Editing Vtk/SimpleCubeTutorial/CubeDetails (section)

===Identifying the normal to each cube face===
* It is important to appreciate that, when identifying the POINTS that will define any individual POLYGON, the ''order in which the POINTS are identified matters.''  VTK will draw the perimeter of the polygon by connecting the points ''in the specified order.''  For example, the top face of the cube (POLYGON "1"), as illustrated above, has been properly drawn because the line of data defining that quadrilateral reads "4 4 5 6 7"; VTK understands that the perimeter of that desired polygon will be traversed by connecting POINT 4 to POINT 5 to POINT 6 to POINT 7, then ''back to POINT 4.''  The same desired result could be achieved by providing a line of data that reads "4 6 7 4 5," but the proper polygon would not have been drawn if the line of data read "4 5 7 6 4."
* For visualization purposes, it is useful to catalog the orientation of the unit vector that is ''normal'' to the face of each polygon.  (It is straightforward to make this identification because each defined polygon is assumed to be perfectly flat.<sup>1</sup>)   But there will always be a ''sign'' ambiguity; is the unit vector pointing "up," or is it pointing "down."  For example, POLYGON "1" in the above illustration &#8212; the face on the top of the cube &#8212; lies parallel to the ''x-y'' plane, so the unit vector that is normal to its surface points in the ''z-''direction.  But is it pointing in the ''plus'' ''z-''direction or the "minus" ''z-''direction?  In order to resolve this ambiguity, by default VTK uses the [http://en.wikipedia.org/wiki/Right-hand_rule right-hand rule] when assigning a NORMAL to each polygon.  More specifically, as the POINTS are being connected ''in sequence'' to define each POLYGON, VTK assumes that it is traversing the polygon's perimeter in a counter-clockwise direction and that the unit normal points "up" as would be indicated by the direction that the thumb on your right hand points as the fingers on your right hand are also curling counter-clockwise.  Hence, referring back to POLYGON "1" in our simple cube example, for which the relevant line of input data reads "4 4 5 6 7," VTK will record (internally) that the NORMAL to POLYGON "1" points in the ''plus z'' direction.  Put another way, the unit vector that sits normal to POLYGON "1" points in the <math>~(x,y,z) = (0,0,1)</math> direction.
* It is possible to override VTK's default specification of the NORMAL for any given POLYGON.  Within the context of the ''Simple Legacy Format,'' this is done by explicitly assigning a triplet of integers (or floating point numbers) to every POLYGON as part of the "CELL_DATA" specification and under an optional "NORMALS" subcategory of the input data file. 

<sup>1</sup>This is certainly true for our illustrated cube and, I presume, it is VTK's default presumption.  With this in mind, it is safest and easiest to build all structures using 3-sided polygons &#8212; that is, triangles &#8212; because the three POINTS that define each triangle are guaranteed to lie in the same plane.