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 <span id="projectnumber">3.1.0</span>
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<div class="title">interval.h</div> </div>
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<a href="interval_8h.html">浏览该文件的文档.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#pragma once</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor">#include <limits></span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>  </div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="keyword">namespace </span><a class="code" href="namespacevde_1_1foundation.html">vde::foundation</a> {</div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  </div>
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<div class="line"><a name="l00020"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html"> 20</a></span> <span class="keyword">class </span><a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> {</div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00022"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c"> 22</a></span>  <span class="keywordtype">double</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>;</div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
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<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a513bd7849e2e5521198340d19f820c8b"> 25</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html#a513bd7849e2e5521198340d19f820c8b">Interval</a>() : <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>(0), <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>(0) {}</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a66158db78aada3139dd0e9e07865872f"> 31</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html#a66158db78aada3139dd0e9e07865872f">Interval</a>(<span class="keywordtype">double</span> v) : <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>(v), <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>(v) {}</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div>
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<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a5f84b35c3de5eb568941c7530dfdb933"> 41</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5f84b35c3de5eb568941c7530dfdb933">Interval</a>(<span class="keywordtype">double</span> l, <span class="keywordtype">double</span> h) : <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>(std::min(l,h)), <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>(std::max(l,h)) {}</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
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<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a8619e852abc13e8b1b7f0e491d5583cc"> 47</a></span>  [[nodiscard]] <span class="keywordtype">double</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a8619e852abc13e8b1b7f0e491d5583cc">mid</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> (<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> + <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>) * 0.5; }</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  </div>
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<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a47e0001ddecda2ec873331b722038e36"> 53</a></span>  [[nodiscard]] <span class="keywordtype">double</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a47e0001ddecda2ec873331b722038e36">width</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> - <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>; }</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
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<div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a1f1ee2ccbd77e563c348c049cb093083"> 60</a></span>  [[nodiscard]] <span class="keywordtype">bool</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a1f1ee2ccbd77e563c348c049cb093083">contains</a>(<span class="keywordtype">double</span> v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> <= v && v <= <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>; }</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div>
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<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a62f6dda3323dc45de44338391945fa99"> 67</a></span>  [[nodiscard]] <span class="keywordtype">bool</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a62f6dda3323dc45de44338391945fa99">is_exact</a>(<span class="keywordtype">double</span> eps = 1e-12)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a47e0001ddecda2ec873331b722038e36">width</a>() < eps; }</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
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<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a8f301412656c4c858d254b8f4452fa66"> 74</a></span>  [[nodiscard]] <span class="keywordtype">bool</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a8f301412656c4c858d254b8f4452fa66">overlaps</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">return</span> !(<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> < o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> || o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> < <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>);</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  }</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  </div>
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<div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#abf6c26f19ac4454879cdc7191e7e0b8b"> 96</a></span>  [[nodiscard]] <span class="keywordtype">int</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html#abf6c26f19ac4454879cdc7191e7e0b8b">cmp</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> < o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>) <span class="keywordflow">return</span> -1; <span class="comment">// 确定 this < o</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> (<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> > o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>) <span class="keywordflow">return</span> 1; <span class="comment">// 确定 this > o</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">return</span> 0; <span class="comment">// 不确定（区间重叠）</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  }</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  </div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// ── 算术运算 ──</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
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<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a2b74a1061b46dc8d8c3c02fe7aa02e71"> 108</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a2b74a1061b46dc8d8c3c02fe7aa02e71">operator+</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">return</span> {<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> + o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> + o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>};</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div>
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<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#ac2301940976c8126b99a825c061b5157"> 116</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#ac2301940976c8126b99a825c061b5157">operator-</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">return</span> {<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> - o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>, <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> - o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>};</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  }</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
