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14 <h3 class="navbar">Contents</h3>
16 <li><a href="index.htm">Boost.Polygon Main Page</a></li>
17 <li><a href="gtl_design_overview.htm">Design Overview</a></li>
18 <li><a href="gtl_isotropy.htm">Isotropy</a></li>
19 <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
20 <li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
21 <li><a href="gtl_point_concept.htm">Point Concept</a></li>
22 <li><a href="gtl_segment_concept.htm">Segment Concept</a></li>
23 <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
24 <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li>
25 <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
26 With Holes Concept</a></li>
27 <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
28 <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
29 With Holes Concept</a></li>
30 <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li>
31 <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With
32 Holes Concept</a></li>
33 <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set
35 <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set
37 <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li>
38 <li><a href="gtl_connectivity_extraction_90.htm">Connectivity
39 Extraction 90</a></li>
40 <li><a href="gtl_connectivity_extraction_45.htm">Connectivity
41 Extraction 45</a></li>
42 <li><a href="gtl_connectivity_extraction.htm">Connectivity
44 <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
45 <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
46 <li><a href="gtl_property_merge.htm">Property Merge</a></li>
47 <li><a href="voronoi_main.htm">Voronoi Main Page<br>
49 <li>Voronoi Benchmark<br>
51 <li><a href="voronoi_builder.htm">Voronoi Builder</a></li>
52 <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li>
54 <h3 class="navbar">Other Resources</h3>
56 <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
57 <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
59 <li><a href="analysis.htm">Performance Analysis</a></li>
60 <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
61 <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
62 <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li>
63 <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced
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71 <h1>Voronoi Benchmark</h1>
72 <h2>Benchmark Details</h2>
73 From the topological perspective Delaunay triangulation is a dual
74 data structure to the Voronoi diagram, thus libraries that provide
75 Delaunay triangulation construction routines were also included into
76 the benchmark. However, from the computation perspective Voronoi
77 diagram contains more information as it embeds information regarding
78 the coordinates of the centers of the inscribed circles tangent to the
79 three or more input geometries.<br>
82 The benchmark consists of the two parts:<br>
84 <li>construction of the Voronoi diagram / Delaunay triangulation of a set of
85 random points uniformly distributed over 32-bit integer grid (<a href="../benchmark/voronoi_benchmark_points.cpp"><span style="text-decoration: underline;">voronoi_benchmark_points.cpp</span></a>)</li><li>construction of the Voronoi diagram / Delaunay triangulation of a set of
86 random non-intersecting
87 segments uniformly distributed over 32-bit integer grid (<a href="../benchmark/voronoi_benchmark_segments.cpp">voronoi_benchmark_segments.cpp</a>).</li>
93 <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
96 <td style="vertical-align: top;"><span style="font-weight: bold;">Library</span><br>
98 <td style="vertical-align: top; font-weight: bold;">Boost.Polygon<br>
100 <td style="vertical-align: top; font-weight: bold;">CGAL<br>
102 <td style="vertical-align: top; font-weight: bold;">SHull<br>
106 <td style="vertical-align: top;">Official page<br>
108 <td style="vertical-align: top;">www.boost.org/libs/polygon‎<br>
110 <td style="vertical-align: top;">http://www.cgal.org<br>
