+/*****************************************************************************
+** This is part of the CTSim program
+** Copyright (c) 1983-2001 Kevin Rosenberg
+**
+** $Id: interpolator.cpp,v 1.1 2001/02/11 21:57:08 kevin Exp $
+**
+** This program is free software; you can redistribute it and/or modify
+** it under the terms of the GNU General Public License (version 2) as
+** published by the Free Software Foundation.
+**
+** This program is distributed in the hope that it will be useful,
+** but WITHOUT ANY WARRANTY; without even the implied warranty of
+** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+** GNU General Public License for more details.
+**
+** You should have received a copy of the GNU General Public License
+** along with this program; if not, write to the Free Software
+** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+******************************************************************************/
+
+
+#include "ctsupport.h"
+#include "interpolator.h"
+
+
+CubicPolyInterpolator::CubicPolyInterpolator (const double* const y, const int n)
+ : m_pdY(y), m_n(n)
+{
+ if (m_n < 2)
+ sys_error (ERR_SEVERE, "Too few points (%d) in CubicPolyInterpolator", m_n);
+}
+
+CubicPolyInterpolator::~CubicPolyInterpolator ()
+{
+}
+
+
+double
+CubicPolyInterpolator::interpolate (double x)
+{
+ int lo = static_cast<int>(floor(x)) - 1;
+ int hi = lo + 3;
+
+ if (lo < -1) {
+ sys_error (ERR_WARNING, "x=%f, out of range [CubicPolyInterpolator]", x);
+ return (0);
+ } else if (lo == -1) // linear interpolate at between x = 0 & 1
+ return m_pdY[0] + x * (m_pdY[1] - m_pdY[0]);
+
+ if (hi > m_n) {
+ sys_error (ERR_WARNING, "x=%f, out of range [CubicPolyInterpolator]", x);
+ return (0);
+ } else if (hi == m_n) {// linear interpolate between x = (n-2) and (n-1)
+ double frac = x - (lo + 1);
+ return m_pdY[m_n - 2] + frac * (m_pdY[m_n - 1] - m_pdY[m_n - 2]);
+ }
+
+ // Lagrange formula for N=4 (cubic)
+
+ double xd_0 = x - lo;
+ double xd_1 = x - (lo + 1);
+ double xd_2 = x - (lo + 2);
+ double xd_3 = x - (lo + 3);
+
+ static double oneSixth = (1. / 6.);
+
+ double y = xd_1 * xd_2 * xd_3 * -oneSixth * m_pdY[lo];
+ y += xd_0 * xd_2 * xd_3 * 0.5 * m_pdY[lo+1];
+ y += xd_0 * xd_1 * xd_3 * -0.5 * m_pdY[lo+2];
+ y += xd_0 * xd_1 * xd_2 * oneSixth * m_pdY[lo+3];
+
+ return (y);
+}
+
+
+
+CubicSplineInterpolator::CubicSplineInterpolator (const double* const y, const int n)
+ : m_pdY(y), m_n(n)
+{
+ // Precalculate 2nd derivative of y and put in m_pdY2
+ // Calculated by solving set of simultaneous CubicSpline spline equations
+ // Only n-2 CubicSpline spline equations, but able to make two more
+ // equations by setting second derivative to 0 at ends
+
+ m_pdY2 = new double [n];
+ m_pdY2[0] = 0; // second deriviative = 0 at beginning and end
+ m_pdY2[n-1] = 0;
+
+ double* temp = new double [n - 1];
+ temp[0] = 0;
+ int i;
+ for (i = 1; i < n - 1; i++) {
+ double t = 2 + (0.5 * m_pdY2[i-1]);
+ temp[i] = y[i+1] + y[i-1] - y[i] - y[i];
+ temp[i] = (3 * temp[i] - 0.5 * temp[i-1]) / t;
+ m_pdY2[i] = -0.5 / t;
+ }
+
+ for (i = n - 2; i >= 0; i--)
+ m_pdY2[i] = temp[i] + m_pdY2[i] * m_pdY2[i + 1];
+
+ delete temp;
+}
+
+CubicSplineInterpolator::~CubicSplineInterpolator ()
+{
+ delete m_pdY2;
+}
+
+
+double
+CubicSplineInterpolator::interpolate (double x)
+{
+ const static double oneSixth = (1. / 6.);
+ int lo = static_cast<int>(floor(x));
+ int hi = lo + 1;
+
+ if (lo < 0 || hi >= m_n) {
+ sys_error (ERR_SEVERE, "X range out of bounds [CubicSplineInterpolator::interpolate]");
+ return (0);
+ }
+
+ double loFr = hi - x;
+ double hiFr = 1 - loFr;
+ double y = loFr * m_pdY[lo] + hiFr * m_pdY[hi];
+ y += oneSixth * ((loFr*loFr*loFr - loFr) * m_pdY2[lo] + (hiFr*hiFr*hiFr - hiFr) * m_pdY2[hi]);
+
+ return y;
+}
+
+
+
projects / ctsim.git / commitdiff