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<big>'''MediaWiki has been successfully installed.'''</big>
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== Implicitization experiments on curves and surfaces ==
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Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
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{| class="experiments sortable"
 +
!  No
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! curve <ref> Many thanks to Tatjana Kalinka for providing this list of curves and surfaces. </ref>
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! class="unsortable" | equation
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! class="unsortable" | supports
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! <nowiki># mixed subdivisions</nowiki>
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! class="run" |
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Enum by reverse search (sec) <ref> This is the computation time of [http://jn.wspc.com.sg/google/pdf/S0218195902000980.pdf  enumeration of regular triangulations algorithm using reverse search]. I would like to thank very much [http://www.purple.dti.ne.jp/pub/cv.html  Fumihiko TAKEUCHI] for running the experiments and providing this results. Experiments were done on a Blade 100, 550Mhz, 2GB memory with SunOS 5.9.</ref>
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! class="run" |
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TOPCOM point2alltriang (sec) <ref> This is the computation time of '''points2alltriangs''' client of [http://www.rambau.wm.uni-bayreuth.de/TOPCOM/ TOPCOM] package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.</ref>
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! class="run" |
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TOPCOM point2triang(sec) <ref> This is the computation time of '''points2triangs''' client of [http://www.rambau.wm.uni-bayreuth.de/TOPCOM/ TOPCOM] package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.</ref>
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! <nowiki># mixed cell configurations</nowiki>
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! <nowiki># extreme terms</nowiki>
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! <nowiki># all terms</nowiki>
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|-
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|
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|-
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| 1.
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|| astroid
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||<math>a\cos(t)^3,a\sin(t)^3</math>
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|
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[curves_supports/supports1.dat supports]
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| class="topcom" | 289
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| 193.62
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| 0.048
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| 0.452
 +
| 289
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| 35
 +
| 454
 +
|-
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| 2.
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| cardioid
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| <math>a(2\cos(t)-\cos(2t)),a(2\sin(t)-\sin(2t))</math>
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|
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[curves_supports/supports2.dat supports]
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| class="topcom" | 37
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| 6.52
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| 0.005
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| 0.024
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| 37
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| 10
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| 33
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|-
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| 3.
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| circle
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|<math> \cos(t),\sin(t)</math>
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|
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[curves_supports/supports3.dat supports]
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| class="topcom" | 5
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| 0.004
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| 0.016
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| 0.004
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| 5
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| 3
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| 4
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|-
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| 4.
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| conchoid
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| <math>a \cos(t),ah \sin(t)</math>
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|
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[curves_supports/supports4.dat supports]
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| class="topcom" | 12
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| 0.84
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| 0.003
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| 0.008
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| 12
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| 4
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| 6
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|-
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| 5.
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| ellipse
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| <math>a\cos(t),b\sin(t)</math>
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|
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[curves_supports/supports5.dat supports]
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| class="topcom" | 5
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| 0.15
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| 0.001
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| 0.004
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| 5
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| 3
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| 4
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|-
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| 6.
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| folium of descartes
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| <math>3ah/(1+ h^3), 3ah^2/(ah^3)</math>
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|
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[curves_supports/supports6.dat supports]
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| class="topcom" | 14
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| 0.94
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| 0.004
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| 0.008
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| 14
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| 6
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| 10
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|-
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| 7.
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| involute of a circle
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| <math>a(\cos(t) t(\sin(t)),a(\sin(t)-t\cos(t))</math>
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|
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[curves_supports/supports7.dat supports]
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| class="topcom" | 14
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| 1.00
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| 0.001
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| 0.007
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| 14
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| 6
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| 7
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|-
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| 8.
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| nephroid
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| <math>a(3\cos(t)-\cos(3t)),a(3\sin(t)-\sin(3t))</math>
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|
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[curves_supports/supports8.dat supports]
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| class="topcom" | 289
 +
| 195.27
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| 0.004
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| 0.240
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| 289
 +
| 35
 +
| 454
 +
|-
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| 9a.
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| plateau curve
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| <math>a\sin(3t)/\sin(t),2a\sin(2t)</math>
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|
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[curves_supports/supports9a.dat supports]
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| class="topcom" | 94
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| 33.02
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| 0.012
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| 0.064
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| 94
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| 15
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| 55
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|-
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| 9b.
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| plateau curve
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| <math>a\sin(6t)/ \sin(2t), 2a\sin(4t)</math>
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|
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[curves_supports/supports9b.dat supports]
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| class="topcom" | 42168
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| class="halt" | halt
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| 25.934
