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<div class="title">opennurbs_optimize.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* $NoKeywords: $ */</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// McNeel & Associates.</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// MERCHANTABILITY ARE HEREBY DISCLAIMED.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// For complete openNURBS copyright information see <http://www.opennurbs.org>.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">//</span><span class="comment"></span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">////////////////////////////////////////////////////////////////</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span>*/</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#if !defined(OPENNURBS_OPTIMIZE_INC_)</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#define OPENNURBS_OPTIMIZE_INC_</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// find a local minimum of a 1 parameter function</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keywordtype">int</span> ON_FindLocalMinimum( <span class="comment">// returns 0 - failed to converge, 1 - success, 2 - failed to converge to requested tolerances</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keywordtype">int</span> (*)(<span class="keywordtype">void</span>*,<span class="keywordtype">double</span>,<span class="keywordtype">double</span>*,<span class="keywordtype">double</span>*), <span class="comment">// f(void*, double t, double* value, double* derivative );</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keywordtype">void</span>*, <span class="comment">// passed as the void* argument to the above function</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="comment">// ax,bx,cx, 3 abcissa ax<bx<cx or ax>bx>cx, and</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="comment">// f(bx) < f(ax), and f(bx) < f(cx)</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keywordtype">double</span>, <span class="comment">// tol > 0 (minimum relative step size (use ON_EPSILON when in doubt)</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordtype">double</span>, <span class="comment">// zeps > 0 (minimum absolute step size (use 1/2*(desired absolute precision))</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordtype">int</span>, <span class="comment">// maximum number of iterations ( use 100 when in doubt)</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">double</span>* <span class="comment">// abcissa of local minimum returned here</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  );</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// find a local zero of a 1 parameter function</span></div><div class="line"><a name="l00033"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html"> 33</a></span> <span class="keyword">class </span><a class="code" href="../../d7/d6a/class_o_n___local_zero1.html">ON_LocalZero1</a></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> {</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a12bd45df187862dab21ddc41d4bd76ab">ON_LocalZero1</a>();</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">virtual</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a0195c001b43960f3a13ba10815c38c7e">~ON_LocalZero1</a>();</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">virtual</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordtype">bool</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a263e5eb2cf1dac012fe08aa027831bff">Evaluate</a>( <span class="comment">// returns true if successful</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordtype">double</span>, <span class="comment">// evaluation parameter</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordtype">double</span>*, <span class="comment">// f(t) returned here - nullptr never passed</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordtype">double</span>*, <span class="comment">// If not nullptr, then f'(t) returned here</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordtype">int</span> <span class="comment">// < 0: evaluate from below</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="comment">// >= 0: evaluate from above</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  ) = 0;</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordtype">bool</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#af9563714d868e6d60d6dae199691a6af">FindZero</a>( <span class="keywordtype">double</span>* ); <span class="comment">// Searches domain between m_t0 and m_t1</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// domain for a root. Returns true if</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// a root is found.</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// m_t0 and m_t1 specify the domain to search and must satisfy </span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">//</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="comment">// 1) m_t0 != m_t1</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// 2) f(m_t0) and f(m_t1) must have different signs</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// or one must have absolute value <= m_f_tolerance</span></div><div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html#a10c3a20ceb868332f8f2b9b0d833acae"> 58</a></span>  <span class="keywordtype">double</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a1f6093a1868e1e245ecc234b101b160d">m_t0</a>, <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a10c3a20ceb868332f8f2b9b0d833acae">m_t1</a>; </div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html#a525e693f275e4229bdc42574ccd673a5"> 60</a></span>  <span class="keywordtype">double</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a525e693f275e4229bdc42574ccd673a5">m_f_tolerance</a>; <span class="comment">// (>= 0.0) If this value is > 0.0, then</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// the search is terminated when a parameter</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// "t" is found where |f(t)| <= m_f_tolerance.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html#a686d344c9784fd5aed87bc493990c296"> 64</a></span>  <span class="keywordtype">double</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a686d344c9784fd5aed87bc493990c296">m_t_tolerance</a>; <span class="comment">// (>= 0.0) If this value is > 0.0, then</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// the search is terminated when a parameter</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// the root is bracketed in a domain with width</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// <= m_t_tolerance.</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// m_k[] is either nullptr or monotone increasing array of length m_k_count.