Date: Mon, 16 Dec 1996 23:40:43 GMT Server: NCSA/1.5 Content-type: text/html Last-modified: Thu, 01 Aug 1996 15:31:03 GMT Content-length: 2648 polygons

Constructing objects using explicit polygon lists


At some level (often hidden from the user) a graphics system based on polygons needs to keep a list of the polygons. The list must include their location in space (vertices) and often includes other data. The data may consist of face lists, normals, nearest neighbors, or perhaps other items.

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 consists of a list of the vertices for that partcular polygon.

An example is shown below. The vertex list contains four entries, each of which is a 3-vector corresponding to the [x,y,z] positions of the vertices. The face list contains four entries, each of which describes one face of the tetrahedron shown. The 3 integers on each line represent the index of the vertex in the vertex list (with zero being the first entry) corresponding to the corners of each polygonal face. The "front" of a polygon is defined as the side you see when you traverse the vertices of that face in a counter-clockwise direction. Each face list entry must have to correct orientation determined by enumerating the vertices a counter-clockwise order.

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 the larger triangle. The image to the right shows the back. The face which is highlighted in the list corresponds to the smaller triangle which sticks out to the left in both images.

A face list can, in general, have any number of vertices for each polygonal entry. Limiting yourself to triangles has a couple of advangages: A triangle is always planar, so its surface normal is well defined. Some commerical renderers will only use triangles.


A Java Applet allows you to design and view polyhedra.


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Last modified, 6/26/95 B. Land.

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