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  77. <a href="#func-members">Functions</a> </div>
  78. <div class="headertitle">
  79. <div class="title">Geometric functions<div class="ingroups"><a class="el" href="a00280.html">Core features</a></div></div> </div>
  80. </div><!--header-->
  81. <div class="contents">
  82. <p>These operate on vectors as vectors, not component-wise.
  83. <a href="#details">More...</a></p>
  84. <table class="memberdecls">
  85. <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
  86. Functions</h2></td></tr>
  87. <tr class="memitem:gaeeec0794212fe84fc9d261de067c9587"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
  88. <tr class="memitem:gaeeec0794212fe84fc9d261de067c9587"><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="a00279.html#gaeeec0794212fe84fc9d261de067c9587">cross</a> (vec&lt; 3, T, Q &gt; const &amp;x, vec&lt; 3, T, Q &gt; const &amp;y)</td></tr>
  89. <tr class="memdesc:gaeeec0794212fe84fc9d261de067c9587"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the cross product of x and y. <a href="a00279.html#gaeeec0794212fe84fc9d261de067c9587">More...</a><br /></td></tr>
  90. <tr class="separator:gaeeec0794212fe84fc9d261de067c9587"><td class="memSeparator" colspan="2">&#160;</td></tr>
  91. <tr class="memitem:gaa68de6c53e20dfb2dac2d20197562e3f"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  92. <tr class="memitem:gaa68de6c53e20dfb2dac2d20197562e3f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#gaa68de6c53e20dfb2dac2d20197562e3f">distance</a> (vec&lt; L, T, Q &gt; const &amp;p0, vec&lt; L, T, Q &gt; const &amp;p1)</td></tr>
  93. <tr class="memdesc:gaa68de6c53e20dfb2dac2d20197562e3f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the distance betwwen p0 and p1, i.e., length(p0 - p1). <a href="a00279.html#gaa68de6c53e20dfb2dac2d20197562e3f">More...</a><br /></td></tr>
  94. <tr class="separator:gaa68de6c53e20dfb2dac2d20197562e3f"><td class="memSeparator" colspan="2">&#160;</td></tr>
  95. <tr class="memitem:gaad6c5d9d39bdc0bf43baf1b22e147a0a"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  96. <tr class="memitem:gaad6c5d9d39bdc0bf43baf1b22e147a0a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#gaad6c5d9d39bdc0bf43baf1b22e147a0a">dot</a> (vec&lt; L, T, Q &gt; const &amp;x, vec&lt; L, T, Q &gt; const &amp;y)</td></tr>
  97. <tr class="memdesc:gaad6c5d9d39bdc0bf43baf1b22e147a0a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the dot product of x and y, i.e., result = x * y. <a href="a00279.html#gaad6c5d9d39bdc0bf43baf1b22e147a0a">More...</a><br /></td></tr>
  98. <tr class="separator:gaad6c5d9d39bdc0bf43baf1b22e147a0a"><td class="memSeparator" colspan="2">&#160;</td></tr>
  99. <tr class="memitem:ga7aed0a36c738169402404a3a5d54e43b"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  100. <tr class="memitem:ga7aed0a36c738169402404a3a5d54e43b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#ga7aed0a36c738169402404a3a5d54e43b">faceforward</a> (vec&lt; L, T, Q &gt; const &amp;N, vec&lt; L, T, Q &gt; const &amp;I, vec&lt; L, T, Q &gt; const &amp;Nref)</td></tr>
  101. <tr class="memdesc:ga7aed0a36c738169402404a3a5d54e43b"><td class="mdescLeft">&#160;</td><td class="mdescRight">If dot(Nref, I) &lt; 0.0, return N, otherwise, return -N. <a href="a00279.html#ga7aed0a36c738169402404a3a5d54e43b">More...</a><br /></td></tr>
  102. <tr class="separator:ga7aed0a36c738169402404a3a5d54e43b"><td class="memSeparator" colspan="2">&#160;</td></tr>
  103. <tr class="memitem:ga0cdabbb000834d994a1d6dc56f8f5263"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  104. <tr class="memitem:ga0cdabbb000834d994a1d6dc56f8f5263"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#ga0cdabbb000834d994a1d6dc56f8f5263">length</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
  105. <tr class="memdesc:ga0cdabbb000834d994a1d6dc56f8f5263"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the length of x, i.e., sqrt(x * x). <a href="a00279.html#ga0cdabbb000834d994a1d6dc56f8f5263">More...</a><br /></td></tr>
  106. <tr class="separator:ga0cdabbb000834d994a1d6dc56f8f5263"><td class="memSeparator" colspan="2">&#160;</td></tr>
