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  66. <a href="#func-members">Functions</a>  </div>
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  67.   <div class="headertitle">
    68. 

  68. <div class="title">GLM_GTX_quaternion<div class="ingroups"><a class="el" href="a00905.html">Experimental extensions</a></div></div>  </div>
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  70. <div class="contents">
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  71. <table class="memberdecls">
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  72. <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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  73. Functions</h2></td></tr>
    74. 

  74. <tr class="memitem:gacbbbf93d24828d6bd9ba48d43abc985e"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
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  75. <tr class="memitem:gacbbbf93d24828d6bd9ba48d43abc985e"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gacbbbf93d24828d6bd9ba48d43abc985e">cross</a> (qua&lt; T, Q &gt; const &amp;q, vec&lt; 3, T, Q &gt; const &amp;v)</td></tr>
    76. 

  76. <tr class="memdesc:gacbbbf93d24828d6bd9ba48d43abc985e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute a cross product between a quaternion and a vector.  <a href="a00972.html#gacbbbf93d24828d6bd9ba48d43abc985e">More...</a><br /></td></tr>
    77. 

  77. <tr class="separator:gacbbbf93d24828d6bd9ba48d43abc985e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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  78. <tr class="memitem:ga7877a1ec00e43bbfccf6dd11894c0536"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    79. 

  79. <tr class="memitem:ga7877a1ec00e43bbfccf6dd11894c0536"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga7877a1ec00e43bbfccf6dd11894c0536">cross</a> (vec&lt; 3, T, Q &gt; const &amp;v, qua&lt; T, Q &gt; const &amp;q)</td></tr>
    80. 

  80. <tr class="memdesc:ga7877a1ec00e43bbfccf6dd11894c0536"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute a cross product between a vector and a quaternion.  <a href="a00972.html#ga7877a1ec00e43bbfccf6dd11894c0536">More...</a><br /></td></tr>
    81. 

  81. <tr class="separator:ga7877a1ec00e43bbfccf6dd11894c0536"><td class="memSeparator" colspan="2">&#160;</td></tr>
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  82. <tr class="memitem:ga321953c1b2e7befe6f5dcfddbfc6b76b"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    83. 

  83. <tr class="memitem:ga321953c1b2e7befe6f5dcfddbfc6b76b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga321953c1b2e7befe6f5dcfddbfc6b76b">extractRealComponent</a> (qua&lt; T, Q &gt; const &amp;q)</td></tr>
    84. 

  84. <tr class="memdesc:ga321953c1b2e7befe6f5dcfddbfc6b76b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Extract the real component of a quaternion.  <a href="a00972.html#ga321953c1b2e7befe6f5dcfddbfc6b76b">More...</a><br /></td></tr>
    85. 

  85. <tr class="separator:ga321953c1b2e7befe6f5dcfddbfc6b76b"><td class="memSeparator" colspan="2">&#160;</td></tr>
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  86. <tr class="memitem:ga264e10708d58dd0ff53b7902a2bd2561"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    87. 

  87. <tr class="memitem:ga264e10708d58dd0ff53b7902a2bd2561"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga264e10708d58dd0ff53b7902a2bd2561">fastMix</a> (qua&lt; T, Q &gt; const &amp;x, qua&lt; T, Q &gt; const &amp;y, T const &amp;a)</td></tr>
    88. 

  88. <tr class="memdesc:ga264e10708d58dd0ff53b7902a2bd2561"><td class="mdescLeft">&#160;</td><td class="mdescRight">Quaternion normalized linear interpolation.  <a href="a00972.html#ga264e10708d58dd0ff53b7902a2bd2561">More...</a><br /></td></tr>
    89. 

  89. <tr class="separator:ga264e10708d58dd0ff53b7902a2bd2561"><td class="memSeparator" colspan="2">&#160;</td></tr>
    90. 

  90. <tr class="memitem:gacc5cd5f3e78de61d141c2355417424de"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    91. 

  91. <tr class="memitem:gacc5cd5f3e78de61d141c2355417424de"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gacc5cd5f3e78de61d141c2355417424de">intermediate</a> (qua&lt; T, Q &gt; const &amp;prev, qua&lt; T, Q &gt; const &amp;curr, qua&lt; T, Q &gt; const &amp;next)</td></tr>
    92. 

  92. <tr class="memdesc:gacc5cd5f3e78de61d141c2355417424de"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns an intermediate control point for squad interpolation.  <a href="a00972.html#gacc5cd5f3e78de61d141c2355417424de">More...</a><br /></td></tr>
    93. 

  93. <tr class="separator:gacc5cd5f3e78de61d141c2355417424de"><td class="memSeparator" colspan="2">&#160;</td></tr>
    94. 

  94. <tr class="memitem:ga08eb643306c5ba9211a81b322bc89543"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    95. 

  95. <tr class="memitem:ga08eb643306c5ba9211a81b322bc89543"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga08eb643306c5ba9211a81b322bc89543">length2</a> (qua&lt; T, Q &gt; const &amp;q)</td></tr>
    96. 