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| 85.597
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| 42168
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| 495
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| class="halt" | not computed
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|-
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| 10.
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| talbot's curve
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| <math>(a^2 + f^2 \sin( t)^2) \cos( t)/a, (a^2 - 2f^2 + (f^2)\sin(t)^2)\sin(t)/b </math>
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|
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[curves_supports/supports10.dat supports]
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| class="topcom" | 1944
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| 3948.80
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| 0.416
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| 2.356
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| 1944
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| 84
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| 1600
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|-
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| 11.
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| tricuspoid
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| <math>a(2\cos(t)+\cos(2t)),a(2\sin(t)-\sin(2t))</math>
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|
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[curves_supports/supports11.dat supports]
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| class="topcom" | 37
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| 6.20
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| 0.008
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| 0.024
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| 37
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| 10
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| 33
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|-
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| 12.
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| witch of agnesi
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| <math>ah,a/(1 h^2)</math>
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|
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[curves_supports/supports12.dat supports]
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| class="topcom" | 2
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| 0.03
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| 0.007
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| 0.004
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| 2
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| 2
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| 2
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|-
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| 13.
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| circle (3 systems)
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| <math>(-t^2 +1)/s, 2t/s, t^2 -s +1</math>
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|
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[curves_supports/supports13.dat supports]
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| class="topcom" | 26
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| 6.00
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| 0.020
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| 0.052
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| 26
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| 6
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| 7
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|}
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== Getting started ==
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* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
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{|class="experiments sortable"
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* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
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! No
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* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]
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! surface
 +
! class="unsortable" | equation
 +
! class="unsortable" | supports
 +
! <nowiki># mixed subdivisions</nowiki>
 +
! class="run" |
 +
Enum by reverse search (sec)
 +
! class="run" |
 +
TOPCOM point2alltriang (sec)
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! class="run" |
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TOPCOM point2triang(sec)
 +
! <nowiki># mixed cell configurations</nowiki>
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! <nowiki># extreme terms</nowiki>
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! <nowiki># all terms</nowiki>
 +
|-
 +
|
 +
|-
 +
| 1.
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| cylinder
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| <math>\cos(t),\sin(t),s</math>
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|
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[surfaces_supports/supports1.dat supports]
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| class="topcom" | 5
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| 0.24
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| 0.003
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| 0.006
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| 5
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| 3
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| 4
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|-
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| 2.
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| cone
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| <math>s\cos(t),s\sin(t),s</math>
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|
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[surfaces_supports/supports2.dat supports]
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| class="topcom" | 122
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| 73.45
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| 0.192
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| 0.288
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| 98
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| 8
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| 14
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|-
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| 3.
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| paraboloid
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| <math>s\cos(t),s\sin(t),s^2</math>
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|
 +
[surfaces_supports/supports3.dat supports]
 +
| class="topcom" | 122
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| 71.60
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| 0.192
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| 0.296
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| 98
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| 8
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| 37
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|-
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| 4.
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| surface of revolution
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| <math>s\cos(t),s\sin(t),\cos(s)</math>
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|
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[surfaces_supports/supports4.dat supports]
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| class="topcom" | 122
 +
| 71.80
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| 0.193
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| 0.288
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| 98
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| 8
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| 37
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|-
 +
| 5.
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| sphere
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| <math>\sin(t)\cos(s),\sin(t)\sin(s),\cos(t)</math>
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|
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[surfaces_supports/supports5.dat supports]
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| class="topcom" | 104148
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| class="halt" | halt
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| 19496.602
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| 714.161
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| 43018
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| 21
 +
| 186
 +
|-
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| 6.
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| sphere2
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| <math>\cos(t)\cos(s),\sin(t)\cos(s),\sin(s)</math>
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|
 +
[surfaces_supports/supports6.dat supports]
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| class="topcom" | 76280
 +
| class="halt" | halt
 +
| 4492.977
 +
| 397.157
 +
| 32076
 +
| 95
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| 776
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|-
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| 7.
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| stereographic shpere
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| <math>2t/(1 t^2 s^2),2s/(1 t^2 s^2),(t^2 s^2-1)/(1 t^2 s^2)</math>
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|
 +
[surfaces_supports/supports7.dat supports]
 +
| class="topcom" | 3540
 +
| 7112.54
 +
| 25.402
 +
| 11.025
 +
| 3126
 +
| 22
 +
| 283
 +
|-
 +
| 8.
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| twisted shpere
 +
| <math>a(\cos(t) t(\sin(t)),a(\sin(t)-t\cos(t))</math>
 +
|
 +
[surfaces_supports/supports8.dat supports]
 +
| class="topcom" | &gt;1812221
 +
| class="halt"  | not computed
 +
| class="halt" | not computed
 +
| class="halt" | not computed
 +
| class="halt" | not computed
 +
| class="halt" | not computed
 +
| class="halt" | not computed
 +
|}
 +
 
