Nef polygon

<h2 id="terminology">Terminology</h2>
<p>In the language of Nef polyhedra you can refer to various objects as 'faces' with different dimensions. What would normally be called a 'corner' or 'vertex' of a shape is called a 'face' with dimension of 0. An 'edge' or 'segment' is a face with dimension 1. A flat shape in 3D space, like a triangle, is called a face with dimension 2 – or a 'facet'. A shape in 3D space, like a cube, is called a face with dimension 3 – or a 'volume'.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>
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<h2 id="implementations">Implementations</h2>
<p>The <a href="/facts/Computational_Geometry_Algorithms_Library/Dyyl9PGD">Computational Geometry Algorithms Library</a>, or CGAL, represents Nef Polyhedra by using two main data structures. The first is a 'Sphere map' and the second is a 'Selective Nef Complex' (or SNC). The 'sphere map' stores information about the polyhedron by creating an imaginary sphere around each vertex, and painting it with various points and lines representing how the polyhedron divides space. The SNC basically stores and organizes the sphere maps. Each face contains a 'label' or 'mark' telling whether it is part of the object or not.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a>
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/CGAL/Dyyl9PGD">CGAL</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"In memoriam Prof. Walter Nef (21/01/1919 - 12/04/2013)" (PDF). math.ch (in German). Retrieved 1 September 2023. <a href="https://math.ch/archive/documents/WalterNef.pdf" target="_blank">https://math.ch/archive/documents/WalterNef.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Nef, W. (1978). Beiträge zur Theorie der Polyeder. Bern: Herbert Lang. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Bieri, Hanspeter (1995). "Nef Polyhedra: A Brief Introduction". Geometric Modelling. Computing Supplement. Vol. 10. pp. 43–60. doi:10.1007/978-3-7091-7584-2_3. ISBN 978-3-211-82666-9. <a href="978-3-211-82666-9" target="_blank">978-3-211-82666-9</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>"2D Boolean Operations on Nef Polygons". the CGAL package overview. <a href="https://www.cgal.org/Manual/latest/doc_html/cgal_manual/packages.html#part_VI" target="_blank">https://www.cgal.org/Manual/latest/doc_html/cgal_manual/packages.html#part_VI</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Tammik, Jeremy (2007). "AutoCAD Nef Polyhedron Implementation". CiteSeerX 10.1.1.89.6020. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Hachenberger, Peter; Kettner, Lutz (June 2005). "Boolean Operations on 3D Selective Nef Complexes: Optimized Implementation and Experiments" (PDF). Proc. of 2005 ACM Symposium on Solid and Physical Modeling. SPM. Boston, MA. doi:10.1145/1060244.1060263. <a href="http://www.win.tue.nl/EWCG2005/Proceedings/36.pdf" target="_blank">http://www.win.tue.nl/EWCG2005/Proceedings/36.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Hachenberger, Peter; Kettner, Lutz; Mehlhorn, Kurt (2006). "Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, Optimized Implementation and Experiments". CiteSeerX 10.1.1.73.157. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Hachenberger, Peter; Kettner, Lutz; Mehlhorn, Kurt (2006). "Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, Optimized Implementation and Experiments". CiteSeerX 10.1.1.73.157. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
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Nef polygon open-in-new

Nef polygon