  96. <tr class="memdesc:ga08eb643306c5ba9211a81b322bc89543"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the squared length of x.  <a href="a00972.html#ga08eb643306c5ba9211a81b322bc89543">More...</a><br /></td></tr>
    97. 

  97. <tr class="separator:ga08eb643306c5ba9211a81b322bc89543"><td class="memSeparator" colspan="2">&#160;</td></tr>
    98. 

  98. <tr class="memitem:ga77d9e2c313b98a1002a1b12408bf5b45"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    99. 

  99. <tr class="memitem:ga77d9e2c313b98a1002a1b12408bf5b45"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL GLM_CONSTEXPR qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga77d9e2c313b98a1002a1b12408bf5b45">quat_identity</a> ()</td></tr>
    100. 

  100. <tr class="memdesc:ga77d9e2c313b98a1002a1b12408bf5b45"><td class="mdescLeft">&#160;</td><td class="mdescRight">Create an identity quaternion.  <a href="a00972.html#ga77d9e2c313b98a1002a1b12408bf5b45">More...</a><br /></td></tr>
    101. 

  101. <tr class="separator:ga77d9e2c313b98a1002a1b12408bf5b45"><td class="memSeparator" colspan="2">&#160;</td></tr>
    102. 

  102. <tr class="memitem:ga07da6ef58646442efe93b0c273d73776"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    103. 

  103. <tr class="memitem:ga07da6ef58646442efe93b0c273d73776"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga07da6ef58646442efe93b0c273d73776">rotate</a> (qua&lt; T, Q &gt; const &amp;q, vec&lt; 3, T, Q &gt; const &amp;v)</td></tr>
    104. 

  104. <tr class="memdesc:ga07da6ef58646442efe93b0c273d73776"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns quarternion square root.  <a href="a00972.html#ga07da6ef58646442efe93b0c273d73776">More...</a><br /></td></tr>
    105. 

  105. <tr class="separator:ga07da6ef58646442efe93b0c273d73776"><td class="memSeparator" colspan="2">&#160;</td></tr>
    106. 

  106. <tr class="memitem:gafcb78dfff45fbf19a7fcb2bd03fbf196"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    107. 

  107. <tr class="memitem:gafcb78dfff45fbf19a7fcb2bd03fbf196"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; 4, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gafcb78dfff45fbf19a7fcb2bd03fbf196">rotate</a> (qua&lt; T, Q &gt; const &amp;q, vec&lt; 4, T, Q &gt; const &amp;v)</td></tr>
    108. 

  108. <tr class="memdesc:gafcb78dfff45fbf19a7fcb2bd03fbf196"><td class="mdescLeft">&#160;</td><td class="mdescRight">Rotates a 4 components vector by a quaternion.  <a href="a00972.html#gafcb78dfff45fbf19a7fcb2bd03fbf196">More...</a><br /></td></tr>
    109. 

  109. <tr class="separator:gafcb78dfff45fbf19a7fcb2bd03fbf196"><td class="memSeparator" colspan="2">&#160;</td></tr>
    110. 

  110. <tr class="memitem:ga03e61282831cc3f52cc76f72f52ad2c5"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    111. 

  111. <tr class="memitem:ga03e61282831cc3f52cc76f72f52ad2c5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga03e61282831cc3f52cc76f72f52ad2c5">rotation</a> (vec&lt; 3, T, Q &gt; const &amp;orig, vec&lt; 3, T, Q &gt; const &amp;dest)</td></tr>
    112. 

  112. <tr class="memdesc:ga03e61282831cc3f52cc76f72f52ad2c5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute the rotation between two vectors.  <a href="a00972.html#ga03e61282831cc3f52cc76f72f52ad2c5">More...</a><br /></td></tr>
    113. 

  113. <tr class="separator:ga03e61282831cc3f52cc76f72f52ad2c5"><td class="memSeparator" colspan="2">&#160;</td></tr>
    114. 

  114. <tr class="memitem:gadc576cc957adc2a568cdcbc3799175bc"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    115. 

  115. <tr class="memitem:gadc576cc957adc2a568cdcbc3799175bc"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gadc576cc957adc2a568cdcbc3799175bc">shortMix</a> (qua&lt; T, Q &gt; const &amp;x, qua&lt; T, Q &gt; const &amp;y, T const &amp;a)</td></tr>
    116. 

  116. <tr class="memdesc:gadc576cc957adc2a568cdcbc3799175bc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Quaternion interpolation using the rotation short path.  <a href="a00972.html#gadc576cc957adc2a568cdcbc3799175bc">More...</a><br /></td></tr>
    117. 

  117. <tr class="separator:gadc576cc957adc2a568cdcbc3799175bc"><td class="memSeparator" colspan="2">&#160;</td></tr>
    118. 

  118. <tr class="memitem:ga0b9bf3459e132ad8a18fe970669e3e35"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    119. 

  119. <tr class="memitem:ga0b9bf3459e132ad8a18fe970669e3e35"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga0b9bf3459e132ad8a18fe970669e3e35">squad</a> (qua&lt; T, Q &gt; const &amp;q1, qua&lt; T, Q &gt; const &amp;q2, qua&lt; T, Q &gt; const &amp;s1, qua&lt; T, Q &gt; const &amp;s2, T const &amp;h)</td></tr>
    120. 

