoever, must
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// reproduce the following acknowledgment in the end-user documentation
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// and/or other materials provided with the product:
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//
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// "This product is based on software from the PixInsight project, developed
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// by Pleiades Astrophoto and its contributors (https://pixinsight.com/)."
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//
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// Alternatively, if that is where third-party acknowledgments normally
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// appear, this acknowledgment must be reproduced in the product itself.
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//
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// THIS SOFTWARE IS PROVIDED BY PLEIADES ASTROPHOTO AND ITS CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS
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// INTERRUPTION; PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; AND LOSS OF USE,
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// DATA OR PROFITS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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// ----------------------------------------------------------------------------
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#ifndef __PCL_AkimaInterpolation_h
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#define __PCL_AkimaInterpolation_h
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/// \file pcl/AkimaInterpolation.h
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#include <pcl/Defs.h>
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#include <pcl/Diagnostics.h>
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#include <pcl/UnidimensionalInterpolation.h>
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namespace pcl
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{
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// ----------------------------------------------------------------------------
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#define m_x this->m_x
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#define m_y this->m_y
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/*!
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* \class AkimaInterpolation
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* \brief Akima subspline interpolation algorithm
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*
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* <b>References</b>
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*
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* Hiroshi Akima, <em>A new method of interpolation and smooth curve fitting
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* based on local procedures</em>, Journal of the ACM, Vol. 17, No. 4, October
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* 1970, pages 589-602.
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*
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* <b>Implementation</b>
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*
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* Our implementation is based on the book <em>Numerical Algorithms with
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* C</em>, by G. Engeln-Mullges and F. Uhlig (Springer, 1996), section 13.1.
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*
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* We properly represent corners when a data point lies between two adjacent
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* straight lines with different slopes. This means that our implementation
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* does not impose continuous differentiability, which deviates from the
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* original work by Akima. Supporting the accurate representation of corners
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* has several practical advantages in our opinion; one of them is the enhanced
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* flexibility for the application of Akima interpolation to graphical
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* representations of curves given by a set of prescribed x,y data points.
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*
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* \sa CubicSplineInterpolation, LinearInterpolation
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*/
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template <typename T = double>
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class PCL_CLASS AkimaInterpolation : public UnidimensionalInterpolation<T>
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{
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public:
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/*!
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* Represents a vector of independent and dependent variable values.
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*/
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typedef typename UnidimensionalInterpolation<T>::vector_type vector_type;
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/*!
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* Represents a vector of interpolation coefficients.
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*/
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typedef vector_type coefficient_vector;
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/*!
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* Constructs an %AkimaInterpolation object.
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*/
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AkimaInterpolation() = default;
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/*!
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* Copy constructor.
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*/
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AkimaInterpolation( const AkimaInterpolation& ) = default;
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/*!
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* Move constructor.
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*/
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AkimaInterpolation( AkimaInterpolation&& ) = default;
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/*!
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* Destroys an %AkimaInterpolation object.
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*/
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virtual ~AkimaInterpolation()
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{
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}
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/*!
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* Initializes a new interpolation.
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*
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* \param x %Vector of x-values:\n
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* \n
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* \li If x is not empty: Must be a vector of monotonically increasing,
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* distinct values: x[0] < x[1] < ... < x[n-1].\n
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* \li If x is empty: The interpolation will use implicit x[i] = i for
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* i = {0,1,...,n-1}.\n
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*
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* \param y %Vector of function values for i = {0,1,...,n-1}.
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*
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* The length of the \a y vector (and also the length of a nonempty \a x
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* vector) must be \e n >= 5. This is because Akima interpolation requires
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* at least 4 subintervals.
