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Qhull output options

This section lists the output options for Qhull. These options are indicated by lower case characters. See Formats, Print, and Geomview for other output options.

ť Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace

Output options

Qhull prints its output to standard out. All output is printed text. The default output is a summary (option 's'). Other outputs may be specified as follows.

f: print all fields of all facets
n: print hyperplane normals with offsets
m: print Mathematica output (2-d and 3-d)
o: print OFF file format (dim, points and facets)
s: print summary to stderr
p: print vertex and point coordinates
i: print vertices incident to each facet

: Related options
F: additional input/output formats
G: Geomview output
P: Print options
Ft: print triangulation with added points

ť f - print all fields of all facets

Print all fields of all facets. The facet is the primary data structure for Qhull.

Option 'f' is for debugging. Most of the fields are available via the 'F' options. If you need specialized information from Qhull, you can use the Qhull library.

Use the 'FF' option to print the facets but not the ridges.

ť i - print vertices incident to each facet

The first line is the number of facets. The remaining lines list the vertices for each facet, one facet per line. The indices are 0-relative indices of the corresponding input points. The facets are oriented. Option 'Fv' displays an unoriented list of vertices with a vertex count per line. Options 'o' and 'Ft' displays coordinates for each vertex prior to the vertices for each facet.

Simplicial facets (e.g., triangles in 3-d) consist of d vertices. Non-simplicial facets in 3-d consist of 4 or more vertices. For example, a facet of a cube consists of 4 vertices.

For 4-d and higher convex hulls and 3-d and higher Delaunay triangulations, d vertices are listed for all facets. A non-simplicial facet is triangulated with its centrum and each ridge. The index of the centrum is higher than any input point. Use option 'Fv' to list the vertices of non-simplicial facets as is. Use option 'Ft' to print the coordinates of the centrums as well as those of the input points.

ť m - print Mathematica output

Qhull writes a Mathematica file for 2-d and 3-d convex hulls, 2-d and 3-d halfspace intersections, and 2-d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << <outputfilename> ". If the object is 2-d, it can be visualized by "Show[Graphics[list]]". For 3-d objects the command is "Show[Graphics3D[list]]". Now the object can be manipulated by commands of the form "Show[%, <parametername> -> <newvalue>]".

For Delaunay triangulation orthogonal projection is better. This can be specified, for example, by "BoxRatios: Show[%, BoxRatios -> {1, 1, 1e-8}]". To see the meaningful side of the 3-d object used to visualize 2-d Delaunay, you need to change the viewpoint: "Show[%, ViewPoint -> {0, 0, -1}]". By specifying different viewpoints you can slowly rotate objects.

For halfspace intersections, Qhull produces the dual convex hull.

See Is Qhull available for Mathematica? for URLs.

ť n - print hyperplane normals with offsets

The first line is the dimension plus one. The second line is the number of facets. The remaining lines are the normals for each facet, one normal per line. The facet's offset follows its normal coefficients.

The normals point outward, i.e., the convex hull satisfies Ax <= -b where A is the matrix of coefficients and b is the vector of offsets.

If cdd output is specified ('FD'), Qhull prints the command line, the keyword "begin", the number of facets, the dimension (plus one), the keyword "real", and the normals for each facet. The facet's negative offset precedes its normal coefficients (i.e., if the origin is an interior point, the offset is positive). Qhull ends the output with the keyword "end".

ť o - print OFF file format

The output is:

The first line is the dimension
The second line is the number of points, the number of facets, and the number of ridges.
All of the input points follow, one per line.
Then Qhull prints the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder is the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets.

Option 'Ft' prints the same information with added points for non-simplicial facets.

Option 'i' displays vertices without the point coordinates. Option 'p' displays the point coordinates without vertex and facet information.

In 3-d, Geomview can load the file directly if you delete the first line (e.g., by piping through 'tail +2').

For Voronoi diagrams (qvoronoi), option 'o' prints Voronoi vertices and Voronoi regions instead of input points and facets. The first vertex is the infinity vertex [-10.101, -10.101, ...]. Then, option 'o' lists the vertices in the Voronoi region for each input site. The regions appear in site ID order. In 2-d, the vertices of a Voronoi region are sorted by adjacency (non-oriented). In 3-d and higher, the Voronoi vertices are sorted by index. See the 'FN' option for listing Voronoi regions without listing Voronoi vertices.

If you are using the Qhull library, options 'v o' have the side effect of reordering the neighbors for a/a> • Precision • Trace