 +
== Remarks ==
 +
 
 +
<references />

Revision as of 21:31, 26 January 2010

Implicitization experiments on curves and surfaces

No curve [1] equation supports # mixed subdivisions

Enum by reverse search (sec) [2]

TOPCOM point2alltriang (sec) [3]

TOPCOM point2triang(sec) [4]

# mixed cell configurations # extreme terms # all terms
1. astroid Failed to parse (Cannot write to or create math temp directory): a\cos(t)^3,a\sin(t)^3

[curves_supports/supports1.dat supports]

289 193.62 0.048 0.452 289 35 454
2. cardioid Failed to parse (Cannot write to or create math temp directory): a(2\cos(t)-\cos(2t)),a(2\sin(t)-\sin(2t))

[curves_supports/supports2.dat supports]

37 6.52 0.005 0.024 37 10 33
3. circle Failed to parse (Cannot write to or create math temp directory): \cos(t),\sin(t)

[curves_supports/supports3.dat supports]

5 0.004 0.016 0.004 5 3 4
4. conchoid Failed to parse (Cannot write to or create math temp directory): a \cos(t),ah \sin(t)

[curves_supports/supports4.dat supports]

12 0.84 0.003 0.008 12 4 6
5. ellipse Failed to parse (Cannot write to or create math temp directory): a\cos(t),b\sin(t)

[curves_supports/supports5.dat supports]

5 0.15 0.001 0.004 5 3 4
6. folium of descartes Failed to parse (Cannot write to or create math temp directory): 3ah/(1+ h^3), 3ah^2/(ah^3)

[curves_supports/supports6.dat supports]

14 0.94 0.004 0.008 14 6 10
7. involute of a circle Failed to parse (Cannot write to or create math temp directory): a(\cos(t) t(\sin(t)),a(\sin(t)-t\cos(t))

[curves_supports/supports7.dat supports]

14 1.00 0.001 0.007 14 6 7
8. nephroid Failed to parse (Cannot write to or create math temp directory): a(3\cos(t)-\cos(3t)),a(3\sin(t)-\sin(3t))

[curves_supports/supports8.dat supports]

289 195.27 0.004 0.240 289 35 454
9a. plateau curve Failed to parse (Cannot write to or create math temp directory): a\sin(3t)/\sin(t),2a\sin(2t)

[curves_supports/supports9a.dat supports]

