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## libqhull_r.c -- top-level functions and basic data types

> 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, `libqhull_r.h`, contains prototypes for these functions.

Copyright © 1995-2020 C.B. Barber

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### Index to libqhull_r.c, libqhull_r.h, and unix_r.c

- libqhull_r.h and unix_r.c data types and constants
- libqhull_r.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

### »libqhull_r.h and unix_r.c data types and constants

- 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 status codes for indicating errors
- qh_FILEstderr Fake stderr to distinguish error output from normal output [C++ only]
- qh_prompt version and long prompt for Qhull
- qh_prompt2 synopsis for Qhull
- qh_prompt3 concise prompt for Qhull
- qh_version version stamp

### »libqhull_r.h other macros

- traceN print trace message if qh.IStracing >= N.
- QHULL_UNUSED declare an unused variable to avoid warnings.

### »Quickhull routines in call order

- 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_buildcone build cone of new facets from furthest to the horizon
- qh_premerge pre-merge non-convex facets
- 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_joggle_restart if joggle ('QJn') and not merging, restart on precision errors

### »Top-level routines for initializing and terminating Qhull (in other modules)

- qh_freebuild free memory used by qh_initbuild and qh_buildhull
- 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_rboxpoints generate points for qhull
- qh_restore_qhull restores a saved qhull
- qh_save_qhull saves qhull for later restoring
- qh_user_memsizes define additional quick allocation sizes

### »Top-level routines for reading and modifying the input (in other modules)

- 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

### »Top-level routines for calling Qhull (in other modules)

- 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

### »Top-level routines for returning results (in other modules)

- 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

### »Top-level routines for testing and debugging (in other modules)

- 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

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Comments to: qhull@qhull.org
Created: May 2, 1997 --- Last modified: see top