Página inicial Explorar Ajuda
Registrar Entrar
devn00b
/
EQ2EMu
9
3
Fork 0
Arquivos Issues 59
Tree: 3d54fd32f3
Branches Tags
EQ2EMu
/
EQ2
/
source
/
depends
/
boost_1_72_0
/
libs
/
math
/
doc
/
html
/
math_toolkit
/
cardinal_quadratic_b.html

cardinal_quadratic_b.html 10 KB
Histórico Raw

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103 
  1. <html>
    2. 

  2. <head>
    3. 

  3. <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
    4. 

  4. <title>Cardinal Quadratic B-spline interpolation</title>
    5. 

  5. <link rel="stylesheet" href="../math.css" type="text/css">
    6. 

  6. <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
    7. 

  7. <link rel="home" href="../index.html" title="Math Toolkit 2.11.0">
    8. 

  8. <link rel="up" href="../interpolation.html" title="Chapter&#160;12.&#160;Interpolation">
    9. 

  9. <link rel="prev" href="cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation">
    10. 

  10. <link rel="next" href="cardinal_quintic_b.html" title="Cardinal Quintic B-spline interpolation">
    11. 

  11. </head>
    12. 

  12. <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
    13. 

  13. <table cellpadding="2" width="100%"><tr>
    14. 

  14. <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
    15. 

  15. <td align="center"><a href="../../../../../index.html">Home</a></td>
    16. 

  16. <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
    17. 

  17. <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
    18. 

  18. <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
    19. 

  19. <td align="center"><a href="../../../../../more/index.htm">More</a></td>
    20. 

  20. </tr></table>
    21. 

  21. <hr>
    22. 

  22. <div class="spirit-nav">
    23. 

  23. <a accesskey="p" href="cardinal_cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cardinal_quintic_b.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
    24. 

  24. </div>
    25. 

  25. <div class="section">
    26. 

  26. <div class="titlepage"><div><div><h2 class="title" style="clear: both">
    27. 

  27. <a name="math_toolkit.cardinal_quadratic_b"></a><a class="link" href="cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation">Cardinal Quadratic B-spline
    28. 

  28.     interpolation</a>
    29. 

  29. </h2></div></div></div>
    30. 

  30. <h4>
    31. 

  31. <a name="math_toolkit.cardinal_quadratic_b.h0"></a>
    32. 

  32.       <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.synopsis"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.synopsis">Synopsis</a>
    33. 

  33.     </h4>
    34. 

  34. <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">cardinal_quadratic_b_spline</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
    35. 

  35. </pre>
    36. 

  36. <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">interpolators</span> <span class="special">{</span>
    37. 

  37. 

  38. <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
    39. 

  39. <span class="keyword">class</span> <span class="identifier">cardinal_quadratic_b_spline</span>
    40. 

  40. <span class="special">{</span>
    41. 

  41. <span class="keyword">public</span><span class="special">:</span>
    42. 

  42.     <span class="comment">// If you don't know the value of the derivative at the endpoints, leave them as NaNs and the routine will estimate them.</span>
    43. 

  43.     <span class="comment">// y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).</span>
    44. 

  44.     <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span><span class="special">*</span> <span class="keyword">const</span> <span class="identifier">y</span><span class="special">,</span>
    45. 

  45.                                 <span class="identifier">size_t</span> <span class="identifier">n</span><span class="special">,</span>
    46. 

  46.                                 <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
    47. 

  47.                                 <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
    48. 

  48.                                 <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
    49. 

  49.                                 <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
    50. 

  50. 

  51.     <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span>
    52. 

  52.                                 <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
    53. 

  53.                                 <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
    54. 

  54.                                 <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
    55. 

  55.                                 <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
    56. 

  56. 

  57.     <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
    58. 

  58. 

  59.     <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
    60. 

  60. <span class="special">};</span>
    61. 

  61. <span class="special">}}}</span>
    62. 

  62. </pre>
    63. 

  63. <h4>
    64. 

  64. <a name="math_toolkit.cardinal_quadratic_b.h1"></a>
    65. 

  65.       <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte">Cardinal
    66. 

  66.       Quadratic B-Spline Interpolation</a>
    67. 

  67.     </h4>
    68. 

  68. <p>
    69. 

  69.       The cardinal quadratic B-spline interpolator is very nearly the same as the
    70. 

  70.       cubic B-spline interpolator, with the modification that the basis functions
    71. 

  71.       are constructed by convolving a box function with itself twice, rather than
    72. 

  72.       three times as is done with the cubic B-spline.
    73. 

  73.     </p>
    74. 

  74. <p>
    75. 

  75.       Since the basis functions are less smooth than the cubic B-spline, you will
    76. 

  76.       nearly always wish to use the cubic B-spline interpolator rather than this.
    77. 

  77.       However, this interpolator is occasionally useful for approximating functions
    78. 

  78.       of reduced smoothness, as hence finds use internally in the Boost.Math library.
    79. 

  79.     </p>
    80. 

  80. <p>
    81. 

  81.       It is reasonable to test this interpolator against the cubic b-spline interpolator
    82. 

  82.       when you are approximating functions which are two or three times continuously
    83. 

  83.       differentiable, but not three or four times differentiable.
    84. 

  84.     </p>
    85. 

  85. </div>
    86. 

  86. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    87. 

  87. <td align="left"></td>
    88. 

  88. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    89. 

  89.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    90. 

  90.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    91. 

  91.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    92. 

  92.       Daryle Walker and Xiaogang Zhang<p>
    93. 

  93.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    94. 

  94.         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
    95. 

  95.       </p>
    96. 

  96. </div></td>
    97. 

  97. </tr></table>
    98. 

  98. <hr>
    99. 

  99. <div class="spirit-nav">
    100. 

  100. <a accesskey="p" href="cardinal_cubic_b.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../interpolation.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="cardinal_quintic_b.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
    101. 

  101. </div>
    102. 

  102. </body>
    103. 

  103. </html>
    104.