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+//----------------------------------------------------------------------------
+// Anti-Grain Geometry - Version 2.3
+// Copyright (C) 2002-2005 Maxim Shemanarev (http://www.antigrain.com)
+//
+// Permission to copy, use, modify, sell and distribute this software
+// is granted provided this copyright notice appears in all copies.
+// This software is provided "as is" without express or implied
+// warranty, and with no claim as to its suitability for any purpose.
+//
+//----------------------------------------------------------------------------
+// Contact: mcseem@antigrain.com
+// mcseemagg@yahoo.com
+// http://www.antigrain.com
+//----------------------------------------------------------------------------
+//
+// class bspline
+//
+//----------------------------------------------------------------------------
+
+
+#include "agg_bspline.h"
+
+namespace agg
+{
+
+ //------------------------------------------------------------------------
+ bspline::~bspline()
+ {
+ delete [] m_am;
+ }
+
+
+ //------------------------------------------------------------------------
+ bspline::bspline() :
+ m_max(0),
+ m_num(0),
+ m_x(0),
+ m_y(0),
+ m_am(0),
+ m_last_idx(-1)
+ {
+ }
+
+ //------------------------------------------------------------------------
+ bspline::bspline(int num) :
+ m_max(0),
+ m_num(0),
+ m_x(0),
+ m_y(0),
+ m_am(0),
+ m_last_idx(-1)
+ {
+ init(num);
+ }
+
+ //------------------------------------------------------------------------
+ bspline::bspline(int num, const double* x, const double* y) :
+ m_max(0),
+ m_num(0),
+ m_x(0),
+ m_y(0),
+ m_am(0),
+ m_last_idx(-1)
+ {
+ init(num, x, y);
+ }
+
+
+ //------------------------------------------------------------------------
+ void bspline::init(int max)
+ {
+ if(max > 2 && max > m_max)
+ {
+ delete [] m_am;
+ m_am = new double[max * 3];
+ m_max = max;
+ m_x = m_am + m_max;
+ m_y = m_am + m_max * 2;
+ }
+ m_num = 0;
+ m_last_idx = -1;
+ }
+
+
+ //------------------------------------------------------------------------
+ void bspline::add_point(double x, double y)
+ {
+ if(m_num < m_max)
+ {
+ m_x[m_num] = x;
+ m_y[m_num] = y;
+ ++m_num;
+ }
+ }
+
+
+ //------------------------------------------------------------------------
+ void bspline::prepare()
+ {
+ if(m_num > 2)
+ {
+ int i, k, n1;
+ double* temp;
+ double* r;
+ double* s;
+ double* al;
+ double h, p, d, f, e;
+
+ for(k = 0; k < m_num; k++)
+ {
+ m_am[k] = 0.0;
+ }
+
+ n1 = 3 * m_num;
+
+ al = new double[n1];
+ temp = al;
+
+ for(k = 0; k < n1; k++)
+ {
+ temp[k] = 0.0;
+ }
+
+ r = temp + m_num;
+ s = temp + m_num * 2;
+
+ n1 = m_num - 1;
+ d = m_x[1] - m_x[0];
+ e = (m_y[1] - m_y[0]) / d;
+
+ for(k = 1; k < n1; k++)
+ {
+ h = d;
+ d = m_x[k + 1] - m_x[k];
+ f = e;
+ e = (m_y[k + 1] - m_y[k]) / d;
+ al[k] = d / (d + h);
+ r[k] = 1.0 - al[k];
+ s[k] = 6.0 * (e - f) / (h + d);
+ }
+
+ for(k = 1; k < n1; k++)
+ {
+ p = 1.0 / (r[k] * al[k - 1] + 2.0);
+ al[k] *= -p;
+ s[k] = (s[k] - r[k] * s[k - 1]) * p;
+ }
+
+ m_am[n1] = 0.0;
+ al[n1 - 1] = s[n1 - 1];
+ m_am[n1 - 1] = al[n1 - 1];
+