  120. <tr class="memdesc:ga0b9bf3459e132ad8a18fe970669e3e35"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute a point on a path according squad equation.  <a href="a00972.html#ga0b9bf3459e132ad8a18fe970669e3e35">More...</a><br /></td></tr>
    121. 

  121. <tr class="separator:ga0b9bf3459e132ad8a18fe970669e3e35"><td class="memSeparator" colspan="2">&#160;</td></tr>
    122. 

  122. <tr class="memitem:gac228e3fcfa813841804362fcae02b337"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    123. 

  123. <tr class="memitem:gac228e3fcfa813841804362fcae02b337"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_QUALIFIER mat&lt; 3, 3, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gac228e3fcfa813841804362fcae02b337">toMat3</a> (qua&lt; T, Q &gt; const &amp;x)</td></tr>
    124. 

  124. <tr class="memdesc:gac228e3fcfa813841804362fcae02b337"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a quaternion to a 3 * 3 matrix.  <a href="a00972.html#gac228e3fcfa813841804362fcae02b337">More...</a><br /></td></tr>
    125. 

  125. <tr class="separator:gac228e3fcfa813841804362fcae02b337"><td class="memSeparator" colspan="2">&#160;</td></tr>
    126. 

  126. <tr class="memitem:gad0d0c14d7d3c852b41d6a6e4d1da6606"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    127. 

  127. <tr class="memitem:gad0d0c14d7d3c852b41d6a6e4d1da6606"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_QUALIFIER mat&lt; 4, 4, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#gad0d0c14d7d3c852b41d6a6e4d1da6606">toMat4</a> (qua&lt; T, Q &gt; const &amp;x)</td></tr>
    128. 

  128. <tr class="memdesc:gad0d0c14d7d3c852b41d6a6e4d1da6606"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a quaternion to a 4 * 4 matrix.  <a href="a00972.html#gad0d0c14d7d3c852b41d6a6e4d1da6606">More...</a><br /></td></tr>
    129. 

  129. <tr class="separator:gad0d0c14d7d3c852b41d6a6e4d1da6606"><td class="memSeparator" colspan="2">&#160;</td></tr>
    130. 

  130. <tr class="memitem:ga7b2be33d948db631c8815e9f2953a451"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    131. 

  131. <tr class="memitem:ga7b2be33d948db631c8815e9f2953a451"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_QUALIFIER qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga7b2be33d948db631c8815e9f2953a451">toQuat</a> (mat&lt; 3, 3, T, Q &gt; const &amp;x)</td></tr>
    132. 

  132. <tr class="memdesc:ga7b2be33d948db631c8815e9f2953a451"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a 3 * 3 matrix to a quaternion.  <a href="a00972.html#ga7b2be33d948db631c8815e9f2953a451">More...</a><br /></td></tr>
    133. 

  133. <tr class="separator:ga7b2be33d948db631c8815e9f2953a451"><td class="memSeparator" colspan="2">&#160;</td></tr>
    134. 

  134. <tr class="memitem:ga4cf12d456770d716b590fd498bce6136"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    135. 

  135. <tr class="memitem:ga4cf12d456770d716b590fd498bce6136"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_QUALIFIER qua&lt; T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00972.html#ga4cf12d456770d716b590fd498bce6136">toQuat</a> (mat&lt; 4, 4, T, Q &gt; const &amp;x)</td></tr>
    136. 

  136. <tr class="memdesc:ga4cf12d456770d716b590fd498bce6136"><td class="mdescLeft">&#160;</td><td class="mdescRight">Converts a 4 * 4 matrix to a quaternion.  <a href="a00972.html#ga4cf12d456770d716b590fd498bce6136">More...</a><br /></td></tr>
    137. 

  137. <tr class="separator:ga4cf12d456770d716b590fd498bce6136"><td class="memSeparator" colspan="2">&#160;</td></tr>
    138. 

  138. </table>
    139. 

  139. <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
    140. 

  140. <p>Include &lt;<a class="el" href="a01714.html" title="GLM_GTX_quaternion">glm/gtx/quaternion.hpp</a>&gt; to use the features of this extension.</p>
    141. 

  141. <p>Extended quaternion types and functions </p>
    142. 

  142. <h2 class="groupheader">Function Documentation</h2>
    143. 

  143. <a id="gacbbbf93d24828d6bd9ba48d43abc985e"></a>
    144. 

  144. <h2 class="memtitle"><span class="permalink"><a href="#gacbbbf93d24828d6bd9ba48d43abc985e">&#9670;&nbsp;</a></span>cross() <span class="overload">[1/2]</span></h2>
    145. 

  145. 

  146. <div class="memitem">
    147. 

  147. <div class="memproto">
    148. 

  148.       <table class="memname">
    149. 

  149.         <tr>
    150. 

  150.           <td class="memname">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt;3, T, Q&gt; glm::cross </td>
    151. 

  151.           <td>(</td>
    152. 

  152.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    153. 

  153.           <td class="paramname"><em>q</em>, </td>
    154. 