112 <td style="vertical-align: top;">http://www.s-hull.org<br>
116 <td style="vertical-align: top;">Algorithm<br>
118 <td style="vertical-align: top;">sweep-line<br>
120 <td style="vertical-align: top;">incremental<br>
122 <td style="vertical-align: top;">sweep-hull<br>
126 <td style="vertical-align: top;">Supported input geometries<br>
128 <td style="vertical-align: top;">points and segments<br>
130 <td style="vertical-align: top;">points and segments<br>
132 <td style="vertical-align: top;">points<br>
136 <td style="vertical-align: top;">Output data structure<br>
138 <td style="vertical-align: top;">Voronoi diagram<br>
140 <td style="vertical-align: top;">Delaunay triangulation<br>
142 <td style="vertical-align: top;">Delaunay triangulation<br>
146 <td style="vertical-align: top;">Complexity<br>
148 <td style="vertical-align: top;">O(N log N)<br>
150 <td style="vertical-align: top;">O(N log N)</td>
151 <td style="vertical-align: top;">O(N log N)</td>
154 <td style="vertical-align: top;">Memory usage<br>
156 <td style="vertical-align: top;">O(N)<br>
158 <td style="vertical-align: top;">O(N)<br>
160 <td style="vertical-align: top;">O(N)<br>
164 <td style="vertical-align: top;">Robustness policies<br>
166 <td style="vertical-align: top;">lazy arithmetic, exact predicates, topology analysis<br>
168 <td style="vertical-align: top;">lazy arithmetic, exact predicates, topology analysis<br>
170 <td style="vertical-align: top;">non-robust<br>
174 <td style="vertical-align: top;">Output coordinates precision<br>
176 <td style="vertical-align: top;">128 machine epsilon<br>
178 <td style="vertical-align: top;">no output coordinates<br>
180 <td style="vertical-align: top;">no output coordinates<br>
184 <td style="vertical-align: top;">External dependencies<br>
186 <td style="vertical-align: top;">No<br>
188 <td style="vertical-align: top;">Boost, GMP, MPFR<br>
190 <td style="vertical-align: top;">No<br>
197 The other known libraries (<a href="https://github.com/aewallin/openvoronoi">OpenVoronoi</a>,
198 <a href="http://www.cs.cmu.edu/%7Equake/triangle.html">Triangle</a>, <a href="http://www.cosy.sbg.ac.at/%7Eheld/projects/vroni/vroni.html">Vroni</a>) will be considered for the inclusion into the benchmark in the future.<br>
217 <h2>System Configuration<br>
221 Hardware: Intel i5-7600 2.8 GHz, 16GiB RAM.<br>
222 OS: Ubuntu 13.04 64-bit.<br>
223 Compiler: GCC 4.7.3.<br>
224 Libraries and dependencies: Boost 1.54.0, CGAL-4.3-beta1, GMP 5.1.4, MPFR 3.1.2, S-Hull.<br>
225 <h2>Benchmark Results</h2>
226 <h3>Random Points Benchmark</h3><img style="border: 1px solid ; width: 500px; height: 350px;" alt="Benchmark Points Chart" src="../benchmark/benchmark_results/plots/benchmark_points.png"><br>
228 <table style="text-align: left; width: 100%; margin-left: auto; margin-right: auto;" border="1" cellpadding="2" cellspacing="2">
231 <td colspan="2" rowspan="1" style="vertical-align: top; text-align: center;">Test specification<br>
233 <td colspan="6" rowspan="1" style="vertical-align: top; text-align: center;">Average construction
238 <td style="vertical-align: top; text-align: center;">Number
241 <td style="vertical-align: top; text-align: center;">Number
247 <td style="vertical-align: top; text-align: center;">Boost
250 <td style="vertical-align: top; text-align: center;">CGAL
253 <td style="vertical-align: top; text-align: center;">S-Hull
259 <td style="vertical-align: top; text-align: right;">100<br>
261 <td style="vertical-align: top; text-align: right;">10000<br>
266 <td style="vertical-align: top; text-align: right;">0.000206<br>
268 <td style="vertical-align: top; text-align: right;"> 0.000073<br>
270 <td style="vertical-align: top; text-align: right;">0.000243<br>
274 <td style="vertical-align: top; text-align: right;">1000<br>
276 <td style="vertical-align: top; text-align: right;">1000<br>
281 <td style="vertical-align: top; text-align: right;">0.002250<br>
