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geom_r.c, geom2_r.c -- geometric and floating point routines
</title>
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<body>
<!-- Navigation links -->
<p><a
name=
"TOP"
><b>
Up:
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<a
href=
"http://www.qhull.org"
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for Qhull
<br>
<b>
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Functions
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Qhull code: Table of Contents
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<b>
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</b>
<a
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"index.htm"
>
Qhull functions
</a>
, macros, and data structures
<br>
<b>
To:
</b>
<a
href=
"qh-geom_r.htm#TOC"
>
Geom
</a>
•
<a
href=
"qh-globa_r.htm"
>
Global
</a>
•
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Io
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Mem
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User
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</p>
<hr>
<!-- Main text of document. -->
<h2>
geom_r.c, geom2_r.c, random_r.c -- geometric and floating point routines
</h2>
<blockquote>
<p>
Geometrically, a vertex is a point with
<em>
d
</em>
coordinates
and a facet is a halfspace. A
<em>
halfspace
</em>
is defined by an
oriented hyperplane through the facet's vertices. A
<em>
hyperplane
</em>
is defined by
<em>
d
</em>
normalized coefficients and an offset. A
point is
<em>
above
</em>
a facet if its distance to the facet is
positive.
</p>
<p>
Qhull uses floating point coordinates for input points,
vertices, halfspace equations, centrums, and an interior point.
</p>
<p>
Qhull may be configured for single precision or double
precision floating point arithmetic (see
<a
href=
"user_r.h#realT"
>
realT
</a>
).
</p>
<p>
Each floating point operation may incur round-off error (see
<a
href=
"qh-merge_r.htm#TOC"
>
Merge
</a>
). The maximum error for distance
computations is determined at initialization. The roundoff error
in halfspace computation is accounted for by computing the
distance from vertices to the halfspace.
</p>
</blockquote>
<p><b>
Copyright
©
1995-2015 C.B. Barber
</b></p>
<hr>
<p><a
href=
"#TOP"
>
»
</a>
<b>
Geom
</b>
<a
name=
"TOC"
>
•
</a>
<a
href=
"qh-globa_r.htm#TOC"
>
Global
</a>
•
<a
href=
"qh-io_r.htm#TOC"
>
Io
</a>
•
<a
href=
"qh-mem_r.htm#TOC"
>
Mem
</a>
•
<a
href=
"qh-merge_r.htm#TOC"
>
Merge
</a>
•
<a
href=
"qh-poly_r.htm#TOC"
>
Poly
</a>
•
<a
href=
"qh-qhull_r.htm#TOC"
>
Qhull
</a>
•
<a
href=
"qh-set_r.htm#TOC"
>
Set
</a>
•
<a
href=
"qh-stat_r.htm#TOC"
>
Stat
</a>
•
<a
href=
"qh-user_r.htm#TOC"
>
User
</a>
</p>
<h3>
Index to
<a
href=
"geom_r.c"
>
geom_r.c
</a>
,
<a
href=
"geom2_r.c"
>
geom2_r.c
</a>
,
<a
href=
"geom_r.h"
>
geom_r.h
</a>
,
<a
href=
"random_r.c"
>
random_r.c
</a>
,
<a
href=
"random_r.h"
>
random_r.h
</a>
</h3>
<ul>
<li><a
href=
"#gtype"
>
geometric data types and constants
</a>
</li>
<li><a
href=
"#gmacro"
>
mathematical macros
</a>
</li>
<li><a
href=
"#gmath"
>
mathematical functions
</a>
</li>
<li><a
href=
"#gcomp"
>
computational geometry functions
</a>
</li>
<li><a
href=
"#gpoint"
>
point array functions
</a>
</li>
<li><a
href=
"#gfacet"
>
geometric facet functions
</a>
</li>
<li><a
href=
"#ground"
