1 /*****************************************************************************
2 ** This is part of the CTSim program
3 ** Copyright (c) 1983-2009 Kevin Rosenberg
5 ** This program is free software; you can redistribute it and/or modify
6 ** it under the terms of the GNU General Public License (version 2) as
7 ** published by the Free Software Foundation.
9 ** This program is distributed in the hope that it will be useful,
10 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
11 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 ** GNU General Public License for more details.
14 ** You should have received a copy of the GNU General Public License
15 ** along with this program; if not, write to the Free Software
16 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 ******************************************************************************/
20 #include "ctsupport.h"
21 #include "interpolator.h"
24 CubicPolyInterpolator::CubicPolyInterpolator (const double* const y, const int n)
28 sys_error (ERR_SEVERE, "Too few points (%d) in CubicPolyInterpolator", m_n);
31 CubicPolyInterpolator::~CubicPolyInterpolator ()
37 CubicPolyInterpolator::interpolate (double x)
39 int lo = static_cast<int>(floor(x)) - 1;
44 sys_error (ERR_WARNING, "x=%f, out of range [CubicPolyInterpolator]", x);
47 } else if (lo == -1) // linear interpolate at between x = 0 & 1
48 return m_pdY[0] + x * (m_pdY[1] - m_pdY[0]);
52 sys_error (ERR_WARNING, "x=%f, out of range [CubicPolyInterpolator]", x);
55 } else if (hi == m_n) {// linear interpolate between x = (n-2) and (n-1)
56 double frac = x - (lo + 1);
57 return m_pdY[m_n - 2] + frac * (m_pdY[m_n - 1] - m_pdY[m_n - 2]);
60 // Lagrange formula for N=4 (cubic)
63 double xd_1 = x - (lo + 1);
64 double xd_2 = x - (lo + 2);
65 double xd_3 = x - (lo + 3);
67 static double oneSixth = (1. / 6.);
69 double y = xd_1 * xd_2 * xd_3 * -oneSixth * m_pdY[lo];
70 y += xd_0 * xd_2 * xd_3 * 0.5 * m_pdY[lo+1];
71 y += xd_0 * xd_1 * xd_3 * -0.5 * m_pdY[lo+2];
72 y += xd_0 * xd_1 * xd_2 * oneSixth * m_pdY[lo+3];
79 CubicSplineInterpolator::CubicSplineInterpolator (const double* const y, const int n)
82 // Precalculate 2nd derivative of y and put in m_pdY2
83 // Calculated by solving set of simultaneous CubicSpline spline equations
84 // Only n-2 CubicSpline spline equations, but able to make two more
85 // equations by setting second derivative to 0 at ends
87 m_pdY2 = new double [n];
88 m_pdY2[0] = 0; // second deriviative = 0 at beginning and end
91 double* temp = new double [n - 1];
94 for (i = 1; i < n - 1; i++) {
95 double t = 2 + (0.5 * m_pdY2[i-1]);
96 temp[i] = y[i+1] + y[i-1] - y[i] - y[i];
97 temp[i] = (3 * temp[i] - 0.5 * temp[i-1]) / t;
101 for (i = n - 2; i >= 0; i--)
102 m_pdY2[i] = temp[i] + m_pdY2[i] * m_pdY2[i + 1];
107 CubicSplineInterpolator::~CubicSplineInterpolator ()
114 CubicSplineInterpolator::interpolate (double x)
116 const static double oneSixth = (1. / 6.);
117 int lo = static_cast<int>(floor(x));
120 if (lo < 0 || hi >= m_n) {
122 sys_error (ERR_SEVERE, "x out of bounds [CubicSplineInterpolator::interpolate]");
127 double loFr = hi - x;
128 double hiFr = 1 - loFr;
129 double y = loFr * m_pdY[lo] + hiFr * m_pdY[hi];
130 y += oneSixth * ((loFr*loFr*loFr - loFr) * m_pdY2[lo] + (hiFr*hiFr*hiFr - hiFr) * m_pdY2[hi]);