  107. <tr class="memitem:ga3b8d3dcae77870781392ed2902cce597"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  108. <tr class="memitem:ga3b8d3dcae77870781392ed2902cce597"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#ga3b8d3dcae77870781392ed2902cce597">normalize</a> (vec&lt; L, T, Q &gt; const &amp;x)</td></tr>
  109. <tr class="memdesc:ga3b8d3dcae77870781392ed2902cce597"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns a vector in the same direction as x but with length of 1. <a href="a00279.html#ga3b8d3dcae77870781392ed2902cce597">More...</a><br /></td></tr>
  110. <tr class="separator:ga3b8d3dcae77870781392ed2902cce597"><td class="memSeparator" colspan="2">&#160;</td></tr>
  111. <tr class="memitem:ga5631dd1d5618de5450b1ea3cf3e94905"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  112. <tr class="memitem:ga5631dd1d5618de5450b1ea3cf3e94905"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#ga5631dd1d5618de5450b1ea3cf3e94905">reflect</a> (vec&lt; L, T, Q &gt; const &amp;I, vec&lt; L, T, Q &gt; const &amp;N)</td></tr>
  113. <tr class="memdesc:ga5631dd1d5618de5450b1ea3cf3e94905"><td class="mdescLeft">&#160;</td><td class="mdescRight">For the incident vector I and surface orientation N, returns the reflection direction : result = I - 2.0 * dot(N, I) * N. <a href="a00279.html#ga5631dd1d5618de5450b1ea3cf3e94905">More...</a><br /></td></tr>
  114. <tr class="separator:ga5631dd1d5618de5450b1ea3cf3e94905"><td class="memSeparator" colspan="2">&#160;</td></tr>
  115. <tr class="memitem:ga01da3dff9e2ef6b9d4915c3047e22b74"><td class="memTemplParams" colspan="2">template&lt;length_t L, typename T , qualifier Q&gt; </td></tr>
  116. <tr class="memitem:ga01da3dff9e2ef6b9d4915c3047e22b74"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL vec&lt; L, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00279.html#ga01da3dff9e2ef6b9d4915c3047e22b74">refract</a> (vec&lt; L, T, Q &gt; const &amp;I, vec&lt; L, T, Q &gt; const &amp;N, T eta)</td></tr>
  117. <tr class="memdesc:ga01da3dff9e2ef6b9d4915c3047e22b74"><td class="mdescLeft">&#160;</td><td class="mdescRight">For the incident vector I and surface normal N, and the ratio of indices of refraction eta, return the refraction vector. <a href="a00279.html#ga01da3dff9e2ef6b9d4915c3047e22b74">More...</a><br /></td></tr>
  118. <tr class="separator:ga01da3dff9e2ef6b9d4915c3047e22b74"><td class="memSeparator" colspan="2">&#160;</td></tr>
  119. </table>
  120. <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
  121. <p>These operate on vectors as vectors, not component-wise. </p>
  122. <p>Include &lt;<a class="el" href="a00036.html" title="Core features ">glm/geometric.hpp</a>&gt; to use these core features. </p>
  123. <h2 class="groupheader">Function Documentation</h2>
  124. <a class="anchor" id="gaeeec0794212fe84fc9d261de067c9587"></a>
  125. <div class="memitem">
  126. <div class="memproto">
  127. <table class="memname">
  128. <tr>
  129. <td class="memname">GLM_FUNC_DECL vec&lt;3, T, Q&gt; glm::cross </td>
  130. <td>(</td>
  131. <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
  132. <td class="paramname"><em>x</em>, </td>
  133. </tr>
  134. <tr>
  135. <td class="paramkey"></td>
  136. <td></td>
  137. <td class="paramtype">vec&lt; 3, T, Q &gt; const &amp;&#160;</td>
  138. <td class="paramname"><em>y</em>&#160;</td>
  139. </tr>
  140. <tr>
  141. <td></td>
  142. <td>)</td>
  143. <td></td><td></td>
  144. </tr>
  145. </table>
  146. </div><div class="memdoc">
  147. <p>Returns the cross product of x and y. </p>
  148. <dl class="tparams"><dt>Template Parameters</dt><dd>
  149. <table class="tparams">
  150. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  151. </table>
  152. </dd>
  153. </dl>
  154. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/cross.xml">GLSL cross man page</a> </dd>
  155. <dd>
  156. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  157. </div>
  158. </div>
  159. <a class="anchor" id="gaa68de6c53e20dfb2dac2d20197562e3f"></a>
  160. <div class="memitem">
  161. <div class="memproto">
  162. <table class="memname">
  163. <tr>
  164. <td class="memname">GLM_FUNC_DECL T glm::distance </td>
  165. <td>(</td>
  166. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  167. <td class="paramname"><em>p0</em>, </td>
  168. </tr>
  169. <tr>
  170. <td class="paramkey"></td>
  171. <td></td>
