284 lines
7.7 KiB
C++
284 lines
7.7 KiB
C++
//----------------------------------------------------------------------------
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// Anti-Grain Geometry - Version 2.4
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// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
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//
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// Permission to copy, use, modify, sell and distribute this software
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// is granted provided this copyright notice appears in all copies.
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// This software is provided "as is" without express or implied
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// warranty, and with no claim as to its suitability for any purpose.
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//
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//----------------------------------------------------------------------------
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// Contact: mcseem@antigrain.com
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// mcseemagg@yahoo.com
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// http://www.antigrain.com
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//----------------------------------------------------------------------------
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//
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// class bspline
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//
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//----------------------------------------------------------------------------
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#include "agg_bspline.h"
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namespace agg
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{
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//------------------------------------------------------------------------
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bspline::bspline() :
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m_max(0),
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m_num(0),
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m_x(0),
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m_y(0),
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m_last_idx(-1)
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{
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}
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//------------------------------------------------------------------------
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bspline::bspline(int num) :
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m_max(0),
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m_num(0),
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m_x(0),
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m_y(0),
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m_last_idx(-1)
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{
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init(num);
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}
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//------------------------------------------------------------------------
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bspline::bspline(int num, const double* x, const double* y) :
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m_max(0),
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m_num(0),
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m_x(0),
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m_y(0),
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m_last_idx(-1)
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{
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init(num, x, y);
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}
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//------------------------------------------------------------------------
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void bspline::init(int max)
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{
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if(max > 2 && max > m_max)
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{
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m_am.resize(max * 3);
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m_max = max;
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m_x = &m_am[m_max];
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m_y = &m_am[m_max * 2];
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}
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m_num = 0;
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m_last_idx = -1;
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}
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//------------------------------------------------------------------------
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void bspline::add_point(double x, double y)
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{
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if(m_num < m_max)
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{
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m_x[m_num] = x;
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m_y[m_num] = y;
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++m_num;
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}
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}
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//------------------------------------------------------------------------
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void bspline::prepare()
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{
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if(m_num > 2)
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{
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int i, k, n1;
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double* temp;
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double* r;
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double* s;
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double h, p, d, f, e;
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for(k = 0; k < m_num; k++)
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{
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m_am[k] = 0.0;
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}
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n1 = 3 * m_num;
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pod_array<double> al(n1);
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temp = &al[0];
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for(k = 0; k < n1; k++)
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{
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temp[k] = 0.0;
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}
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r = temp + m_num;
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s = temp + m_num * 2;
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n1 = m_num - 1;
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d = m_x[1] - m_x[0];
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e = (m_y[1] - m_y[0]) / d;
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for(k = 1; k < n1; k++)
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{
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h = d;
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d = m_x[k + 1] - m_x[k];
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f = e;
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e = (m_y[k + 1] - m_y[k]) / d;
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al[k] = d / (d + h);
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r[k] = 1.0 - al[k];
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s[k] = 6.0 * (e - f) / (h + d);
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}
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for(k = 1; k < n1; k++)
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{
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p = 1.0 / (r[k] * al[k - 1] + 2.0);
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al[k] *= -p;
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s[k] = (s[k] - r[k] * s[k - 1]) * p;
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}
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m_am[n1] = 0.0;
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al[n1 - 1] = s[n1 - 1];
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m_am[n1 - 1] = al[n1 - 1];
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for(k = n1 - 2, i = 0; i < m_num - 2; i++, k--)
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{
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al[k] = al[k] * al[k + 1] + s[k];
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m_am[k] = al[k];
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}
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}
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m_last_idx = -1;
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}
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//------------------------------------------------------------------------
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void bspline::init(int num, const double* x, const double* y)
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{
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if(num > 2)
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{
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init(num);
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int i;
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for(i = 0; i < num; i++)
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{
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add_point(*x++, *y++);
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}
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prepare();
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}
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m_last_idx = -1;
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}
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//------------------------------------------------------------------------
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void bspline::bsearch(int n, const double *x, double x0, int *i)
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{
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int j = n - 1;
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int k;
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for(*i = 0; (j - *i) > 1; )
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{
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if(x0 < x[k = (*i + j) >> 1]) j = k;
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else *i = k;
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}
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}
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//------------------------------------------------------------------------
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double bspline::interpolation(double x, int i) const
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{
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int j = i + 1;
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double d = m_x[i] - m_x[j];
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double h = x - m_x[j];
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double r = m_x[i] - x;
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double p = d * d / 6.0;
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return (m_am[j] * r * r * r + m_am[i] * h * h * h) / 6.0 / d +
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((m_y[j] - m_am[j] * p) * r + (m_y[i] - m_am[i] * p) * h) / d;
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}
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//------------------------------------------------------------------------
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double bspline::extrapolation_left(double x) const
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{
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double d = m_x[1] - m_x[0];
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return (-d * m_am[1] / 6 + (m_y[1] - m_y[0]) / d) *
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(x - m_x[0]) +
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m_y[0];
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}
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//------------------------------------------------------------------------
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double bspline::extrapolation_right(double x) const
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{
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double d = m_x[m_num - 1] - m_x[m_num - 2];
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return (d * m_am[m_num - 2] / 6 + (m_y[m_num - 1] - m_y[m_num - 2]) / d) *
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(x - m_x[m_num - 1]) +
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m_y[m_num - 1];
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}
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//------------------------------------------------------------------------
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double bspline::get(double x) const
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{
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if(m_num > 2)
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{
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int i;
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// Extrapolation on the left
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if(x < m_x[0]) return extrapolation_left(x);
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// Extrapolation on the right
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if(x >= m_x[m_num - 1]) return extrapolation_right(x);
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// Interpolation
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bsearch(m_num, m_x, x, &i);
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return interpolation(x, i);
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}
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return 0.0;
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}
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//------------------------------------------------------------------------
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double bspline::get_stateful(double x) const
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{
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if(m_num > 2)
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{
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// Extrapolation on the left
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if(x < m_x[0]) return extrapolation_left(x);
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// Extrapolation on the right
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if(x >= m_x[m_num - 1]) return extrapolation_right(x);
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if(m_last_idx >= 0)
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{
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// Check if x is not in current range
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if(x < m_x[m_last_idx] || x > m_x[m_last_idx + 1])
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{
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// Check if x between next points (most probably)
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if(m_last_idx < m_num - 2 &&
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x >= m_x[m_last_idx + 1] &&
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x <= m_x[m_last_idx + 2])
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{
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++m_last_idx;
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}
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else
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if(m_last_idx > 0 &&
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x >= m_x[m_last_idx - 1] &&
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x <= m_x[m_last_idx])
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{
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// x is between pevious points
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--m_last_idx;
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}
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else
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{
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// Else perform full search
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bsearch(m_num, m_x, x, &m_last_idx);
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}
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}
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return interpolation(x, m_last_idx);
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}
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else
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{
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// Interpolation
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bsearch(m_num, m_x, x, &m_last_idx);
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return interpolation(x, m_last_idx);
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}
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}
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return 0.0;
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}
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}
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