<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=utf-8"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:Wingdings;
panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:Wingdings;
panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
{mso-style-priority:99;
mso-style-link:"Balloon Text Char";
margin:0in;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:"Tahoma","sans-serif";}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
p.m-6693326458691273489msolistparagraph, li.m-6693326458691273489msolistparagraph, div.m-6693326458691273489msolistparagraph
{mso-style-name:m_-6693326458691273489msolistparagraph;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
span.BalloonTextChar
{mso-style-name:"Balloon Text Char";
mso-style-priority:99;
mso-style-link:"Balloon Text";
font-family:"Tahoma","sans-serif";}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri","sans-serif";}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:1909146792;
mso-list-type:hybrid;
mso-list-template-ids:248548336 -1329720138 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;}
@list l0:level1
{mso-level-start-at:0;
mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:22.5pt;
text-indent:-.25in;
font-family:Wingdings;
mso-fareast-font-family:Calibri;
mso-bidi-font-family:"Times New Roman";}
@list l0:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:58.5pt;
text-indent:-.25in;
font-family:"Courier New";}
@list l0:level3
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:94.5pt;
text-indent:-.25in;
font-family:Wingdings;}
@list l0:level4
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:130.5pt;
text-indent:-.25in;
font-family:Symbol;}
@list l0:level5
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:166.5pt;
text-indent:-.25in;
font-family:"Courier New";}
@list l0:level6
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:202.5pt;
text-indent:-.25in;
font-family:Wingdings;}
@list l0:level7
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:238.5pt;
text-indent:-.25in;
font-family:Symbol;}
@list l0:level8
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:274.5pt;
text-indent:-.25in;
font-family:"Courier New";}
@list l0:level9
{mso-level-number-format:bullet;
mso-level-text:;
mso-level-tab-stop:none;
mso-level-number-position:left;
margin-left:310.5pt;
text-indent:-.25in;
font-family:Wingdings;}
ol
{margin-bottom:0in;}
ul
{margin-bottom:0in;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hi –<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Note that standards documents are intended for experts in the field. Mathematical notation should be a standard part of this expertise and need not be explained.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoListParagraph style='margin-left:22.5pt;text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:Wingdings;color:#1F497D'><span style='mso-list:Ignore'>n<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Dick<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>/******************************************<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Richard F. Puk, Ph.D., President<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Intelligraphics Incorporated<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| 7644 Cortina Court<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Carlsbad, CA 92009-8206<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Tel: +1-760-753-9027 Mobile: +1-760-809-9027<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Email: <a href="mailto:puk@igraphics.com"><span style='color:blue'>puk@igraphics.com</span></a><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>\****************************************** <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Andreas Plesch [mailto:andreasplesch@gmail.com] <br><b>Sent:</b> Monday, October 2, 2017 8:28 AM<br><b>To:</b> puk Richard<br><b>Cc:</b> X3D Graphics public mailing list; vmarchetti@kshell.com<br><b>Subject:</b> RE: [x3d-public] Sequencer interval definition<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Thanks, this is very reasonable. For the less mathematically fluent, it may still be helpful to add an explanation, perhaps in the tooltips.<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>If there aren't any more suggestions with regards to Vince's proposal for a corrected function definition, I could submit the function as a standards comment.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Andreas<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>On Oct 2, 2017 1:16 AM, "Richard F. Puk" <<a href="mailto:puk@igraphics.com">puk@igraphics.com</a>> wrote:<o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hi –</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>As editor of these standards, we used normal mathematical notation. We consider infinity as a number that cannot be expressed. This is why there is always an indication of an open interval whenever infinity (+ or -) is at one end of the interval.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=m-6693326458691273489msolistparagraph style='margin-left:22.5pt'><span style='font-size:11.0pt;font-family:Wingdings;color:#1F497D'>n</span><span style='font-size:7.0pt;color:#1F497D'> </span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Dick</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>/******************************************</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Richard F. Puk, Ph.D., President</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Intelligraphics Incorporated</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| <a href="https://maps.google.com/?q=7644+Cortina+Court+%7C+Carlsbad,+CA%C2%A0+92009&entry=gmail&source=g">7644 Cortina Court</a></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><a href="https://maps.google.com/?q=7644+Cortina+Court+%7C+Carlsbad,+CA%C2%A0+92009&entry=gmail&source=g">| Carlsbad, CA 92009</a>-8206</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Tel: <a href="tel:(760)%20753-9027" target="_blank">+1-760-753-9027</a> Mobile: <a href="tel:(760)%20809-9027" target="_blank">+1-760-809-9027</a></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>| Email: <a