/usr/include/libqhull_r/qh-geom_r.htm is in libqhull-dev 2015.2-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 | <!-- Do not edit with Front Page, it adds too many spaces -->
<html>
<head>
<meta http-equiv="Content-Type"
content="text/html; charset=iso-8859-1">
<title>geom_r.c, geom2_r.c -- geometric and floating point routines</title>
</head>
<body>
<!-- Navigation links -->
<p><a name="TOP"><b>Up:</b></a> <a
href="http://www.qhull.org">Home page</a> for Qhull<br>
<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <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#TOC">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">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>
</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>
|