283 <td style="vertical-align: top; text-align: right;">0.000753<br>
285 <td style="vertical-align: top; text-align: right;">0.002184<br>
289 <td style="vertical-align: top; text-align: right;">10000<br>
291 <td style="vertical-align: top; text-align: right;">100<br>
296 <td style="vertical-align: top; text-align: right;">0.024100<br>
298 <td style="vertical-align: top; text-align: right;">0.007917<br>
300 <td style="vertical-align: top; text-align: right;">0.030552<br>
304 <td style="vertical-align: top; text-align: right;">100000<br>
306 <td style="vertical-align: top; text-align: right;">10<br>
311 <td style="vertical-align: top; text-align: right;">0.292000<br>
313 <td style="vertical-align: top; text-align: right;">0.084336<br>
315 <td style="vertical-align: top; text-align: right;">0.451913<br>
319 <td style="vertical-align: top; text-align: right;">1000000<br>
321 <td style="vertical-align: top; text-align: right;">1<br>
326 <td style="vertical-align: top; text-align: right;">3.470000<br>
328 <td style="vertical-align: top; text-align: right;">0.902300<br>
330 <td style="vertical-align: top; text-align: right;">6.603814<br>
336 <h3>Random Segments Benchmark</h3><img style="border: 1px solid ; width: 500px; height: 350px;" alt="Benchmark Segment Chart" src="../benchmark/benchmark_results/plots/benchmark_segments.png"><br>
338 <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
341 <td colspan="2" rowspan="1" style="vertical-align: top; text-align: center;">Test specification<br>
343 <td colspan="4" rowspan="1" style="vertical-align: top; text-align: center;">Average construction
347 <td style="vertical-align: top; text-align: center;">Number
350 <td style="vertical-align: top; text-align: center;">Number
355 <td style="vertical-align: top; text-align: center;">Boost
358 <td style="vertical-align: top; text-align: center;">CGAL
364 <td style="vertical-align: top; text-align: right;">100<br>
366 <td style="vertical-align: top; text-align: right;">10000<br>
370 <td style="vertical-align: top; text-align: right;">0.002284<br>
372 <td style="vertical-align: top; text-align: right;">0.002985<br>
376 <td style="vertical-align: top; text-align: right;">1000<br>
378 <td style="vertical-align: top; text-align: right;">1000<br>
382 <td style="vertical-align: top; text-align: right;">0.023240<br>
384 <td style="vertical-align: top; text-align: right;">0.032180<br>
388 <td style="vertical-align: top; text-align: right;">10000<br>
390 <td style="vertical-align: top; text-align: right;">100<br>
394 <td style="vertical-align: top; text-align: right;"> 0.237700<br>
396 <td style="vertical-align: top; text-align: right;">0.337400<br>
400 <td style="vertical-align: top; text-align: right;">100000<br>
402 <td style="vertical-align: top; text-align: right;">10<br>
406 <td style="vertical-align: top; text-align: right;">2.488000<br>
408 <td style="vertical-align: top; text-align: right;">3.633000<br>
412 <td style="vertical-align: top; text-align: right;">1000000<br>
414 <td style="vertical-align: top; text-align: right;">1<br>
418 <td style="vertical-align: top; text-align: right;">25.00000<br>
420 <td style="vertical-align: top; text-align: right;">39.090000<br>
425 <br><span style="font-weight: bold;"></span></td>
428 <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top"> </td>
429 <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
430 <table class="docinfo" id="table2" frame="void" rules="none">
431 <colgroup> <col class="docinfo-name"><col class="docinfo-content"> </colgroup> <tbody valign="top">
433 <th class="docinfo-name">Copyright:</th>
434 <td>Copyright © Andrii Sydorchuk 2010-2012.</td>
437 <th class="docinfo-name">License:</th>
438 <td class="field-body">Distributed under the Boost Software
439 License, Version 1.0. (See accompanying file <tt class="literal"><span class="pre">LICENSE_1_0.txt</span></tt> or copy at <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
440 http://www.boost.org/LICENSE_1_0.txt</a>)</td>