94 33.02 0.012 0.064 94 15 55
9b. plateau curve Failed to parse (Cannot write to or create math temp directory): a\sin(6t)/ \sin(2t), 2a\sin(4t)

[curves_supports/supports9b.dat supports]

42168 halt 25.934 85.597 42168 495 not computed
10. talbot's curve Failed to parse (Cannot write to or create math temp directory): (a^2 + f^2 \sin( t)^2) \cos( t)/a, (a^2 - 2f^2 + (f^2)\sin(t)^2)\sin(t)/b

[curves_supports/supports10.dat supports]

1944 3948.80 0.416 2.356 1944 84 1600
11. tricuspoid Failed to parse (Cannot write to or create math temp directory): a(2\cos(t)+\cos(2t)),a(2\sin(t)-\sin(2t))

[curves_supports/supports11.dat supports]

37 6.20 0.008 0.024 37 10 33
12. witch of agnesi Failed to parse (Cannot write to or create math temp directory): ah,a/(1 h^2)

[curves_supports/supports12.dat supports]

2 0.03 0.007 0.004 2 2 2
13. circle (3 systems) Failed to parse (Cannot write to or create math temp directory): (-t^2 +1)/s, 2t/s, t^2 -s +1

[curves_supports/supports13.dat supports]

26 6.00 0.020 0.052 26 6 7


No surface equation supports # mixed subdivisions

Enum by reverse search (sec)

TOPCOM point2alltriang (sec)

TOPCOM point2triang(sec)

# mixed cell configurations # extreme terms # all terms
1. cylinder Failed to parse (Cannot write to or create math temp directory): \cos(t),\sin(t),s

[surfaces_supports/supports1.dat supports]

5 0.24 0.003 0.006 5 3 4
2. cone Failed to parse (Cannot write to or create math temp directory): s\cos(t),s\sin(t),s

[surfaces_supports/supports2.dat supports]

122 73.45 0.192 0.288 98 8 14
3. paraboloid Failed to parse (Cannot write to or create math temp directory): s\cos(t),s\sin(t),s^2

[surfaces_supports/supports3.dat supports]

122 71.60 0.192 0.296 98 8 37
4. surface of revolution Failed to parse (Cannot write to or create math temp directory): s\cos(t),s\sin(t),\cos(s)

[surfaces_supports/supports4.dat supports]

122 71.80 0.193 0.288 98 8 37
5. sphere Failed to parse (Cannot write to or create math temp directory): \sin(t)\cos(s),\sin(t)\sin(s),\cos(t)

[surfaces_supports/supports5.dat supports]

104148 halt 19496.602 714.161 43018 21 186
6. sphere2 Failed to parse (Cannot write to or create math temp directory): \cos(t)\cos(s),\sin(t)\cos(s),\sin(s)

[surfaces_supports/supports6.dat supports]

76280 halt 4492.977 397.157 32076 95 776
7. stereographic shpere Failed to parse (Cannot write to or create math temp directory): 2t/(1 t^2 s^2),2s/(1 t^2 s^2),(t^2 s^2-1)/(1 t^2 s^2)

[surfaces_supports/supports7.dat supports]

3540 7112.54 25.402 11.025 3126 22 283
8. twisted shpere Failed to parse (Cannot write to or create math temp directory): a(\cos(t) t(\sin(t)),a(\sin(t)-t\cos(t))

[surfaces_supports/supports8.dat supports]

>1812221 not computed not computed not computed not computed not computed not computed

Remarks

  1. ↑ Many thanks to Tatjana Kalinka for providing this list of curves and surfaces.
  2. ↑ This is the computation time of enumeration of regular triangulations algorithm using reverse search. I would like to thank very much Fumihiko TAKEUCHI for running the experiments and providing this results. Experiments were done on a Blade 100, 550Mhz, 2GB memory with SunOS 5.9.
  3. ↑ This is the computation time of points2alltriangs client of TOPCOM package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.
  4. ↑ This is the computation time of points2triangs client of TOPCOM package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.
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