>
geometric roundoff functions
</a></li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gtype"
>
geometric data types
and constants
</a></h3>
<ul>
<li><a
href=
"libqhull_r.h#coordT"
>
coordT
</a>
coordinates and
coefficients are stored as realT
</li>
<li><a
href=
"libqhull_r.h#pointT"
>
pointT
</a>
a point is an array
of
<tt>
DIM3
</tt>
coordinates
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gmacro"
>
mathematical macros
</a></h3>
<ul>
<li><a
href=
"geom_r.h#fabs_"
>
fabs_
</a>
returns the absolute
value of a
</li>
<li><a
href=
"geom_r.h#fmax_"
>
fmax_
</a>
returns the maximum
value of a and b
</li>
<li><a
href=
"geom_r.h#fmin_"
>
fmin_
</a>
returns the minimum
value of a and b
</li>
<li><a
href=
"geom_r.h#maximize_"
>
maximize_
</a>
maximize a value
</li>
<li><a
href=
"geom_r.h#minimize_"
>
minimize_
</a>
minimize a value
</li>
<li><a
href=
"geom_r.h#det2_"
>
det2_
</a>
compute a 2-d
determinate
</li>
<li><a
href=
"geom_r.h#det3_"
>
det3_
</a>
compute a 3-d
determinate
</li>
<li><a
href=
"geom_r.h#dX"
>
dX, dY, dZ
</a>
compute the difference
between two coordinates
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gmath"
>
mathematical functions
</a></h3>
<ul>
<li><a
href=
"geom_r.c#backnormal"
>
qh_backnormal
</a>
solve for
normal using back substitution
</li>
<li><a
href=
"geom2_r.c#crossproduct"
>
qh_crossproduct
</a>
compute the cross product of two 3-d vectors
</li>
<li><a
href=
"geom2_r.c#determinant"
>
qh_determinant
</a>
compute
the determinant of a square matrix
</li>
<li><a
href=
"geom_r.c#gausselim"
>
qh_gausselim
</a>
Gaussian
elimination with partial pivoting
</li>
<li><a
href=
"geom2_r.c#gram_schmidt"
>
qh_gram_schmidt
</a>
implements Gram-Schmidt orthogonalization by rows
</li>
<li><a
href=
"geom2_r.c#maxabsval"
>
qh_maxabsval
</a>
return max
absolute value of a vector
</li>
<li><a
href=
"geom2_r.c#minabsval"
>
qh_minabsval
</a>
return min
absolute value of a dim vector
</li>
<li><a
href=
"geom2_r.c#mindiff"
>
qh_mindiff
</a>
return index of
min absolute difference of two vectors
</li>
<li><a
href=
"geom_r.c#normalize"
>
qh_normalize
</a>
normalize a
vector
</li>
<li><a
href=
"geom_r.c#normalize2"
>
qh_normalize2
</a>
normalize a
vector and report if too small
</li>
<li><a
href=
"geom2_r.c#printmatrix"
>
qh_printmatrix
</a>
print
matrix given by row vectors
</li>
<li><a
href=
"random_r.c#rand"
>
qh_rand/srand
</a>
generate random
numbers
</li>
<li><a
href=
"random_r.c#randomfactor"
>
qh_randomfactor
</a>
return
a random factor near 1.0
</li>
<li><a
href=
"random_r.c#randommatrix"
>
qh_randommatrix
</a>
generate a random dimXdim matrix in range (-1,1)
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gcomp"
>
computational geometry functions
</a></h3>
<ul>
<li><a
href=
"geom2_r.c#detsimplex"
>
qh_detsimplex
</a>
compute
determinate of a simplex of points
</li>
<li><a
href=
"io_r.c#detvnorm"
>
qh_detvnorm
</a>
determine normal for Voronoi ridge
</li>
<li><a
href=
"geom2_r.c#distnorm"
>
qh_distnorm
</a>
compute
distance from point to hyperplane as defined by normal and offset
</li>
<li><a
href=
"geom2_r.c#facetarea_simplex"
>
qh_facetarea_simplex
</a>
return area of a simplex
</li>
<li><a
href=
"geom_r.c#getangle"
>
qh_getangle
</a>
return cosine
of angle (i.e., dot product)
</li>
<li><a
href=
"geom_r.c#getcenter"
>
qh_getcenter
</a>