  154.         </tr>
    155. 

  155.         <tr>
    156. 

  156.           <td class="paramkey"></td>
    157. 

  157.           <td></td>
    158. 

  158.           <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
    159. 

  159.           <td class="paramname"><em>v</em>&#160;</td>
    160. 

  160.         </tr>
    161. 

  161.         <tr>
    162. 

  162.           <td></td>
    163. 

  163.           <td>)</td>
    164. 

  164.           <td></td><td></td>
    165. 

  165.         </tr>
    166. 

  166.       </table>
    167. 

  167. </div><div class="memdoc">
    168. 

  168. 

  169. <p>Compute a cross product between a quaternion and a vector. </p>
    170. 

  170. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    171. 

  171. 

  172. </div>
    173. 

  173. </div>
    174. 

  174. <a id="ga7877a1ec00e43bbfccf6dd11894c0536"></a>
    175. 

  175. <h2 class="memtitle"><span class="permalink"><a href="#ga7877a1ec00e43bbfccf6dd11894c0536">&#9670;&nbsp;</a></span>cross() <span class="overload">[2/2]</span></h2>
    176. 

  176. 

  177. <div class="memitem">
    178. 

  178. <div class="memproto">
    179. 

  179.       <table class="memname">
    180. 

  180.         <tr>
    181. 

  181.           <td class="memname">GLM_FUNC_DECL GLM_CONSTEXPR vec&lt;3, T, Q&gt; glm::cross </td>
    182. 

  182.           <td>(</td>
    183. 

  183.           <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
    184. 

  184.           <td class="paramname"><em>v</em>, </td>
    185. 

  185.         </tr>
    186. 

  186.         <tr>
    187. 

  187.           <td class="paramkey"></td>
    188. 

  188.           <td></td>
    189. 

  189.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    190. 

  190.           <td class="paramname"><em>q</em>&#160;</td>
    191. 

  191.         </tr>
    192. 

  192.         <tr>
    193. 

  193.           <td></td>
    194. 

  194.           <td>)</td>
    195. 

  195.           <td></td><td></td>
    196. 

  196.         </tr>
    197. 

  197.       </table>
    198. 

  198. </div><div class="memdoc">
    199. 

  199. 

  200. <p>Compute a cross product between a vector and a quaternion. </p>
    201. 

  201. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    202. 

  202. 

  203. </div>
    204. 

  204. </div>
    205. 

  205. <a id="ga321953c1b2e7befe6f5dcfddbfc6b76b"></a>
    206. 

  206. <h2 class="memtitle"><span class="permalink"><a href="#ga321953c1b2e7befe6f5dcfddbfc6b76b">&#9670;&nbsp;</a></span>extractRealComponent()</h2>
    207. 

  207. 

  208. <div class="memitem">
    209. 

  209. <div class="memproto">
    210. 

  210.       <table class="memname">
    211. 

  211.         <tr>
    212. 

  212.           <td class="memname">GLM_FUNC_DECL T glm::extractRealComponent </td>
    213. 

  213.           <td>(</td>
    214. 

  214.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    215. 

  215.           <td class="paramname"><em>q</em></td><td>)</td>
    216. 

  216.           <td></td>
    217. 

  217.         </tr>
    218. 

  218.       </table>
    219. 

  219. </div><div class="memdoc">
    220. 

  220. 

  221. <p>Extract the real component of a quaternion. </p>
    222. 

  222. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    223. 

  223. 

  224. </div>
    225. 

  225. </div>
    226. 

  226. <a id="ga264e10708d58dd0ff53b7902a2bd2561"></a>
    227. 

  227. <h2 class="memtitle"><span class="permalink"><a href="#ga264e10708d58dd0ff53b7902a2bd2561">&#9670;&nbsp;</a></span>fastMix()</h2>
    228. 

  228. 

  229. <div class="memitem">
    230. 

  230. <div class="memproto">
    231. 

  231.       <table class="memname">
    232. 

  232.         <tr>
    233. 

  233.           <td class="memname">GLM_FUNC_DECL qua&lt;T, Q&gt; glm::fastMix </td>
    234. 

  234.           <td>(</td>
    235. 

  235.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    236. 

  236.           <td class="paramname"><em>x</em>, </td>
    237. 

  237.         </tr>
    238. 

  238.         <tr>
    239. 

  239.           <td class="paramkey"></td>
    240. 

  240.           <td></td>
    241. 

  241.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    242. 

  242.           <td class="paramname"><em>y</em>, </td>
    243. 

  243.         </tr>
    244. 

  244.         <tr>
    245. 

  245.           <td class="paramkey"></td>
    246. 

  246.           <td></td>
    247. 

  247.           <td class="paramtype">T const &amp;&#160;</td>
    248. 

  248.           <td class="paramname"><em>a</em>&#160;</td>
    249. 

  249.         </tr>
    250. 

  250.         <tr>
    251. 

  251.           <td></td>
    252. 

  252.           <td>)</td>
    253. 

  253.           <td></td><td></td>
    254. 

  254.         </tr>
    255. 

  255.       </table>
    256. 

  256. </div><div class="memdoc">
    257. 

