Mathematica Import/Export Format

OFF (.off, .coff, .noff, .cnoff)

OFF 3D geometry format.
Used for storing and exchanging 3D models.
OFF is an acronym for Object File Format.
Occasionally called COFF if color information is present.
Related to NOFF and CNOFF.
ASCII or binary format.
Represents a single 2D or 3D object.
Stores a collection of planar polygons with possibly shared vertices.
Supports polygon and vertex colors.

Import and Export support ASCII and binary versions of the OFF file format.

Mathematica reads and writes vertex or face colors.

If both vertex and face colors are present in the file, Import returns the vertex color information.

IMPORT AND EXPORT

Import["file.off"]imports an OFF file as graphics.

Export["file.off", expr] exports graphics to a binary OFF file.

For OFF files representing a 3D object, Import["file.off"] returns an expression of the form Graphics3D[ GraphicsComplex[vertices, primitives, opts]].

Planar objects are imported as Graphics[ GraphicsComplex[vertices, primitives, opts].

Import["file.off", elem] imports the specified element from an OFF file.

Import["file.off", {elem, sub_a, sub_b, ...}] imports a subelement.

Import["file.off", {{elem₁, elem₂, ...}}] imports multiple elements.

The import format can be specified with Import["file", "OFF"] or Import["file", {"OFF", elem, ...}].

Export["file.off", expr, elem] creates a binary OFF file by treating expr as specifying element elem.

Export["file.off", {expr₁, expr₂, ...}, {{elem₁, elem₂, ...}}] treats each expr_i as specifying the corresponding elem_i.

Export["file.off", expr, opt₁->val₁, ...] exports expr with the specified option elements taken to have the specified values.

Export["file.off", {elem₁->expr₁, elem₂->expr₂, ...}, "Rules"] uses rules to specify the elements to be exported.

See the reference pages for full general information on Import and Export.

ImportString and ExportString support the OFF format.

ELEMENTS

General Import elements:

	"Elements"	list of elements and options available in this file
	"Rules"	full list of rules for each element and option
	"Options"	list of rules for options, properties and settings

Data representation elements:

	"Graphics"	2D OFF file represented as a Graphics object
	"Graphics3D"	3D geometry represented as a Graphics3D object
	"GraphicsComplex"	OFF file as a GraphicsComplex object
	"PolygonColors"	face color information, given as a list of color primitives associated with each polygon
	"PolygonData"	the polygon elements in indexed form
	"PolygonObjects"	list of Polygon primitives given in absolute coordinates
	"VertexColors"	colors associated with each vertex, given as a list of color primitives
	"VertexData"	list of vertex coordinates

Import and Export by default use the "Graphics3D" element to represent 3D geometries, and the "Graphics" element for 2-dimensional objects.

The "VertexData" element corresponds to the first argument of GraphicsComplex.

When rendering an OFF color model, Import automatically uses the setting Lighting->"Neutral".

OPTIONS

General Import options:

Background	Automatic	what background color to use
ImageSize	Automatic	overall size of the graphics to display
Lighting	Automatic	what simulated lighting to use in coloring 3D surfaces

All options of Graphics3D can be given when importing from OFF.

Detailed properties and settings:

"BinaryFormat"	True	whether the file is in ASCII or binary format
"InvertNormals"	False	whether to invert the orientation of vertex normals
"VerticalAxis"	{0,0,1}	orientation to assume for the coordinate system used in the file

Binary OFF files store information as "Integer32" and "Real32" data types, always using the setting "ByteOrdering"->1.

By default, Mathematica assumes that in the coordinate system used by the OFF format the vertical axis corresponds to the third coordinate.

With the setting "VerticalAxis"->{0, 1, 0}, Mathematica will apply the transformation {x, y, z}->{x, -z, y} to all graphics coordinates when importing from OFF, and the inverse transformation when exporting to OFF.