return
arithmetic center for a set of vertices
</li>
<li><a
href=
"geom2_r.c#pointdist"
>
qh_pointdist
</a>
return
distance between two points
</li>
<li><a
href=
"geom2_r.c#rotatepoints"
>
qh_rotatepoints
</a>
rotate
numpoints points by a row matrix
</li>
<li><a
href=
"geom2_r.c#sethalfspace"
>
qh_sethalfspace
</a>
set
coords to dual of halfspace relative to an interior point
</li>
<li><a
href=
"geom_r.c#sethyperplane_det"
>
qh_sethyperplane_det
</a>
return hyperplane for oriented simplex using determinates
</li>
<li><a
href=
"geom_r.c#sethyperplane_gauss"
>
qh_sethyperplane_gauss
</a>
return hyperplane for oriented simplex using Gaussian
elimination
</li>
<li><a
href=
"geom2_r.c#voronoi_center"
>
qh_voronoi_center
</a>
return Voronoi center for a set of points
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gpoint"
>
point array functions
</a></h3>
<ul>
<li><a
href=
"geom2_r.c#copypoints"
>
qh_copypoints
</a>
return
malloc'd copy of points
</li>
<li><a
href=
"geom2_r.c#joggleinput"
>
qh_joggleinput
</a>
joggle
input points by qh.JOGGLEmax
</li>
<li><a
href=
"geom2_r.c#maxmin"
>
qh_maxmin
</a>
return max/min
points for each dimension
</li>
<li><a
href=
"geom2_r.c#maxsimplex"
>
qh_maxsimplex
</a>
determines
maximum simplex for a set of points
</li>
<li><a
href=
"geom2_r.c#printpoints"
>
qh_printpoints
</a>
print ids for a
set of points
</li>
<li><a
href=
"geom2_r.c#projectinput"
>
qh_projectinput
</a>
project
input using qh DELAUNAY and qh low_bound/high_bound
</li>
<li><a
href=
"geom2_r.c#projectpoints"
>
qh_projectpoints
</a>
project points along one or more dimensions
</li>
<li><a
href=
"geom2_r.c#rotateinput"
>
qh_rotateinput
</a>
rotate
input points using row matrix
</li>
<li><a
href=
"geom2_r.c#scaleinput"
>
qh_scaleinput
</a>
scale
input points using qh low_bound/high_bound
</li>
<li><a
href=
"geom2_r.c#scalelast"
>
qh_scalelast
</a>
scale last
coordinate to [0,m] for Delaunay triangulations
</li>
<li><a
href=
"geom2_r.c#scalepoints"
>
qh_scalepoints
</a>
scale
points to new lowbound and highbound
</li>
<li><a
href=
"geom2_r.c#setdelaunay"
>
qh_setdelaunay
</a>
project
points to paraboloid for Delaunay triangulation
</li>
<li><a
href=
"geom2_r.c#sethalfspace_all"
>
qh_sethalfspace_all
</a>
generate dual for halfspace intersection with interior
point
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"gfacet"
>
geometric facet functions
</a></h3>
<ul>
<li><a
href=
"geom_r.c#distplane"
>
qh_distplane
</a>
return
distance from point to facet
</li>
<li><a
href=
"geom2_r.c#facetarea"
>
qh_facetarea
</a>
return area
of a facet
</li>
<li><a
href=
"geom2_r.c#facetcenter"
>
qh_facetcenter
</a>
return
Voronoi center for a facet's vertices
</li>
<li><a
href=
"geom_r.c#findbest"
>
qh_findbest
</a>
find visible
facet or best facet for a point
</li>
<li><a
href=
"geom_r.c#findbesthorizon"
>
qh_findbesthorizon
</a>
update best new facet with horizon facets
</li>
<li><a
href=
"geom_r.c#findbestnew"
>
qh_findbestnew
</a>
find best
new facet for point
</li>
<li><a
href=
"geom2_r.c#getarea"
>
qh_getarea
</a>
get area of all
facets in facetlist, collect statistics
</li>
<li><a
href=
"geom_r.c#getcentrum"
>
qh_getcentrum
</a>
return
centrum for a facet
</li>
<li><a
href=
"geom_r.c#getdistance"
>
qh_getdistance
</a>
returns
the max and min distance of a facet's vertices to a