  257. 

  258. <p>Quaternion normalized linear interpolation. </p>
    259. 

  259. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    260. 

  260. 

  261. </div>
    262. 

  262. </div>
    263. 

  263. <a id="gacc5cd5f3e78de61d141c2355417424de"></a>
    264. 

  264. <h2 class="memtitle"><span class="permalink"><a href="#gacc5cd5f3e78de61d141c2355417424de">&#9670;&nbsp;</a></span>intermediate()</h2>
    265. 

  265. 

  266. <div class="memitem">
    267. 

  267. <div class="memproto">
    268. 

  268.       <table class="memname">
    269. 

  269.         <tr>
    270. 

  270.           <td class="memname">GLM_FUNC_DECL qua&lt;T, Q&gt; glm::intermediate </td>
    271. 

  271.           <td>(</td>
    272. 

  272.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    273. 

  273.           <td class="paramname"><em>prev</em>, </td>
    274. 

  274.         </tr>
    275. 

  275.         <tr>
    276. 

  276.           <td class="paramkey"></td>
    277. 

  277.           <td></td>
    278. 

  278.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    279. 

  279.           <td class="paramname"><em>curr</em>, </td>
    280. 

  280.         </tr>
    281. 

  281.         <tr>
    282. 

  282.           <td class="paramkey"></td>
    283. 

  283.           <td></td>
    284. 

  284.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    285. 

  285.           <td class="paramname"><em>next</em>&#160;</td>
    286. 

  286.         </tr>
    287. 

  287.         <tr>
    288. 

  288.           <td></td>
    289. 

  289.           <td>)</td>
    290. 

  290.           <td></td><td></td>
    291. 

  291.         </tr>
    292. 

  292.       </table>
    293. 

  293. </div><div class="memdoc">
    294. 

  294. 

  295. <p>Returns an intermediate control point for squad interpolation. </p>
    296. 

  296. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    297. 

  297. 

  298. </div>
    299. 

  299. </div>
    300. 

  300. <a id="ga08eb643306c5ba9211a81b322bc89543"></a>
    301. 

  301. <h2 class="memtitle"><span class="permalink"><a href="#ga08eb643306c5ba9211a81b322bc89543">&#9670;&nbsp;</a></span>length2()</h2>
    302. 

  302. 

  303. <div class="memitem">
    304. 

  304. <div class="memproto">
    305. 

  305.       <table class="memname">
    306. 

  306.         <tr>
    307. 

  307.           <td class="memname">GLM_FUNC_DECL GLM_CONSTEXPR T glm::length2 </td>
    308. 

  308.           <td>(</td>
    309. 

  309.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    310. 

  310.           <td class="paramname"><em>q</em></td><td>)</td>
    311. 

  311.           <td></td>
    312. 

  312.         </tr>
    313. 

  313.       </table>
    314. 

  314. </div><div class="memdoc">
    315. 

  315. 

  316. <p>Returns the squared length of x. </p>
    317. 

  317. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    318. 

  318. 

  319. </div>
    320. 

  320. </div>
    321. 

  321. <a id="ga77d9e2c313b98a1002a1b12408bf5b45"></a>
    322. 

  322. <h2 class="memtitle"><span class="permalink"><a href="#ga77d9e2c313b98a1002a1b12408bf5b45">&#9670;&nbsp;</a></span>quat_identity()</h2>
    323. 

  323. 

  324. <div class="memitem">
    325. 

  325. <div class="memproto">
    326. 

  326.       <table class="memname">
    327. 

  327.         <tr>
    328. 

  328.           <td class="memname">GLM_FUNC_DECL GLM_CONSTEXPR qua&lt;T, Q&gt; glm::quat_identity </td>
    329. 

  329.           <td>(</td>
    330. 

  330.           <td class="paramname"></td><td>)</td>
    331. 

  331.           <td></td>
    332. 

  332.         </tr>
    333. 

  333.       </table>
    334. 

  334. </div><div class="memdoc">
    335. 

  335. 

  336. <p>Create an identity quaternion. </p>
    337. 

  337. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    338. 

  338. 

  339. </div>
    340. 

  340. </div>
    341. 

  341. <a id="ga07da6ef58646442efe93b0c273d73776"></a>
    342. 

  342. <h2 class="memtitle"><span class="permalink"><a href="#ga07da6ef58646442efe93b0c273d73776">&#9670;&nbsp;</a></span>rotate() <span class="overload">[1/2]</span></h2>
    343. 

  343. 

  344. <div class="memitem">
    345. 

  345. <div class="memproto">
    346. 

  346.       <table class="memname">
    347. 

  347.         <tr>
    348. 

  348.           <td class="memname">GLM_FUNC_DECL vec&lt;3, T, Q&gt; glm::rotate </td>
    349. 

  349.           <td>(</td>
    350. 

  350.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    351. 

  351.           <td class="paramname"><em>q</em>, </td>
    352. 

  352.         </tr>
    353. 

  353.         <tr>
    354. 

  354.           <td class="paramkey"></td>
    355. 

  355.           <td></td>
    356. 

  356.           <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
    357. 