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<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a94a315382cbe430157354b1bb0dbe3ec"> 127</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a94a315382cbe430157354b1bb0dbe3ec">operator*</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordtype">double</span> a = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>*o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, b = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>*o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>, c = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>*o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, d = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>*o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordflow">return</span> {std::min({a,b,c,d}), std::max({a,b,c,d})};</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  }</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
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<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a992ee44fc66758e9e75817373ea38c79"> 139</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a992ee44fc66758e9e75817373ea38c79">operator/</a>(<span class="keyword">const</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>& o)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">if</span> (o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a> <= 0 && o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a> >= 0) <span class="keywordflow">return</span> {-std::numeric_limits<double>::max(),</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  std::numeric_limits<double>::max()};</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordtype">double</span> a = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>/o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, b = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>/o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>, c = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>/o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>, d = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>/o.<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>;</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">return</span> {std::min({a,b,c,d}), std::max({a,b,c,d})};</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  </div>
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<div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#aa6bc5f91fe0b6c0137b72ef1108ee211"> 147</a></span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#aa6bc5f91fe0b6c0137b72ef1108ee211">operator-</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> {-<a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>, -<a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>}; }</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  </div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// ── 数学函数（保守区间）──</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  </div>
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<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#ac7b1ecc127128caeedac48534b79621b"> 158</a></span>  [[nodiscard]] <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#ac7b1ecc127128caeedac48534b79621b">sqrt</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">return</span> {std::sqrt(std::max(0.0, <a class="code" href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">lo</a>)), std::sqrt(std::max(0.0, <a class="code" href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">hi</a>))};</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  }</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
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<div class="line"><a name="l00169"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a66083ca9d23a0aa7deb6635d83377579"> 169</a></span>  <span class="keyword">static</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a66083ca9d23a0aa7deb6635d83377579">from_double</a>(<span class="keywordtype">double</span> v, <span class="keywordtype">double</span> error = 0) {</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">return</span> {v - error, v + error};</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  }</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  </div>
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<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff"> 181</a></span>  <span class="keyword">static</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">from_coord</a>(<span class="keywordtype">double</span> v) {</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordtype">double</span> eps = std::abs(v) * 2.22e-16 + 1e-300;</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">return</span> {v - eps, v + eps};</div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> };</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
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<div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="group__foundation.html#ga4082e53f9e3afe884a6ea7b2005abfd1"> 200</a></span> <span class="keyword">inline</span> <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> <a class="code" href="group__foundation.html#ga4082e53f9e3afe884a6ea7b2005abfd1">orient_2d_interval</a>(<span class="keywordtype">double</span> ax, <span class="keywordtype">double</span> ay, <span class="keywordtype">double</span> bx, <span class="keywordtype">double</span> by, <span class="keywordtype">double</span> cx, <span class="keywordtype">double</span> cy) {</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> acx = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">Interval::from_coord</a>(ax - cx);</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> acy = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">Interval::from_coord</a>(ay - cy);</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> bcx = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">Interval::from_coord</a>(bx - cx);</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> bcy = <a class="code" href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">Interval::from_coord</a>(by - cy);</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">return</span> acx * bcy - acy * bcx;</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> }</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
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<div class="line"><a name="l00232"></a><span class="lineno"><a class="line" href="group__foundation.html#ga90b3b7375e3ad4e30cf60a286515d95b"> 232</a></span> <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="group__foundation.html#ga90b3b7375e3ad4e30cf60a286515d95b">orient_2d_verified</a>(<span class="keywordtype">double</span> ax, <span class="keywordtype">double</span> ay, <span class="keywordtype">double</span> bx, <span class="keywordtype">double</span> by, <span class="keywordtype">double</span> cx, <span class="keywordtype">double</span> cy) {</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a> det = <a class="code" href="group__foundation.html#ga4082e53f9e3afe884a6ea7b2005abfd1">orient_2d_interval</a>(ax, ay, bx, by, cx, cy);</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">return</span> det.<a class="code" href="classvde_1_1foundation_1_1Interval.html#abf6c26f19ac4454879cdc7191e7e0b8b">cmp</a>(<a class="code" href="classvde_1_1foundation_1_1Interval.html">Interval</a>(0.0));</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> }</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  </div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> } <span class="comment">// namespace vde::foundation</span></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html">vde::foundation::Interval</a></div><div class="ttdoc">双精度区间算术类</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00020">interval.h:20</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a1f1ee2ccbd77e563c348c049cb093083"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a1f1ee2ccbd77e563c348c049cb093083">vde::foundation::Interval::contains</a></div><div class="ttdeci">bool contains(double v) const</div><div class="ttdoc">判断区间是否包含给定值</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00060">interval.h:60</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a2b74a1061b46dc8d8c3c02fe7aa02e71"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a2b74a1061b46dc8d8c3c02fe7aa02e71">vde::foundation::Interval::operator+</a></div><div