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	<title>Reference:Smooth Triangle - Revision history</title>
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	<updated>2026-10-09T03:49:34Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://wiki.povray.org/content?title=Reference:Smooth_Triangle&amp;diff=7034&amp;oldid=prev</id>
		<title>Jholsenback: 1 revision: Reference Migration Initial Load</title>
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		<updated>2012-03-15T19:08:49Z</updated>

		<summary type="html">&lt;p&gt;1 revision: Reference Migration Initial Load&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left diff-editfont-monospace&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:08, 15 March 2012&lt;/td&gt;
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&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Jholsenback</name></author>
	</entry>
	<entry>
		<id>https://wiki.povray.org/content?title=Reference:Smooth_Triangle&amp;diff=7033&amp;oldid=prev</id>
		<title>Jholsenback: 1 revision: Initial Load (TF)</title>
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		<updated>2012-03-11T22:27:06Z</updated>

		<summary type="html">&lt;p&gt;1 revision: Initial Load (TF)&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;[[Category:Objects]]&lt;br /&gt;
[[Category:Finite Patch Primitives]]&lt;br /&gt;
{{#indexentry:smooth_triangle, keyword}}&lt;br /&gt;
{{#indexentry:keyword, smooth_triangle}}&lt;br /&gt;
&amp;lt;p&amp;gt;The &amp;lt;code&amp;gt;smooth_triangle&amp;lt;/code&amp;gt; primitive is used for just such purposes.&lt;br /&gt;
The smooth triangles use a formula called Phong normal interpolation to&lt;br /&gt;
calculate the surface normal for any point on the triangle based on normal&lt;br /&gt;
vectors which you define for the three corners. This makes the triangle&lt;br /&gt;
appear to be a smooth curved surface. A smooth triangle is defined by&amp;lt;/p&amp;gt;&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
SMOOTH_TRIANGLE:&lt;br /&gt;
  smooth_triangle {&lt;br /&gt;
  &amp;amp;lt;Corner_1&amp;amp;gt;, &amp;amp;lt;Normal_1&amp;amp;gt;, &amp;amp;lt;Corner_2&amp;amp;gt;,&lt;br /&gt;
  &amp;amp;lt;Normal_2&amp;amp;gt;, &amp;amp;lt;Corner_3&amp;amp;gt;, &amp;amp;lt;Normal_3&amp;amp;gt;&lt;br /&gt;
  [OBJECT_MODIFIER...]&lt;br /&gt;
  }&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;p&amp;gt;where the corners are defined as in regular triangles and &amp;lt;em&amp;gt;&amp;lt;code&amp;gt;&lt;br /&gt;
&amp;amp;lt;Normal_n&amp;amp;gt;&amp;lt;/code&amp;gt;&amp;lt;/em&amp;gt; is a vector describing the direction of the&lt;br /&gt;
surface normal at each corner.&amp;lt;/p&amp;gt;&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
These normal vectors are prohibitively difficult to compute by hand.&lt;br /&gt;
Therefore smooth triangles are almost always generated by utility programs.&lt;br /&gt;
To achieve smooth results, any triangles which share a common vertex should&lt;br /&gt;
have the same normal vector at that vertex. Generally the smoothed normal&lt;br /&gt;
should be the average of all the actual normals of the triangles which share&lt;br /&gt;
that point.&amp;lt;/p&amp;gt;&lt;br /&gt;
&amp;lt;p&amp;gt;&lt;br /&gt;
The &amp;lt;code&amp;gt;mesh&amp;lt;/code&amp;gt; object is a way to combine many &amp;lt;code&amp;gt;triangle&amp;lt;/code&amp;gt;&lt;br /&gt;
and &amp;lt;code&amp;gt;smooth_triangle&amp;lt;/code&amp;gt; objects together in a very efficient way.&lt;br /&gt;
See [[Reference:Mesh|:Mesh|Mesh]] for details.&amp;lt;/p&amp;gt;&lt;/div&gt;</summary>
		<author><name>Jholsenback</name></author>
	</entry>
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