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Qhull implements the Quickhull algorithm for computing the convex hull. The Quickhull algorithm combines two well-known algorithms: the 2-d quickhull algorithm and the n-d beneath-beyond algorithm. See Description of Qhull.

This section provides an index to the top-level functions and base data types. The top-level header file,

qhull.h, contains prototypes for these functions.

**Copyright © 1995-2002 The Geometry Center, Minneapolis MN**

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- qhull.h and unix.c data types and constants
- qhull.h other macros
- Quickhull routines in call order
- Top-level routines for initializing and terminating Qhull
- Top-level routines for reading and modifying the input
- Top-level routines for calling Qhull
- Top-level routines for returning results
- Top-level routines for testing and debugging

- flagT Boolean flag as a bit
- boolT boolean value, either True or False
- CENTERtype to distinguish facet->center
- qh_PRINT output formats for printing (qh.PRINTout)
- qh_ALL argument flag for selecting everything
- qh_ERR Qhull exit codes for indicating errors
- qh_prompt version and long prompt for Qhull
- qh_prompt2 synopsis for Qhull
- qh_prompt3 concise prompt for Qhull
- qh_VERSION version stamp

- traceN print trace
message if
*qh.IStracing >= N*.

- main processes the command line, calls qhull() to do the work, and exits
- qh_qhull construct the convex hull of a set of points
- qh_build_withrestart allow restarts while calling qh_buildhull
- qh_initbuild initialize hull and outside sets with point array
- qh_partitionall partition all points into outside sets
- qh_buildhull construct a convex hull by adding points one at a time
- qh_nextfurthest return next furthest point for processing
- qh_buildtracing trace an iteration of buildhull
- qh_addpoint add a point to the convex hull
- qh_findhorizon find the horizon and visible facets for a point
- qh_partitionvisible partition points from facets in qh.visible_list to facets in qh.newfacet_list
- qh_partitionpoint partition a point as inside, coplanar with, or outside a facet
- qh_partitioncoplanar partition coplanar point into a facet
- qh_precision restart on precision errors if not merging and if 'QJn'

- qh_freebuild free memory used by qh_initbuild and qh_buildhull
- qh_checkflags check flags for multiple frontends to qhull
- qh_freeqhull free memory used by qhull
- qh_init_A called before error handling initialized
- qh_init_B called after points are defined
- qh_initflags set flags and constants from command line
- qh_restore_qhull restores a saved qhull
- qh_save_qhull saves qhull for later restoring
- qh_user_memsizes define additional quick allocation sizes

- qh_gram_schmidt implements Gram-Schmidt orthogonalization by rows
- qh_projectinput project input along one or more dimensions + Delaunay projection
- qh_randommatrix generate a random dimXdim matrix in range (-1,1)
- qh_readpoints read points from input
- qh_rotateinput rotate input points using row matrix
- qh_scaleinput scale input points using qh low_bound/high_bound
- qh_setdelaunay project points to paraboloid for Delaunay triangulation
- qh_sethalfspace_all generate dual for halfspace intersection with interior point

- qh_addpoint add point to convex hull
- qh_findbestfacet find facet that is furthest below a point
- qh_findfacet_all exhaustive search for facet below a point
- qh_qhull construct the convex hull of a set of points

- qh_collectstatistics collect statistics for qh.facet_list
- qh_nearvertex return nearest vertex to point
- qh_point return point for a point ID
- qh_pointfacet return temporary set of facets indexed by point ID
- qh_pointid return ID for a point
- qh_pointvertex return vertices (if any) for all points
- qh_printallstatistics print all statistics
- qh_printneighborhood print neighborhood of one or two facets
- qh_printsummary print summary
- qh_produce_output print the results of qh_qhull()
- qh_setvoronoi_all compute Voronoi centers for all facets

- dfacet print facet by ID from debugger
- dvertex print vertex by ID from debugger
- qh_check_output check output
- qh_check_points verify that all points are inside the convex hull
- qh_errexit report error with a facet and a ridge
- qh_errexit2 report error with two facets
- qh_errprint print erroneous facets, ridge, and vertex
- qh_printfacetlist print all fields for a list of facets

**Up:**
Home page for
Qhull

**Up:** Qhull manual: Table of Contents

**Up:** Programs
• Options
• Output
• Formats
• Geomview
• Print
• Qhull
• Precision
• Trace

**Up:** Qhull internals: Table of Contents

**To:** Qhull functions, macros, and data structures

**To:** Geom •
Global • Io
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• Poly • Qhull
• Set • Stat
• User

Comments to: qhull@geom.umn.edu

Created: May 2, 1997 --- Last modified: see top