class="ttdeci">Interval operator+(const Interval &o) const</div><div class="ttdoc">区间加法</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00108">interval.h:108</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a47e0001ddecda2ec873331b722038e36"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a47e0001ddecda2ec873331b722038e36">vde::foundation::Interval::width</a></div><div class="ttdeci">double width() const</div><div class="ttdoc">区间宽度</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00053">interval.h:53</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a513bd7849e2e5521198340d19f820c8b"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a513bd7849e2e5521198340d19f820c8b">vde::foundation::Interval::Interval</a></div><div class="ttdeci">Interval()</div><div class="ttdoc">默认构造：空区间 [0, 0]</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00025">interval.h:25</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a5513b8d4cdc8c12dd44af8cdc1d8fbe7"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a5513b8d4cdc8c12dd44af8cdc1d8fbe7">vde::foundation::Interval::lo</a></div><div class="ttdeci">double lo</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00022">interval.h:22</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a5f84b35c3de5eb568941c7530dfdb933"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a5f84b35c3de5eb568941c7530dfdb933">vde::foundation::Interval::Interval</a></div><div class="ttdeci">Interval(double l, double h)</div><div class="ttdoc">从上下界构造区间</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00041">interval.h:41</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a62f6dda3323dc45de44338391945fa99"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a62f6dda3323dc45de44338391945fa99">vde::foundation::Interval::is_exact</a></div><div class="ttdeci">bool is_exact(double eps=1e-12) const</div><div class="ttdoc">判断区间是否足够窄（收敛）</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00067">interval.h:67</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a66083ca9d23a0aa7deb6635d83377579"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a66083ca9d23a0aa7deb6635d83377579">vde::foundation::Interval::from_double</a></div><div class="ttdeci">static Interval from_double(double v, double error=0)</div><div class="ttdoc">从双精度值创建区间（含舍入误差带）</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00169">interval.h:169</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a66158db78aada3139dd0e9e07865872f"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a66158db78aada3139dd0e9e07865872f">vde::foundation::Interval::Interval</a></div><div class="ttdeci">Interval(double v)</div><div class="ttdoc">从单值构造精确区间（退化为点）</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00031">interval.h:31</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a835e5615a8c670408c7f4ba438332b1c"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a835e5615a8c670408c7f4ba438332b1c">vde::foundation::Interval::hi</a></div><div class="ttdeci">double hi</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00022">interval.h:22</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a8619e852abc13e8b1b7f0e491d5583cc"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a8619e852abc13e8b1b7f0e491d5583cc">vde::foundation::Interval::mid</a></div><div class="ttdeci">double mid() const</div><div class="ttdoc">区间中点</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00047">interval.h:47</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a8f301412656c4c858d254b8f4452fa66"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a8f301412656c4c858d254b8f4452fa66">vde::foundation::Interval::overlaps</a></div><div class="ttdeci">bool overlaps(const Interval &o) const</div><div class="ttdoc">判断两个区间是否有重叠</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00074">interval.h:74</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a94a315382cbe430157354b1bb0dbe3ec"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a94a315382cbe430157354b1bb0dbe3ec">vde::foundation::Interval::operator*</a></div><div class="ttdeci">Interval operator*(const Interval &o) const</div><div class="ttdoc">区间乘法</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00127">interval.h:127</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a98405097d818464d2ec44d9a12d4afff"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a98405097d818464d2ec44d9a12d4afff">vde::foundation::Interval::from_coord</a></div><div class="ttdeci">static Interval from_coord(double v)</div><div class="ttdoc">从坐标值创建区间（含 ULP 误差带）</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00181">interval.h:181</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_a992ee44fc66758e9e75817373ea38c79"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#a992ee44fc66758e9e75817373ea38c79">vde::foundation::Interval::operator/</a></div><div class="ttdeci">Interval operator/(const Interval &o) const</div><div class="ttdoc">区间除法</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00139">interval.h:139</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_aa6bc5f91fe0b6c0137b72ef1108ee211"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#aa6bc5f91fe0b6c0137b72ef1108ee211">vde::foundation::Interval::operator-</a></div><div class="ttdeci">Interval operator-() const</div><div class="ttdoc">取负</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00147">interval.h:147</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_abf6c26f19ac4454879cdc7191e7e0b8b"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#abf6c26f19ac4454879cdc7191e7e0b8b">vde::foundation::Interval::cmp</a></div><div class="ttdeci">int cmp(const Interval &o) const</div><div class="ttdoc">确定性区间比较</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00096">interval.h:96</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_ac2301940976c8126b99a825c061b5157"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#ac2301940976c8126b99a825c061b5157">vde::foundation::Interval::operator-</a></div><div class="ttdeci">Interval operator-(const Interval &o) const</div><div class="ttdoc">区间减法</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00116">interval.h:116</a></div></div>
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<div class="ttc" id="aclassvde_1_1foundation_1_1Interval_html_ac7b1ecc127128caeedac48534b79621b"><div class="ttname"><a href="classvde_1_1foundation_1_1Interval.html#ac7b1ecc127128caeedac48534b79621b">vde::foundation::Interval::sqrt</a></div><div class="ttdeci">Interval sqrt() const</div><div class="ttdoc">区间平方根</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00158">interval.h:158</a></div></div>
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<div class="ttc" id="agroup__foundation_html_ga4082e53f9e3afe884a6ea7b2005abfd1"><div class="ttname"><a href="group__foundation.html#ga4082e53f9e3afe884a6ea7b2005abfd1">vde::foundation::orient_2d_interval</a></div><div class="ttdeci">Interval orient_2d_interval(double ax, double ay, double bx, double by, double cx, double cy)</div><div class="ttdoc">二维定向行列式的区间验证</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00200">interval.h:200</a></div></div>
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<div class="ttc" id="agroup__foundation_html_ga90b3b7375e3ad4e30cf60a286515d95b"><div class="ttname"><a href="group__foundation.html#ga90b3b7375e3ad4e30cf60a286515d95b">vde::foundation::orient_2d_verified</a></div><div class="ttdeci">int orient_2d_verified(double ax, double ay, double bx, double by, double cx, double cy)</div><div class="ttdoc">使用区间算术验证 orient_2d 结果</div><div class="ttdef"><b>Definition:</b> <a href="interval_8h_source.html#l00232">interval.h:232</a></div></div>
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<div class="ttc" id="anamespacevde_1_1foundation_html"><div class="ttname"><a href="namespacevde_1_1foundation.html">vde::foundation</a></div><div class="ttdoc">自适应双精度谓词后端（默认）</div><div class="ttdef"><b>Definition:</b> <a href="error__codes_8h_source.html#l00004">error_codes.h:4</a></div></div>
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