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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>*** Apologies for Cross-posting ***<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><st1:PersonName w:st="on"><b><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial;font-weight:bold'>Hamish Carr</span></font></b></st1:PersonName><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>, <st1:place
w:st="on"><st1:PlaceName w:st="on">UCD</st1:PlaceName> <st1:PlaceType w:st="on">School</st1:PlaceType></st1:place>
of Computer Science and Informatics <b><span style='font-weight:bold'>"(No)
More Marching Cubes" <o:p></o:p></span></b></span></font></p>
<p class=MsoNormal><b><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial;font-weight:bold'><o:p> </o:p></span></font></b></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Friday 12th October 2007, 2-3pm Room 1:10, Kilburn Building
The <st1:place w:st="on"><st1:PlaceType w:st="on">University</st1:PlaceType> of
<st1:PlaceName w:st="on">Manchester</st1:PlaceName></st1:place><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Isosurfaces, one of the most fundamental volumetric
visualization tools, are commonly rendered using the well-known Marching Cubes
cases that approximate contours of trilinearly-interpolated scalar fields.
While a complete set of cases has recently been published by Nielson, the
formal proof that these cases are the only ones possible and that they are
topologically correct is difficult to follow. We present a more straightforward
proof of the correctness and completeness of these cases based on a variation
of the Dividing Cubes algorithm. Since this proof is based on topological
arguments and a divide-and- conquer approach, this also sets the stage for
developing tessellation cases for higher-order interpolants and for the
quadrilinear interpolant in four dimensions. We also demonstrate that, apart
from degenerate cases, Nielson's cases are in fact subsets of two basic
configurations of the trilinear interpolant.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><b><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial;font-weight:bold'>Access Grid Information:<o:p></o:p></span></font></b></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Anyone wishing to view a seminar via Access Grid should note
the following:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Virtual venue: <st1:place w:st="on"><st1:PlaceType w:st="on">University</st1:PlaceType>
of <st1:PlaceName w:st="on">Manchester</st1:PlaceName></st1:place> (1.10)<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Jabber room: uom1.10@conference.mcs.anl.gov<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>For technical assistance regarding the Access Grid, please
contact <st1:PersonName w:st="on">support@agsc.ja.net</st1:PersonName><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>If possible, please let us know in advance if your site
intends to join a seminar.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><b><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial;font-weight:bold'>Further Information:<o:p></o:p></span></font></b></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><a
href="http://www.kato.mvc.mcc.ac.uk/rss-wiki/ACM_SIGGRAPH_Chapter">http://www.kato.mvc.mcc.ac.uk/rss-wiki/ACM_SIGGRAPH_Chapter</a>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><a href="http://www.rcs.manchester.ac.uk/research/seminars/">http://www.rcs.manchester.ac.uk/research/seminars/</a>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Part of the ACM SIGGRAPH University of Manchester
Professional Chapter, and sponsored by vizNET<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Best regards,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><st1:PersonName w:st="on"><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial'>Martin Turner</span></font></st1:PersonName><br>
<font size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>Mob:
+44 7990 918 509<br>
Tel: +44 161 275 0613 <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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