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*/
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void Initialize( const vector_type& x, const vector_type& y ) override
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{
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if ( y.Length() < 5 )
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throw Error( "AkimaInterpolation::Initialize(): Less than five data points specified." );
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try
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{
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Clear();
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UnidimensionalInterpolation<T>::Initialize( x, y );
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int n = m_y.Length();
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int N = n-1; // Number of subintervals
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m_b = coefficient_vector( N );
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m_c = coefficient_vector( N );
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m_d = coefficient_vector( N );
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// Chordal slopes
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coefficient_vector m0( N+4 ); // room for 4 additional prescribed slopes
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T* m = m0.At( 2 ); // allow negative subscripts m[-1] and m[-2]
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// Akima left-hand slopes to support corners
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coefficient_vector tL( n );
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// Calculate chordal slopes for each subinterval
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if ( m_x )
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for ( int i = 0; i < N; ++i )
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{
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T h = m_x[i+1] - m_x[i];
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if ( 1 + h*h == 1 )
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throw Error( "AkimaInterpolation::Initialize(): Empty interpolation subinterval(s)." );
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m[i] = (m_y[i+1] - m_y[i])/h;
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}
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else
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for ( int i = 0; i < N; ++i )
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m[i] = m_y[i+1] - m_y[i];
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// Prescribed slopes at ending locations
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m[-2 ] = 3*m[ 0] - 2*m[ 1];
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m[-1 ] = 2*m[ 0] - m[ 1];
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m[ N ] = 2*m[N-1] - m[N-2];
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m[N+1] = 3*m[N-1] - 2*m[N-2];
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/*
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* Akima left-hand and right-hand slopes.
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* Right-hand slopes are just the interpolation coefficients bi.
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*/
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for ( int i = 0; i < n; ++i )
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{
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T f = Abs( m[i-1] - m[i-2] );
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T e = Abs( m[i+1] - m[i] ) + f;
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if ( 1 + e != 1 )
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{
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tL[i] = m[i-1] + f*(m[i] - m[i-1])/e;
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if ( i < N )
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m_b[i] = tL[i];
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}
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else
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{
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tL[i] = m[i-1];
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if ( i < N )
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m_b[i] = m[i];
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}
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}
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/*
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* Interpolation coefficients m_b[i], m_c[i], m_d[i]. 'ai'
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* coefficients are the m_y[i] ordinate values.
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*/
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for ( int i = 0; i < N; ++i )
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{
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m_c[i] = 3*m[i] - 2*m_b[i] - tL[i+1];
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m_d[i] = m_b[i] + tL[i+1] - 2*m[i];
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if ( m_x )
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{
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T h = m_x[i+1] - m_x[i];
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m_c[i] /= h;
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m_d[i] /= h*h;
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}
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}
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}
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catch ( ... )
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{
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Clear();
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throw;
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}
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}
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/*!
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* Returns an interpolated function value at \a x location.
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*/
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PCL_HOT_FUNCTION
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double operator()( double x ) const override
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{
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PCL_PRECONDITION( IsValid() )
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/*
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* Find the subinterval i0 such that m_x[i0] <= x < m_x[i0+1].
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* Find the distance dx = x - m_x[i], or dx = x - i for implicit x = {0,1,...n-1}.
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*/
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int i0;
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double dx;
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if ( m_x )
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{
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i0 = 0;
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int i1 = m_x.Length() - 1;
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while ( i1-i0 > 1 )
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{
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int im = (i0 + i1) >> 1;
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if ( x < m_x[im] )
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i1 = im;
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else
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i0 = im;
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}
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dx = x - double( m_x[i0] );
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}
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else
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{
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if ( x <= 0 )
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return m_y[0];
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if ( x >= m_y.Length()-1 )
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return m_y[m_y.Length()-1];
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i0 = TruncInt( x );
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dx = x - i0;
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}
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/*
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* Use a Horner scheme to calculate b[i]*dx + c[i]*dx^2 + d[i]*dx^3.
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*/
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return m_y[i0] + dx*(m_b[i0] + dx*(m_c[i0] + dx*m_d[i0]));
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}
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/*!
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* Frees internal data structures in this AkimaInterpolation object.
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*/
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void Clear() override
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{
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m_b.Clear();
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m_c.Clear();
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m_d.Clear();
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UnidimensionalInterpolation<T>::Clear();
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}
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/*!
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* Returns true iff this interpolation is valid, i.e. if it has been
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* correctly initialized and is ready to interpolate function values.
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*/
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bool IsValid() const override
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{
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return m_b && m_c && m_d;
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}
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protected:
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/*
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* Interpolating coefficients for each subinterval.
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* The coefficients for dx^0 are the input ordinate values in the m_y vector.
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*/
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coefficient_vector m_b; // coefficients for dx^1
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coefficient_vector m_c; // coefficients for dx^2
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coefficient_vector m_d; // coefficients for dx^3
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};
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#undef m_x
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#undef m_y
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// ----------------------------------------------------------------------------
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} // pcl
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#endif // __PCL_AkimaInterpolation_h
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// ----------------------------------------------------------------------------
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// EOF pcl/AkimaInterpolation.h - Released 2022-03-12T18:59:29Z
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