  172. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  173. <td class="paramname"><em>p1</em>&#160;</td>
  174. </tr>
  175. <tr>
  176. <td></td>
  177. <td>)</td>
  178. <td></td><td></td>
  179. </tr>
  180. </table>
  181. </div><div class="memdoc">
  182. <p>Returns the distance betwwen p0 and p1, i.e., length(p0 - p1). </p>
  183. <dl class="tparams"><dt>Template Parameters</dt><dd>
  184. <table class="tparams">
  185. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  186. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  187. </table>
  188. </dd>
  189. </dl>
  190. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/distance.xml">GLSL distance man page</a> </dd>
  191. <dd>
  192. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  193. </div>
  194. </div>
  195. <a class="anchor" id="gaad6c5d9d39bdc0bf43baf1b22e147a0a"></a>
  196. <div class="memitem">
  197. <div class="memproto">
  198. <table class="memname">
  199. <tr>
  200. <td class="memname">GLM_FUNC_DECL T glm::dot </td>
  201. <td>(</td>
  202. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  203. <td class="paramname"><em>x</em>, </td>
  204. </tr>
  205. <tr>
  206. <td class="paramkey"></td>
  207. <td></td>
  208. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  209. <td class="paramname"><em>y</em>&#160;</td>
  210. </tr>
  211. <tr>
  212. <td></td>
  213. <td>)</td>
  214. <td></td><td></td>
  215. </tr>
  216. </table>
  217. </div><div class="memdoc">
  218. <p>Returns the dot product of x and y, i.e., result = x * y. </p>
  219. <dl class="tparams"><dt>Template Parameters</dt><dd>
  220. <table class="tparams">
  221. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  222. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  223. </table>
  224. </dd>
  225. </dl>
  226. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/dot.xml">GLSL dot man page</a> </dd>
  227. <dd>
  228. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  229. </div>
  230. </div>
  231. <a class="anchor" id="ga7aed0a36c738169402404a3a5d54e43b"></a>
  232. <div class="memitem">
  233. <div class="memproto">
  234. <table class="memname">
  235. <tr>
  236. <td class="memname">GLM_FUNC_DECL vec&lt;L, T, Q&gt; glm::faceforward </td>
  237. <td>(</td>
  238. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  239. <td class="paramname"><em>N</em>, </td>
  240. </tr>
  241. <tr>
  242. <td class="paramkey"></td>
  243. <td></td>
  244. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  245. <td class="paramname"><em>I</em>, </td>
  246. </tr>
  247. <tr>
  248. <td class="paramkey"></td>
  249. <td></td>
  250. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  251. <td class="paramname"><em>Nref</em>&#160;</td>
  252. </tr>
  253. <tr>
  254. <td></td>
  255. <td>)</td>
  256. <td></td><td></td>
  257. </tr>
  258. </table>
  259. </div><div class="memdoc">
  260. <p>If dot(Nref, I) &lt; 0.0, return N, otherwise, return -N. </p>
  261. <dl class="tparams"><dt>Template Parameters</dt><dd>
  262. <table class="tparams">
  263. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  264. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  265. </table>
  266. </dd>
  267. </dl>
  268. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/faceforward.xml">GLSL faceforward man page</a> </dd>
  269. <dd>
  270. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  271. </div>
  272. </div>
  273. <a class="anchor" id="ga0cdabbb000834d994a1d6dc56f8f5263"></a>
  274. <div class="memitem">
  275. <div class="memproto">
  276. <table class="memname">
  277. <tr>
  278. <td class="memname">GLM_FUNC_DECL T glm::length </td>
  279. <td>(</td>
  280. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  281. <td class="paramname"><em>x</em></td><td>)</td>
  282. <td></td>
  283. </tr>
  284. </table>
  285. </div><div class="memdoc">
  286. <p>Returns the length of x, i.e., sqrt(x * x). </p>
  287. <dl class="tparams"><dt>Template Parameters</dt><dd>
  288. <table class="tparams">
  289. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  290. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  291. </table>
  292. </dd>
  293. </dl>
  294. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/length.xml">GLSL length man page</a> </dd>
  295. <dd>
