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Date: Mon, 16 Dec 1996 23:40:43 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Thu, 01 Aug 1996 15:31:03 GMTContent-length: 2648<html><head><title>polygons</title></head><body><h2>Constructing objects using explicit polygon lists</h2><hr>At some level (often hidden from the user) a graphics system based onpolygons needs to keep a list of the polygons. The list must includetheir location in space (vertices) and often includes other data.The data may consist of face lists, normals, nearest neighbors, or perhapsother items.<p>The structure we will use here to represent polygons consists of two lists: The first is a list of all vertices which make up an object.The second is a list of polygonal faces. Each face in the second list consistsof a list of the vertices for that partcular polygon. <p>An example isshown below. The vertex list contains four entries, each of which isa 3-vector corresponding to the [x,y,z] positions of the vertices.The face list contains four entries, each of which describes one faceof the tetrahedron shown. The 3 integers on each line represent theindex of the vertex in the vertex list (with zero being the firstentry) corresponding to the corners of each polygonal face.The "front" of a polygon is defined as the side you see when you traversethe vertices of that face in a counter-clockwise direction. Each face listentry must have to correct orientation determined by enumerating thevertices a counter-clockwise order.<p><!WA0><!WA0><!WA0><!WA0><img src="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/polygons.list.tetrahedron.gif"><!WA1><!WA1><!WA1><!WA1><img src="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/polygons.image.tetrahedron.gif"><p>Another example is shown below with 4 vertices, but just two triangles.Two images are shown. The image to the left shows the front of thelarger triangle. The image to the right shows the back.The face which is highlighted in the list corresponds to the smallertriangle which sticks out to the left in both images.<p><!WA2><!WA2><!WA2><!WA2><img src="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/polygons.list.triangle.gif"><!WA3><!WA3><!WA3><!WA3><img src="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/polygons.image.triangles.front.gif"><!WA4><!WA4><!WA4><!WA4><img src="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/polygons.image.triangles.back.gif"><p>A face list can, in general, have any number of vertices for eachpolygonal entry. Limiting yourself to triangles has a couple of advangages:A triangle is always planar, so its surface normal is well defined. Somecommerical renderers will only use triangles.<hr>A  <!WA5><!WA5><!WA5><!WA5><a href="http://www.tc.cornell.edu/Visualization/contrib/cs490-95to96/suzuki/User/index.html">Java Applet </a> allows you to design and view polyhedra. <p><hr>Comments about Theory Center online documents are welcome and may be sent to<i>doc-comments@tc.cornell.edu</i>. <p>Last modified, 6/26/95 B. Land. <! Revision history:	Original document: P.Maxfield, 10/94><p><!WA6><!WA6><!WA6><!WA6><iMG SRC="http://www.tc.cornell.edu/copyright.xbm"><!WA7><!WA7><!WA7><!WA7><A HREF="http://www.tc.cornell.edu/ctcCopyright.html"> <i>Copyright Statement </I></A></body> </html>

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