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agg_bspline.cpp
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284 lines (242 loc) · 7.69 KB
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//----------------------------------------------------------------------------
// Anti-Grain Geometry - Version 2.4
// 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: [email protected]
// http://www.antigrain.com
//----------------------------------------------------------------------------
//
// class bspline
//
//----------------------------------------------------------------------------
#include "agg_bspline.h"
namespace agg
{
//------------------------------------------------------------------------
bspline::bspline() :
m_max(0),
m_num(0),
m_x(0),
m_y(0),
m_last_idx(-1)
{
}
//------------------------------------------------------------------------
bspline::bspline(int num) :
m_max(0),
m_num(0),
m_x(0),
m_y(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_last_idx(-1)
{
init(num, x, y);
}
//------------------------------------------------------------------------
void bspline::init(int max)
{
if(max > 2 && max > m_max)
{
m_am.resize(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 h, p, d, f, e;
for(k = 0; k < m_num; k++)
{
m_am[k] = 0.0;
}
n1 = 3 * m_num;
pod_array<double> al(n1);
temp = &al[0];
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];
}
}
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;
}
}