  296. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  297. </div>
  298. </div>
  299. <a class="anchor" id="ga3b8d3dcae77870781392ed2902cce597"></a>
  300. <div class="memitem">
  301. <div class="memproto">
  302. <table class="memname">
  303. <tr>
  304. <td class="memname">GLM_FUNC_DECL vec&lt;L, T, Q&gt; glm::normalize </td>
  305. <td>(</td>
  306. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  307. <td class="paramname"><em>x</em></td><td>)</td>
  308. <td></td>
  309. </tr>
  310. </table>
  311. </div><div class="memdoc">
  312. <p>Returns a vector in the same direction as x but with length of 1. </p>
  313. <p>According to issue 10 GLSL 1.10 specification, if length(x) == 0 then result is undefined and generate an error.</p>
  314. <dl class="tparams"><dt>Template Parameters</dt><dd>
  315. <table class="tparams">
  316. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  317. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  318. </table>
  319. </dd>
  320. </dl>
  321. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/normalize.xml">GLSL normalize man page</a> </dd>
  322. <dd>
  323. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  324. </div>
  325. </div>
  326. <a class="anchor" id="ga5631dd1d5618de5450b1ea3cf3e94905"></a>
  327. <div class="memitem">
  328. <div class="memproto">
  329. <table class="memname">
  330. <tr>
  331. <td class="memname">GLM_FUNC_DECL vec&lt;L, T, Q&gt; glm::reflect </td>
  332. <td>(</td>
  333. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  334. <td class="paramname"><em>I</em>, </td>
  335. </tr>
  336. <tr>
  337. <td class="paramkey"></td>
  338. <td></td>
  339. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  340. <td class="paramname"><em>N</em>&#160;</td>
  341. </tr>
  342. <tr>
  343. <td></td>
  344. <td>)</td>
  345. <td></td><td></td>
  346. </tr>
  347. </table>
  348. </div><div class="memdoc">
  349. <p>For the incident vector I and surface orientation N, returns the reflection direction : result = I - 2.0 * dot(N, I) * N. </p>
  350. <dl class="tparams"><dt>Template Parameters</dt><dd>
  351. <table class="tparams">
  352. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  353. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  354. </table>
  355. </dd>
  356. </dl>
  357. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/reflect.xml">GLSL reflect man page</a> </dd>
  358. <dd>
  359. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  360. </div>
  361. </div>
  362. <a class="anchor" id="ga01da3dff9e2ef6b9d4915c3047e22b74"></a>
  363. <div class="memitem">
  364. <div class="memproto">
  365. <table class="memname">
  366. <tr>
  367. <td class="memname">GLM_FUNC_DECL vec&lt;L, T, Q&gt; glm::refract </td>
  368. <td>(</td>
  369. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  370. <td class="paramname"><em>I</em>, </td>
  371. </tr>
  372. <tr>
  373. <td class="paramkey"></td>
  374. <td></td>
  375. <td class="paramtype">vec&lt; L, T, Q &gt; const &amp;&#160;</td>
  376. <td class="paramname"><em>N</em>, </td>
  377. </tr>
  378. <tr>
  379. <td class="paramkey"></td>
  380. <td></td>
  381. <td class="paramtype">T&#160;</td>
  382. <td class="paramname"><em>eta</em>&#160;</td>
  383. </tr>
  384. <tr>
  385. <td></td>
  386. <td>)</td>
  387. <td></td><td></td>
  388. </tr>
  389. </table>
  390. </div><div class="memdoc">
  391. <p>For the incident vector I and surface normal N, and the ratio of indices of refraction eta, return the refraction vector. </p>
  392. <dl class="tparams"><dt>Template Parameters</dt><dd>
  393. <table class="tparams">
  394. <tr><td class="paramname">L</td><td>An integer between 1 and 4 included that qualify the dimension of the vector. </td></tr>
  395. <tr><td class="paramname">T</td><td>Floating-point scalar types.</td></tr>
  396. </table>
  397. </dd>
  398. </dl>
  399. <dl class="section see"><dt>See also</dt><dd><a href="http://www.opengl.org/sdk/docs/manglsl/xhtml/refract.xml">GLSL refract man page</a> </dd>
  400. <dd>
  401. <a href="http://www.opengl.org/registry/doc/GLSLangSpec.4.20.8.pdf">GLSL 4.20.8 specification, section 8.5 Geometric Functions</a> </dd></dl>
  402. </div>
  403. </div>
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