href="mailto:puk@igraphics.com" target="_blank">puk@igraphics.com</a></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>\****************************************** </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a name="m_-6693326458691273489__MailEndCompose"><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> x3d-public [mailto:<a href="mailto:x3d-public-bounces@web3d.org" target="_blank">x3d-public-bounces@web3d.org</a>] <b>On Behalf Of </b>Andreas Plesch<br><b>Sent:</b> Saturday, September 30, 2017 10:47 PM<br><b>To:</b> <a href="mailto:vmarchetti@kshell.com" target="_blank">vmarchetti@kshell.com</a><br><b>Cc:</b> X3D Graphics public mailing list<br><b>Subject:</b> Re: [x3d-public] Sequencer interval definition</span><o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Sep 30, 2017 7:49 PM, "<a href="mailto:vmarchetti@kshell.com" target="_blank">vmarchetti@kshell.com</a>" <<a href="mailto:vmarchetti@kshell.com" target="_blank">vmarchetti@kshell.com</a>> wrote:<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><br>> On Sep 4, 2017, at 11:45 AM, Andreas Plesch <<a href="mailto:andreasplesch@gmail.com" target="_blank">andreasplesch@gmail.com</a>> wrote:<br>><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>> Resending this without html formatting to ensure proper transmission:<br>><br>> 30.2.4 defines how sequencer values are assigned to key intervals:<br>><br>> <a href="http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/utils.html#SequencingEvents" target="_blank">http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/utils.html#SequencingEvents</a><br>><br>> (−infinity, t0), [t0, t1), [t1, t2), ... , [tn-1, +infinity)<br>><br>> are the intervals.<br>><br>> The square bracket [ seems to indicate that the limiting value does not belong to the interval. Is that the case ?<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I'm more used to the square bracket indicating a closed boundary, so that the for the interval denoted [a,b) ; x is in the interval a <= x < b<br>so a is an element of the interval but b is not. Take the view that neither +infinity nor -infinity is a number; so (-infinity,a) is just shorthand for the set x < a, while [a,+infinity) is x >= a.<o:p></o:p></p></div></div></div></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>VRML97 seems to be when the bracket for the interval was introduced:<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="http://tecfa.unige.ch/guides/vrml/vrml97/spec/part1/concepts.html#4.6.8" target="_blank">http://tecfa.unige.ch/guides/vrml/vrml97/spec/part1/concepts.html#4.6.8</a><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>But it is not accompanied by an explanation. For interpolators it may not matter if the limit is included in the interval since the function is continuous.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>For sequencers, the function produces different values depending on from which side an interval limit is approached.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I guess it is time to look up how various browsers behave at sequencer interval limits.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><br><br>><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>> For example, in the second interval [t0, t1) t0 does not belong to the interval but t1 does.<br>> I have seen other notations where this interval would be described as ]t0, t1] which I would offer as a suggestion for an improvement.<br>><br>> The next question is about the piecewise function definition:<br>><br>> f(t) = v_n, if t_n <= t < t_(n-1)<br>><br>> Given that the keys t_i are given in a monotonically non-decreasing order, t_n is always larger (or equal to) than t_(n-1). Therefore, a t larger than t_n can never be smaller than t_(n-1). But this is the condition described in the function for value v_n. There is no possible t which can fulfill this condition.<br>> Presumably this condition was designed as:<br>><br>> f(t) = v_n, if t_n >= t > t_(n-1)<br>><br>> If this is the case I can submit a spec. comment but I very much would appreciate additional eyes on that since it seems like a rather fundamental oversight. Did I overlook something ?<br>><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>My set of eyes agrees with yours that the formula form in the v 3.3 version of section 30.2.4 is incorrect, I would propose a corrected version:<br><br>f(t) = v_i, if t_{i-1} ≤ t < t_{i} for 1 <= i < n-1<br> = v_0, if t < t_0,<br> = v_{n−1}, if t ≥ t_{n−1}<o:p></o:p></p></div></blockquote></div></div></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Looks good to me if [ is meant to include the limit in the interval.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Andreas<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><br><br><o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>> The Interpolator component spec. may provide additional insight:<br>><br>> <a href="http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/interp.html#Linearinterpolation" target="_blank">http://www.web3d.org/documents/specifications/19775-1/V3.3/Part01/components/interp.html#Linearinterpolation</a><br>><br>> Here the equivalent piecewise function definition is:<br>><br>> f(t) = linterp(t, v_i, v_(i+1)), if t_i <= t <= t_(i+1),<br>><br>> Note that the interval condition here is between t_i and t_(i+1) and not t_(i-1). So this is correct. But why change for Sequencer to t_(n-1) ? Perhaps there is a reason ?<br>><br>> Also note that i is used rather than n which is also more correct since n is reserved for the fixed, total number of keys, whereas i is the variable index depending on the whatever time t is considered.<br>><br>> -Andreas<br>><br>> --<br>> Andreas Plesch<br>> Waltham, MA 02453<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>> _______________________________________________<br>> x3d-public mailing list<br>> <a href="mailto:x3d-public@web3d.org" target="_blank">x3d-public@web3d.org</a><br>> <a href="http://web3d.org/mailman/listinfo/x3d-public_web3d.org" target="_blank">http://web3d.org/mailman/listinfo/x3d-public_web3d.org</a><o:p></o:p></p></div></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div></div></div></div></div></div><p class=MsoNormal><o:p> </o:p></p></div></div></div></div></body></html>