<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Inner and outer rings are usually distinguished by the direction in which the coordinates are strung together. <DIV><BR class="khtml-block-placeholder"></DIV><DIV>from the shapefile spec:</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">A polygon consists of one or more rings.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">A ring is a connected sequence of four or more</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">points that form a closed, non-self-intersecting loop.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">A polygon may contain multiple</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">outer rings.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">The order of vertices or orientation for a ring indicates which side of the ring</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">is the interior of the polygon.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">The neighborhood to the right of an observer walking along</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">the ring in vertex order is the neighborhood inside the polygon.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">Vertices of rings defining</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">holes in polygons are in a counterclockwise direction.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">Vertices for a single, ringed</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">polygon are, therefore, always in clockwise order.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">The rings of a polygon are referred to</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;">as its parts.</SPAN></FONT><FONT class="Apple-style-span" face="Times" size="2"><SPAN class="Apple-style-span" style="font-size: 10px;"> </SPAN></FONT></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>--josh</DIV><DIV><BR class="khtml-block-placeholder"><DIV><DIV>On Jun 7, 2005, at 6:33 PM, Ethan Alpert wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The problem is if it's a multipolygon you can have 3 consecutive outer</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">rings with no inner rings which will look the same as your example.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I opened up the shp2pgsql.c code and sure enough it computes the area of</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">the polygon for each polygon. If the area is negative it's an inner ring</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">if it's positive it's a new outer ring.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-e</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-----Original Message-----</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">From: <A href="mailto:postgis-users-bounces@postgis.refractions.net">postgis-users-bounces@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">[<A href="mailto:postgis-users-bounces@postgis.refractions.net">mailto:postgis-users-bounces@postgis.refractions.net</A>] On Behalf Of Sean</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">M. Montague</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Sent: Tuesday, June 07, 2005 4:25 PM</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">To: PostGIS Users Discussion</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Subject: RE: [postgis-users] Intersection errors</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I may be wrong, but I believe it's the order.<SPAN class="Apple-converted-space"> </SPAN>If a poly has two inner</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">rings, There will be a list of 3 polys, the first of which is the outer</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">poly, the two inner come next.<SPAN class="Apple-converted-space"> </SPAN>At least this been my experience</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">exporting shape files.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-----Original Message-----</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">From: <A href="mailto:postgis-users-bounces@postgis.refractions.net">postgis-users-bounces@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">[<A href="mailto:postgis-users-bounces@postgis.refractions.net">mailto:postgis-users-bounces@postgis.refractions.net</A>] On Behalf Of</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Ethan Alpert</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Sent: Tuesday, June 07, 2005 2:05 PM</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">To: PostGIS Users Discussion</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Subject: RE: [postgis-users] Intersection errors</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">While we're on the topic of multipolygons. I've noticed that the</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">shapefile specification doesn't have any convention for communicating</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">outer and inner rings. That said how do apps like shp2pgsql and ogr2ogr</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">determine whether the next polygon in a list is an inner or a new outer?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I understand that the convention is that inner rings are counter</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">clockwise. But still how is the direction of the ring determined</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">efficiently?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-e</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-----Original Message-----</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">From: <A href="mailto:postgis-users-bounces@postgis.refractions.net">postgis-users-bounces@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">[<A href="mailto:postgis-users-bounces@postgis.refractions.net">mailto:postgis-users-bounces@postgis.refractions.net</A>] On Behalf Of</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Markus Schaber</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Sent: Tuesday, June 07, 2005 2:02 PM</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">To: PostGIS Users Discussion</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Subject: Re: [postgis-users] Intersection errors</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hi, Sean,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Sean M. Montague schrieb:</DIV> <BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I've been working on it, and I now realize the problem...not sure if</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">it will solve my intersect problem, but I'll get to that later.<SPAN class="Apple-converted-space"> </SPAN>There</DIV> <BR></BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> <BR><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">is a logical reason for dissolving some of layers, such as lakes at</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">certain scales.<SPAN class="Apple-converted-space"> </SPAN>If they are multi polys, there is a significant size<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">savings when writing out as SVG.<SPAN class="Apple-converted-space"> </SPAN>I just need to see if I can<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">distinguish between a hole, and say another lake.<SPAN class="Apple-converted-space"> </SPAN>Examining what you<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">suggested looks like a good start.<SPAN class="Apple-converted-space"> </SPAN>Thanks.</DIV> <BR></BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Yes, it is easily possible. Maybe you should take a look at the Well</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Known Text format specification from the OpenGIS consortium (Part of</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">their "Simple features for SQL" specification, or use the PostGIS source</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">or some other program that correctly exports WKT to find out how it</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">works.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The basic idea for Multipolygon is:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">MULTIPOLYGON(((First polygon outer ring),(1st poly first hole),(1st poly</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">2nd hole)),((2nd Poly outer ring)(2nd Poly hole)),((3rd Poly with no</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">hole)),((4th Poly outer ring)(4th poly 1st hole)(4th poly 2nd hole)))</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">All holes (inner rings) have to be completely inside their outer ring,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and may not overlap each other. A polygon may be contained completely</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">inside the hole of another polygon (like an island), but they may not</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">overlap.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">For the exact rules how the inner and outer rings may touch and</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">intersect, please see geometry model part of the aforementioned</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">specification.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">HTH,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Markus</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">postgis-users mailing list <A href="mailto:postgis-users@postgis.refractions.net">postgis-users@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://postgis.refractions.net/mailman/listinfo/postgis-users">http://postgis.refractions.net/mailman/listinfo/postgis-users</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">postgis-users mailing list <A href="mailto:postgis-users@postgis.refractions.net">postgis-users@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://postgis.refractions.net/mailman/listinfo/postgis-users">http://postgis.refractions.net/mailman/listinfo/postgis-users</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">postgis-users mailing list <A href="mailto:postgis-users@postgis.refractions.net">postgis-users@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://postgis.refractions.net/mailman/listinfo/postgis-users">http://postgis.refractions.net/mailman/listinfo/postgis-users</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">postgis-users mailing list</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="mailto:postgis-users@postgis.refractions.net">postgis-users@postgis.refractions.net</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://postgis.refractions.net/mailman/listinfo/postgis-users">http://postgis.refractions.net/mailman/listinfo/postgis-users</A></DIV> <BR class="Apple-interchange-newline"></BLOCKQUOTE></DIV><BR></DIV></BODY></HTML>