  357.           <td class="paramname"><em>v</em>&#160;</td>
    358. 

  358.         </tr>
    359. 

  359.         <tr>
    360. 

  360.           <td></td>
    361. 

  361.           <td>)</td>
    362. 

  362.           <td></td><td></td>
    363. 

  363.         </tr>
    364. 

  364.       </table>
    365. 

  365. </div><div class="memdoc">
    366. 

  366. 

  367. <p>Returns quarternion square root. </p>
    368. 

  368. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> Rotates a 3 components vector by a quaternion.</dd>
    369. 

  369. <dd>
    370. 

  370. <a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    371. 

  371. 

  372. </div>
    373. 

  373. </div>
    374. 

  374. <a id="gafcb78dfff45fbf19a7fcb2bd03fbf196"></a>
    375. 

  375. <h2 class="memtitle"><span class="permalink"><a href="#gafcb78dfff45fbf19a7fcb2bd03fbf196">&#9670;&nbsp;</a></span>rotate() <span class="overload">[2/2]</span></h2>
    376. 

  376. 

  377. <div class="memitem">
    378. 

  378. <div class="memproto">
    379. 

  379.       <table class="memname">
    380. 

  380.         <tr>
    381. 

  381.           <td class="memname">GLM_FUNC_DECL vec&lt;4, T, Q&gt; glm::rotate </td>
    382. 

  382.           <td>(</td>
    383. 

  383.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    384. 

  384.           <td class="paramname"><em>q</em>, </td>
    385. 

  385.         </tr>
    386. 

  386.         <tr>
    387. 

  387.           <td class="paramkey"></td>
    388. 

  388.           <td></td>
    389. 

  389.           <td class="paramtype">vec&lt; 4, T, Q &gt; const &amp;&#160;</td>
    390. 

  390.           <td class="paramname"><em>v</em>&#160;</td>
    391. 

  391.         </tr>
    392. 

  392.         <tr>
    393. 

  393.           <td></td>
    394. 

  394.           <td>)</td>
    395. 

  395.           <td></td><td></td>
    396. 

  396.         </tr>
    397. 

  397.       </table>
    398. 

  398. </div><div class="memdoc">
    399. 

  399. 

  400. <p>Rotates a 4 components vector by a quaternion. </p>
    401. 

  401. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    402. 

  402. 

  403. </div>
    404. 

  404. </div>
    405. 

  405. <a id="ga03e61282831cc3f52cc76f72f52ad2c5"></a>
    406. 

  406. <h2 class="memtitle"><span class="permalink"><a href="#ga03e61282831cc3f52cc76f72f52ad2c5">&#9670;&nbsp;</a></span>rotation()</h2>
    407. 

  407. 

  408. <div class="memitem">
    409. 

  409. <div class="memproto">
    410. 

  410.       <table class="memname">
    411. 

  411.         <tr>
    412. 

  412.           <td class="memname">GLM_FUNC_DECL qua&lt;T, Q&gt; glm::rotation </td>
    413. 

  413.           <td>(</td>
    414. 

  414.           <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
    415. 

  415.           <td class="paramname"><em>orig</em>, </td>
    416. 

  416.         </tr>
    417. 

  417.         <tr>
    418. 

  418.           <td class="paramkey"></td>
    419. 

  419.           <td></td>
    420. 

  420.           <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
    421. 

  421.           <td class="paramname"><em>dest</em>&#160;</td>
    422. 

  422.         </tr>
    423. 

  423.         <tr>
    424. 

  424.           <td></td>
    425. 

  425.           <td>)</td>
    426. 

  426.           <td></td><td></td>
    427. 

  427.         </tr>
    428. 

  428.       </table>
    429. 

  429. </div><div class="memdoc">
    430. 

  430. 

  431. <p>Compute the rotation between two vectors. </p>
    432. 

  432. <dl class="params"><dt>Parameters</dt><dd>
    433. 

  433.   <table class="params">
    434. 

  434.     <tr><td class="paramname">orig</td><td>vector, needs to be normalized </td></tr>
    435. 

  435.     <tr><td class="paramname">dest</td><td>vector, needs to be normalized</td></tr>
    436. 

  436.   </table>
    437. 

  437.   </dd>
    438. 

  438. </dl>
    439. 

  439. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    440. 

  440. 

  441. </div>
    442. 

  442. </div>
    443. 

  443. <a id="gadc576cc957adc2a568cdcbc3799175bc"></a>
    444. 

  444. <h2 class="memtitle"><span class="permalink"><a href="#gadc576cc957adc2a568cdcbc3799175bc">&#9670;&nbsp;</a></span>shortMix()</h2>
    445. 

  445. 

  446. <div class="memitem">
    447. 

  447. <div class="memproto">
    448. 

  448.       <table class="memname">
    449. 

  449.         <tr>
    450. 

  450.           <td class="memname">GLM_FUNC_DECL qua&lt;T, Q&gt; glm::shortMix </td>
    451. 

  451.           <td>(</td>
    452. 

  452.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    453. 

  453.           <td class="paramname"><em>x</em>, </td>
    454. 

  454.         </tr>
    455. 

  455.         <tr>
    456. 