</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">//</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// This zero finder works on continuous piecewise c2 functions.</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// If the function is c2 on the interior of the domain </span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">//</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// [min(t0,t1), max(m_t0,m_t1)]</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">//</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// then there is no need to initialize m_k[]. If the function</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// is not c2 on the domain in question, then the m_k[m_count] array</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// is a list of parameters that define the c2 domains. When m_k[] </span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// is not nullptr, m_count must be >= 2 and m_k[] must be monotone </span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// increasing and satisfy </span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">//</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// m_k[0] <= min(m_t0,m_t1) </span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// and</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// m_k[m_count-1] >= max(m_t0,m_t1).</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">//</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">// Duplicate values in m_k[] are permitted so that NURBS knot</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="comment">// vector arrays may be used directly.</span></div><div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html#a0c79c99c1ca5b7e9689ff0a69f1fc56b"> 88</a></span>  <span class="keyword">const</span> <span class="keywordtype">double</span>* <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#a0c79c99c1ca5b7e9689ff0a69f1fc56b">m_k</a>;</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// length of m_k[] array ( 0 or >= 2 ).</span></div><div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="../../d7/d6a/class_o_n___local_zero1.html#ad34e2fde582baf1383b0f9cea310cadd"> 91</a></span>  <span class="keywordtype">int</span> <a class="code" href="../../d7/d6a/class_o_n___local_zero1.html#ad34e2fde582baf1383b0f9cea310cadd">m_k_count</a>; </div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> </div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">double</span> m_s0, m_f0, m_s1, m_f1;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">bool</span> BracketZero(<span class="keywordtype">double</span>,<span class="keywordtype">double</span>,<span class="keywordtype">double</span>,<span class="keywordtype">double</span>,<span class="keywordtype">int</span>=0);</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">bool</span> BracketSpan(<span class="keywordtype">double</span>,<span class="keywordtype">double</span>,<span class="keywordtype">double</span>,<span class="keywordtype">double</span>);</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordtype">bool</span> NewtonRaphson( <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">double</span>, <span class="keywordtype">int</span>, <span class="keywordtype">double</span>* );</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> };</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div><div class="ttc" id="class_o_n___local_zero1_html_a10c3a20ceb868332f8f2b9b0d833acae"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a10c3a20ceb868332f8f2b9b0d833acae">ON_LocalZero1::m_t1</a></div><div class="ttdeci">double m_t1</div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:58</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_ad34e2fde582baf1383b0f9cea310cadd"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#ad34e2fde582baf1383b0f9cea310cadd">ON_LocalZero1::m_k_count</a></div><div class="ttdeci">int m_k_count</div><div class="ttdoc">length of m_k[] array ( 0 or >= 2 ). </div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:91</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a263e5eb2cf1dac012fe08aa027831bff"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a263e5eb2cf1dac012fe08aa027831bff">ON_LocalZero1::Evaluate</a></div><div class="ttdeci">virtual bool Evaluate(double, double *, double *, int)=0</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_af9563714d868e6d60d6dae199691a6af"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#af9563714d868e6d60d6dae199691a6af">ON_LocalZero1::FindZero</a></div><div class="ttdeci">bool FindZero(double *)</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a525e693f275e4229bdc42574ccd673a5"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a525e693f275e4229bdc42574ccd673a5">ON_LocalZero1::m_f_tolerance</a></div><div class="ttdeci">double m_f_tolerance</div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:60</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a0c79c99c1ca5b7e9689ff0a69f1fc56b"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a0c79c99c1ca5b7e9689ff0a69f1fc56b">ON_LocalZero1::m_k</a></div><div class="ttdeci">const double * m_k</div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:88</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a1f6093a1868e1e245ecc234b101b160d"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a1f6093a1868e1e245ecc234b101b160d">ON_LocalZero1::m_t0</a></div><div class="ttdeci">double m_t0</div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:58</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a0195c001b43960f3a13ba10815c38c7e"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a0195c001b43960f3a13ba10815c38c7e">ON_LocalZero1::~ON_LocalZero1</a></div><div class="ttdeci">virtual ~ON_LocalZero1()</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html">ON_LocalZero1</a></div><div class="ttdoc">find a local zero of a 1 parameter function </div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:33</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a12bd45df187862dab21ddc41d4bd76ab"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a12bd45df187862dab21ddc41d4bd76ab">ON_LocalZero1::ON_LocalZero1</a></div><div class="ttdeci">ON_LocalZero1()</div></div>
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<div class="ttc" id="class_o_n___local_zero1_html_a686d344c9784fd5aed87bc493990c296"><div class="ttname"><a href="../../d7/d6a/class_o_n___local_zero1.html#a686d344c9784fd5aed87bc493990c296">ON_LocalZero1::m_t_tolerance</a></div><div class="ttdeci">double m_t_tolerance</div><div class="ttdef"><b>Definition:</b> opennurbs_optimize.h:64</div></div>
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