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#### 4.2.5 OFF Files

The conventional suffix for `OFF` files is `.off`.

Syntax:

         [ST][C][N][4][n]OFF     # Header keyword
         [Ndim]            # Space dimension of vertices, present only if nOFF
         NVertices  NFaces  NEdges   # NEdges not used or checked

         x[0]  y[0]  z[0]      # Vertices, possibly with normals,
                                 # colors, and/or texture coordinates, in that order,
                                 # if the prefixes N, C, ST
                                 # are present.
                                 # If 4OFF, each vertex has 4 components,
                                 # including a final homogeneous component.
                                 # If nOFF, each vertex has Ndim components.
                                 # If 4nOFF, each vertex has Ndim+1 components.
         ...
         x[NVertices-1]  y[NVertices-1]  z[NVertices-1]

                                 # Faces
                                 # Nv = # vertices on this face
                                 # v[0] ... v[Nv-1]: vertex indices
                                 #               in range 0..NVertices-1
         Nv  v[0] v[1] ... v[Nv-1]  colorspec
         ...
                                 # colorspec continues past v[Nv-1]
                                 # to end-of-line; may be 0 to 4 numbers
                                 # nothing: default
                                 # integer: colormap index
                                 # 3 or 4 integers: RGB[A] values 0..255
                                 # 3 or 4 floats: RGB[A] values 0..1

`OFF` files (name for "object file format") represent collections of planar polygons with possibly shared vertices, a convenient way to describe polyhedra. The polygons may be concave but there's no provision for polygons containing holes.

An `OFF` file may begin with the keyword `OFF`; it's recommended but optional, as many existing files lack this keyword.

Three ASCII integers follow: NVertices, NFaces, and NEdges. These are the number of vertices, faces, and edges, respectively. Current software does not use nor check NEdges; it needn't be correct but must be present.

The vertex coordinates follow: dimension * Nvertices floating-point values. They're implicitly numbered 0 through NVertices-1. dimension is either 3 (default) or 4 (specified by the key character `4` directly before `OFF` in the keyword).

Following these are the face descriptions, typically written with one line per face. Each has the form

         N  Vert1 Vert2 ... VertN  [color]

Here N is the number of vertices on this face, and Vert1 through VertN are indices into the list of vertices (in the range 0..NVertices-1).

The optional color may take several forms. Line breaks are significant here: the color description begins after VertN and ends with the end of the line (or the next # comment). A color may be:

nothing
  the default color
one integer
  index into "the" colormap; see below
three or four integers
  RGB and possibly alpha values in the range 0..255
three or four floating-point numbers
  RGB and possibly alpha values in the range 0..1

For the one-integer case, the colormap is currently read from the file `cmap.fmap` in Geomview's `data` directory. Some better mechanism for supplying a colormap is likely someday.

The meaning of "default color" varies. If no face of the object has a color, all inherit the environment's default material color. If some but not all faces have colors, the default is gray (R,G,B,A=.666).

A `[ST][C][N][n]OFF BINARY` format is accepted; See Binary format. It resembles the ASCII format in almost the way you'd expect, with 32-bit integers for all counters and vertex indices and 32-bit floats for vertex positions (and texture coordinates or vertex colors or normals if `COFF`/`NOFF`/`CNOFF`/`STCNOFF`/etc. format).

Exception: each face's vertex indices are followed by an integer indicating how many color components accompany it. Face color components must be floats, not integer values. Thus a colorless triangular face might be represented as

         int int int int int
         3   17   5   9   0

while the same face colored red might be

         int int int int int float float float float
          3  17   5   9   4   1.0   0.0   0.0   1.0