  456.           <td class="paramkey"></td>
    457. 

  457.           <td></td>
    458. 

  458.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    459. 

  459.           <td class="paramname"><em>y</em>, </td>
    460. 

  460.         </tr>
    461. 

  461.         <tr>
    462. 

  462.           <td class="paramkey"></td>
    463. 

  463.           <td></td>
    464. 

  464.           <td class="paramtype">T const &amp;&#160;</td>
    465. 

  465.           <td class="paramname"><em>a</em>&#160;</td>
    466. 

  466.         </tr>
    467. 

  467.         <tr>
    468. 

  468.           <td></td>
    469. 

  469.           <td>)</td>
    470. 

  470.           <td></td><td></td>
    471. 

  471.         </tr>
    472. 

  472.       </table>
    473. 

  473. </div><div class="memdoc">
    474. 

  474. 

  475. <p>Quaternion interpolation using the rotation short path. </p>
    476. 

  476. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    477. 

  477. 

  478. </div>
    479. 

  479. </div>
    480. 

  480. <a id="ga0b9bf3459e132ad8a18fe970669e3e35"></a>
    481. 

  481. <h2 class="memtitle"><span class="permalink"><a href="#ga0b9bf3459e132ad8a18fe970669e3e35">&#9670;&nbsp;</a></span>squad()</h2>
    482. 

  482. 

  483. <div class="memitem">
    484. 

  484. <div class="memproto">
    485. 

  485.       <table class="memname">
    486. 

  486.         <tr>
    487. 

  487.           <td class="memname">GLM_FUNC_DECL qua&lt;T, Q&gt; glm::squad </td>
    488. 

  488.           <td>(</td>
    489. 

  489.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    490. 

  490.           <td class="paramname"><em>q1</em>, </td>
    491. 

  491.         </tr>
    492. 

  492.         <tr>
    493. 

  493.           <td class="paramkey"></td>
    494. 

  494.           <td></td>
    495. 

  495.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    496. 

  496.           <td class="paramname"><em>q2</em>, </td>
    497. 

  497.         </tr>
    498. 

  498.         <tr>
    499. 

  499.           <td class="paramkey"></td>
    500. 

  500.           <td></td>
    501. 

  501.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    502. 

  502.           <td class="paramname"><em>s1</em>, </td>
    503. 

  503.         </tr>
    504. 

  504.         <tr>
    505. 

  505.           <td class="paramkey"></td>
    506. 

  506.           <td></td>
    507. 

  507.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    508. 

  508.           <td class="paramname"><em>s2</em>, </td>
    509. 

  509.         </tr>
    510. 

  510.         <tr>
    511. 

  511.           <td class="paramkey"></td>
    512. 

  512.           <td></td>
    513. 

  513.           <td class="paramtype">T const &amp;&#160;</td>
    514. 

  514.           <td class="paramname"><em>h</em>&#160;</td>
    515. 

  515.         </tr>
    516. 

  516.         <tr>
    517. 

  517.           <td></td>
    518. 

  518.           <td>)</td>
    519. 

  519.           <td></td><td></td>
    520. 

  520.         </tr>
    521. 

  521.       </table>
    522. 

  522. </div><div class="memdoc">
    523. 

  523. 

  524. <p>Compute a point on a path according squad equation. </p>
    525. 

  525. <p>q1 and q2 are control points; s1 and s2 are intermediate control points.</p>
    526. 

  526. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    527. 

  527. 

  528. </div>
    529. 

  529. </div>
    530. 

  530. <a id="gac228e3fcfa813841804362fcae02b337"></a>
    531. 

  531. <h2 class="memtitle"><span class="permalink"><a href="#gac228e3fcfa813841804362fcae02b337">&#9670;&nbsp;</a></span>toMat3()</h2>
    532. 

  532. 

  533. <div class="memitem">
    534. 

  534. <div class="memproto">
    535. 

  535.       <table class="memname">
    536. 

  536.         <tr>
    537. 

  537.           <td class="memname">GLM_FUNC_QUALIFIER mat&lt;3, 3, T, Q&gt; glm::toMat3 </td>
    538. 

  538.           <td>(</td>
    539. 

  539.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    540. 

  540.           <td class="paramname"><em>x</em></td><td>)</td>
    541. 

  541.           <td></td>
    542. 

  542.         </tr>
    543. 

  543.       </table>
    544. 

  544. </div><div class="memdoc">
    545. 

  545. 

  546. <p>Converts a quaternion to a 3 * 3 matrix. </p>
    547. 

  547. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    548. 

  548. 

  549. <p class="definition">Definition at line <a class="el" href="a01714_source.html#l00111">111</a> of file <a class="el" href="a01714_source.html">gtx/quaternion.hpp</a>.</p>
    550. 

  550. 

  551. <p class="reference">References <a class="el" href="a00917.html#ga333ab70047fbe4132406100c292dbc89">glm::mat3_cast()</a>.</p>
    552. 

  552. 

  553. </div>
    554. 

  554. </div>
    555. 

  555. <a id="gad0d0c14d7d3c852b41d6a6e4d1da6606"></a>
    556. 