+ for(k = n1 - 2, i = 0; i < m_num - 2; i++, k--)
+ {
+ al[k] = al[k] * al[k + 1] + s[k];
+ m_am[k] = al[k];
+ }
+ delete [] al;
+ }
+ m_last_idx = -1;
+ }
+
+
+
+ //------------------------------------------------------------------------
+ void bspline::init(int num, const double* x, const double* y)
+ {
+ if(num > 2)
+ {
+ init(num);
+ int i;
+ for(i = 0; i < num; i++)
+ {
+ add_point(*x++, *y++);
+ }
+ prepare();
+ }
+ m_last_idx = -1;
+ }
+
+
+ //------------------------------------------------------------------------
+ void bspline::bsearch(int n, const double *x, double x0, int *i)
+ {
+ int j = n - 1;
+ int k;
+
+ for(*i = 0; (j - *i) > 1; )
+ {
+ if(x0 < x[k = (*i + j) >> 1]) j = k;
+ else *i = k;
+ }
+ }
+
+
+
+ //------------------------------------------------------------------------
+ double bspline::interpolation(double x, int i) const
+ {
+ int j = i + 1;
+ double d = m_x[i] - m_x[j];
+ double h = x - m_x[j];
+ double r = m_x[i] - x;
+ double p = d * d / 6.0;
+ return (m_am[j] * r * r * r + m_am[i] * h * h * h) / 6.0 / d +
+ ((m_y[j] - m_am[j] * p) * r + (m_y[i] - m_am[i] * p) * h) / d;
+ }
+
+
+ //------------------------------------------------------------------------
+ double bspline::extrapolation_left(double x) const
+ {
+ double d = m_x[1] - m_x[0];
+ return (-d * m_am[1] / 6 + (m_y[1] - m_y[0]) / d) *
+ (x - m_x[0]) +
+ m_y[0];
+ }
+
+ //------------------------------------------------------------------------
+ double bspline::extrapolation_right(double x) const
+ {
+ double d = m_x[m_num - 1] - m_x[m_num - 2];
+ return (d * m_am[m_num - 2] / 6 + (m_y[m_num - 1] - m_y[m_num - 2]) / d) *
+ (x - m_x[m_num - 1]) +
+ m_y[m_num - 1];
+ }
+
+ //------------------------------------------------------------------------
+ double bspline::get(double x) const
+ {
+ if(m_num > 2)
+ {
+ int i;
+
+ // Extrapolation on the left
+ if(x < m_x[0]) return extrapolation_left(x);
+
+ // Extrapolation on the right
+ if(x >= m_x[m_num - 1]) return extrapolation_right(x);
+
+ // Interpolation
+ bsearch(m_num, m_x, x, &i);
+ return interpolation(x, i);
+ }
+ return 0.0;
+ }
+
+
+ //------------------------------------------------------------------------
+ double bspline::get_stateful(double x) const
+ {
+ if(m_num > 2)
+ {
+ // Extrapolation on the left
+ if(x < m_x[0]) return extrapolation_left(x);
+
+ // Extrapolation on the right
+ if(x >= m_x[m_num - 1]) return extrapolation_right(x);
+
+ if(m_last_idx >= 0)
+ {
+ // Check if x is not in current range
+ if(x < m_x[m_last_idx] || x > m_x[m_last_idx + 1])
+ {
+ // Check if x between next points (most probably)
+ if(m_last_idx < m_num - 2 &&
+ x >= m_x[m_last_idx + 1] &&
+ x <= m_x[m_last_idx + 2])
+ {
+ ++m_last_idx;
+ }
+ else
+ if(m_last_idx > 0 &&
+ x >= m_x[m_last_idx - 1] &&
+ x <= m_x[m_last_idx])
+ {
+ // x is between pevious points
+ --m_last_idx;
+ }
+ else
+ {
+ // Else perform full search
+ bsearch(m_num, m_x, x, &m_last_idx);
+ }
+ }
+ return interpolation(x, m_last_idx);
+ }
+ else
+ {
+ // Interpolation
+ bsearch(m_num, m_x, x, &m_last_idx);
+ return interpolation(x, m_last_idx);
+ }
+ }
+ return 0.0;
+ }
+
+}
+