.off - Geomview's polyhedral file format

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.off is the one of the popular file formats of Geomview - an interactive 3D viewing program for Unix/Linux. It represents 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.

The description of .off file format can be easily found elsewhere in the internet. Below is a simple discription of this file format.

OFF numVertices numFaces numEdges
x y z
x y z
... numVertices like above
NVertices v1 v2 v3 ... vN
MVertices v1 v2 v3 ... vM
... numFaces like above

Note that vertices are numbered starting at 0 (not starting at 1), and that numEdges will always be zero.

A simple example for a cube:

OFF
8 6 0
-0.500000 -0.500000 0.500000
0.500000 -0.500000 0.500000
-0.500000 0.500000 0.500000
0.500000 0.500000 0.500000
-0.500000 0.500000 -0.500000
0.500000 0.500000 -0.500000
-0.500000 -0.500000 -0.500000
0.500000 -0.500000 -0.500000
4 0 1 3 2
4 2 3 5 4
4 4 5 7 6
4 6 7 1 0
4 1 7 5 3
4 6 0 2 4

Here is an example of using TetGen to read (-p) a polyhedron described in .off file format (socket.off), compute its constrained Delaunay tetrahedralization and output (-O) the CDT in .off file format (socket.1.off). 

tetgen -pO socket.off
The picture of the socket.

Source file: socket.off

A big repository of free 3D models in OFF file format are available at The Princeton Shape Benchmark. Please note, these models may not be piecewise linear complexes. You can check them with the -d switch of TetGen.

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