  556. <h2 class="memtitle"><span class="permalink"><a href="#gad0d0c14d7d3c852b41d6a6e4d1da6606">&#9670;&nbsp;</a></span>toMat4()</h2>
    557. 

  557. 

  558. <div class="memitem">
    559. 

  559. <div class="memproto">
    560. 

  560.       <table class="memname">
    561. 

  561.         <tr>
    562. 

  562.           <td class="memname">GLM_FUNC_QUALIFIER mat&lt;4, 4, T, Q&gt; glm::toMat4 </td>
    563. 

  563.           <td>(</td>
    564. 

  564.           <td class="paramtype">qua&lt; T, Q &gt; const &amp;&#160;</td>
    565. 

  565.           <td class="paramname"><em>x</em></td><td>)</td>
    566. 

  566.           <td></td>
    567. 

  567.         </tr>
    568. 

  568.       </table>
    569. 

  569. </div><div class="memdoc">
    570. 

  570. 

  571. <p>Converts a quaternion to a 4 * 4 matrix. </p>
    572. 

  572. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    573. 

  573. 

  574. <p class="definition">Definition at line <a class="el" href="a01714_source.html#l00118">118</a> of file <a class="el" href="a01714_source.html">gtx/quaternion.hpp</a>.</p>
    575. 

  575. 

  576. <p class="reference">References <a class="el" href="a00917.html#ga1113212d9bdefc2e31ad40e5bbb506f3">glm::mat4_cast()</a>.</p>
    577. 

  577. 

  578. </div>
    579. 

  579. </div>
    580. 

  580. <a id="ga7b2be33d948db631c8815e9f2953a451"></a>
    581. 

  581. <h2 class="memtitle"><span class="permalink"><a href="#ga7b2be33d948db631c8815e9f2953a451">&#9670;&nbsp;</a></span>toQuat() <span class="overload">[1/2]</span></h2>
    582. 

  582. 

  583. <div class="memitem">
    584. 

  584. <div class="memproto">
    585. 

  585.       <table class="memname">
    586. 

  586.         <tr>
    587. 

  587.           <td class="memname">GLM_FUNC_QUALIFIER qua&lt;T, Q&gt; glm::toQuat </td>
    588. 

  588.           <td>(</td>
    589. 

  589.           <td class="paramtype">mat&lt; 3, 3, T, Q &gt; const &amp;&#160;</td>
    590. 

  590.           <td class="paramname"><em>x</em></td><td>)</td>
    591. 

  591.           <td></td>
    592. 

  592.         </tr>
    593. 

  593.       </table>
    594. 

  594. </div><div class="memdoc">
    595. 

  595. 

  596. <p>Converts a 3 * 3 matrix to a quaternion. </p>
    597. 

  597. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    598. 

  598. 

  599. <p class="definition">Definition at line <a class="el" href="a01714_source.html#l00125">125</a> of file <a class="el" href="a01714_source.html">gtx/quaternion.hpp</a>.</p>
    600. 

  600. 

  601. <p class="reference">References <a class="el" href="a00917.html#ga1108a4ab88ca87bac321454eea7702f8">glm::quat_cast()</a>.</p>
    602. 

  602. 

  603. </div>
    604. 

  604. </div>
    605. 

  605. <a id="ga4cf12d456770d716b590fd498bce6136"></a>
    606. 

  606. <h2 class="memtitle"><span class="permalink"><a href="#ga4cf12d456770d716b590fd498bce6136">&#9670;&nbsp;</a></span>toQuat() <span class="overload">[2/2]</span></h2>
    607. 

  607. 

  608. <div class="memitem">
    609. 

  609. <div class="memproto">
    610. 

  610.       <table class="memname">
    611. 

  611.         <tr>
    612. 

  612.           <td class="memname">GLM_FUNC_QUALIFIER qua&lt;T, Q&gt; glm::toQuat </td>
    613. 

  613.           <td>(</td>
    614. 

  614.           <td class="paramtype">mat&lt; 4, 4, T, Q &gt; const &amp;&#160;</td>
    615. 

  615.           <td class="paramname"><em>x</em></td><td>)</td>
    616. 

  616.           <td></td>
    617. 

  617.         </tr>
    618. 

  618.       </table>
    619. 

  619. </div><div class="memdoc">
    620. 

  620. 

  621. <p>Converts a 4 * 4 matrix to a quaternion. </p>
    622. 

  622. <dl class="section see"><dt>See also</dt><dd><a class="el" href="a00972.html">GLM_GTX_quaternion</a> </dd></dl>
    623. 

  623. 

  624. <p class="definition">Definition at line <a class="el" href="a01714_source.html#l00132">132</a> of file <a class="el" href="a01714_source.html">gtx/quaternion.hpp</a>.</p>
    625. 

  625. 

  626. <p class="reference">References <a class="el" href="a00917.html#ga1108a4ab88ca87bac321454eea7702f8">glm::quat_cast()</a>.</p>
    627. 

  627. 

  628. </div>
    629. 

  629. </div>
    630. 

  630. </div><!-- contents -->
    631. 

  631. <!-- start footer part -->
    632. 

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    639.