neighboring facet
</li>
<li><a
href=
"geom2_r.c#findgooddist"
>
qh_findgooddist
</a>
find
best good facet visible for point from facet
</li>
<li><a
href=
"geom2_r.c#inthresholds"
>
qh_inthresholds
</a>
return
True if facet normal within 'Pdn' and 'PDn'
</li>
<li><a
href=
"geom2_r.c#orientoutside"
>
qh_orientoutside
</a>
orient facet so that
<tt>
qh.interior_point
</tt>
is inside
</li>
<li><a
href=
"geom_r.c#projectpoint"
>
qh_projectpoint
</a>
project
point onto a facet
</li>
<li><a
href=
"geom_r.c#setfacetplane"
>
qh_setfacetplane
</a>
sets
the hyperplane for a facet
</li>
<li><a
href=
"geom2_r.c#sharpnewfacets"
>
qh_sharpnewfacets
</a>
true
if new facets contains a sharp corner
</li>
</ul>
<h3><a
href=
"qh-geom_r.htm#TOC"
>
»
</a><a
name=
"ground"
>
geometric roundoff functions
</a></h3>
<ul>
<li><a
href=
"geom2_r.c#detjoggle"
>
qh_detjoggle
</a>
determine
default joggle for points and distance roundoff error
</li>
<li><a
href=
"geom2_r.c#detroundoff"
>
qh_detroundoff
</a>
determine maximum roundoff error and other precision constants
</li>
<li><a
href=
"geom2_r.c#distround"
>
qh_distround
</a>
compute
maximum roundoff error due to a distance computation to a
normalized hyperplane
</li>
<li><a
href=
"geom2_r.c#divzero"
>
qh_divzero
</a>
divide by a
number that is nearly zero
</li>
<li><a
href=
"geom2_r.c#maxouter"
>
qh_maxouter
</a>
return maximum outer
plane
</li>
<li><a
href=
"geom2_r.c#outerinner"
>
qh_outerinner
</a>
return actual
outer and inner planes
</ul>
<p>
<!-- Navigation links -->
</p>
<hr>
<p><b>
Up:
</b>
<a
href=
"http://www.qhull.org"
>
Home page for
Qhull
</a>
<br>
<b>
Up:
</b>
<a
href=
"index.htm#TOC"
>
Qhull manual: Table of Contents
</a>
<br>
<b>
Up:
</b>
<a
href=
"../../html/qh-quick.htm#programs"
>
Programs
</a>
•
<a
href=
"../../html/qh-quick.htm#options"
>
Options
</a>
•
<a
href=
"../../html/qh-opto.htm#output"
>
Output
</a>
•
<a
href=
"../../html/qh-optf.htm#format"
>
Formats
</a>
•
<a
href=
"../../html/qh-optg.htm#geomview"
>
Geomview
</a>
•
<a
href=
"../../html/qh-optp.htm#print"
>
Print
</a>
•
<a
href=
"../../html/qh-optq.htm#qhull"
>
Qhull
</a>
•
<a
href=
"../../html/qh-optc.htm#prec"
>
Precision
</a>
•
<a
href=
"../../html/qh-optt.htm#trace"
>
Trace
</a>
•
<a
href=
"index.htm"
>
Functions
</a><br>
<b>
Up:
</b>
<a
href=
"../../html/qh-code.htm#TOC"
>
Qhull code: Table of Contents
</a>
<br>
<b>
To:
</b>
<a
href=
"index.htm"
>
Qhull functions
</a>
, macros, and data structures
<br>
<b>
To:
</b>
<a
href=
"qh-geom_r.htm"
>
Geom
</a>
•
<a
href=
"qh-globa_r.htm"
>
Global
</a>
•
<a
href=
"qh-io_r.htm"
>
Io
</a>
•
<a
href=
"qh-mem_r.htm"
>
Mem
</a>
•
<a
href=
"qh-merge_r.htm"
>
Merge
</a>
•
<a
href=
"qh-poly_r.htm"
>
Poly
</a>
•
<a
href=
"qh-qhull_r.htm#TOC"
>
Qhull
</a>
•
<a
href=
"qh-set_r.htm"
>
Set
</a>
•
<a
href=
"qh-stat_r.htm"
>
Stat
</a>
•
<a
href=
"qh-user_r.htm"
>
User
</a><br>
<p>
<!-- GC common information -->
</p>
<hr>
<p><a
href=
"http://www.geom.uiuc.edu/"
><img
src=
"../../html/qh--geom.gif"
align=
"middle"
width=
"40"
height=
"40"
></a><i>
The
Geometry Center Home Page
</i></p>
<p>
Comments to:
<a
href=
mailto:qhull@qhull.org
>
qhull@qhull.org
</a>
</a><br>
Created: May 2, 1997 ---
<!-- hhmts start -->
Last modified: see top
<!-- hhmts end -->
</p>
</body>
</html>
Event Timeline
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