<!-- MHonArc v2.4.4 -->
<!--X-Subject: Re: Quadtrees? -->
<!--X-From-R13: "Qnegre F Eubpx" <pgfbNhzvnpf.hzq.rqh> -->
<!--X-Date: from babe.globecomm.net [207.51.48.8] by mx01.ny.us.ibm.net id 857310090.131406-1 Sun Mar 2 13:41:30 1997 -->
<!--X-Message-Id: 199703021110.LAA18892#lupa,umiacs.umd.edu -->
<!--X-Content-Type: text/plain -->
<!--X-Head-End-->
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<html>
<head>
<title>MUD-Dev message, Re: Quadtrees?</title>
<!-- meta name="robots" content="noindex,nofollow" -->
<link rev="made" href="mailto:ctso#umiacs,umd.edu">
</head>
<body background="/backgrounds/paperback.gif" bgcolor="#ffffff"
text="#000000" link="#0000FF" alink="#FF0000" vlink="#006000">
<font size="+4" color="#804040">
<strong><em>MUD-Dev<br>mailing list archive</em></strong>
</font>
<br>
[ <a href="../">Other Periods</a>
| <a href="../../">Other mailing lists</a>
| <a href="/search.php3">Search</a>
]
<br clear=all><hr>
<!--X-Body-Begin-->
<!--X-User-Header-->
<!--X-User-Header-End-->
<!--X-TopPNI-->
Date:
[ <a href="msg00033.html">Previous</a>
| <a href="msg00035.html">Next</a>
]
Thread:
[ <a href="msg00030.html">Previous</a>
| <a href="msg00040.html">Next</a>
]
Index:
[ <A HREF="author.html#00034">Author</A>
| <A HREF="#00034">Date</A>
| <A HREF="thread.html#00034">Thread</A>
]
<!--X-TopPNI-End-->
<!--X-MsgBody-->
<!--X-Subject-Header-Begin-->
<H1>Re: Quadtrees?</H1>
<HR>
<!--X-Subject-Header-End-->
<!--X-Head-of-Message-->
<UL>
<LI><em>To</em>: <<A HREF="mailto:mud-dev#null,net">mud-dev#null,net</A>></LI>
<LI><em>Subject</em>: Re: Quadtrees?</LI>
<LI><em>From</em>: "Carter T Shock" <<A HREF="mailto:ctso#umiacs,umd.edu">ctso#umiacs,umd.edu</A>></LI>
<LI><em>Date</em>: Sun, 2 Mar 1997 06:09:56 -0500</LI>
</UL>
<!--X-Head-of-Message-End-->
<!--X-Head-Body-Sep-Begin-->
<HR>
<!--X-Head-Body-Sep-End-->
<!--X-Body-of-Message-->
<PRE>
> [Discussion of "B-tree with space-filling curve to index the tree"]
>
> Ahm, you've totally lost me here! I know what B-trees are (did one for
> a database system I wrote), and I've heard of space-filling curves, but
> I can't imagine how a curve can be used to index things. Can you say
> some more about this?
Lessee... if it's a curve, then there is a function that generates it. For
the Morton curve we'll call that function M(x,y). The range and domain of M
are both the set of Integers (i.e. the function is not continuous, but is
defined for all integral values of x and y). So, if we generate values of
M(x,y) for all values of x and y, the result is a series of integers. In
this case it's called the Morton series.
What I'm getting at is that the set of integer x and y is an infinite,
dense matrix of equidistant points in 2 dimensional space. For each of
these points there exists a unique value in the Morton series. This value
is derived by interleaving the bits of the x and y coordinates as described
in previous mail.
So.. now we want to index a collection of points in 2 dimensional space
(btw, it all works in any number of dimensions you want). Any index
(B-Trees included) requires that we have some key for each datum we index.
For simplicity's sake, we'll say that the key must have >, <, and ==
defined for it. Now, if you wanted to, you could store off both the x and y
from your points and derive >, <, and == operators that compared the
tuples. Equality is pretty easy, but greater than and less than get a
little funky.. is [2,3] greater than or less than [3,2]? But wait! For any
point (x,y) there exists some value in the morton series M(x,y). M(x,y) is
just an integer and >, <, == are all trivially defined for integers. In
short, you use the morton codes for the points to sort the points in your
index.
You don't have to use a B-Tree.. anything will do, but the B-Tree is
attractive for large data sets used with limited core space. Next mail
shows how to do a linear quadtree.
-Todd
</PRE>
<!--X-Body-of-Message-End-->
<!--X-MsgBody-End-->
<!--X-Follow-Ups-->
<HR>
<!--X-Follow-Ups-End-->
<!--X-References-->
<!--X-References-End-->
<!--X-BotPNI-->
<UL>
<LI>Prev by Date:
<STRONG><A HREF="msg00033.html">Linear Quadtrees</A></STRONG>
</LI>
<LI>Next by Date:
<STRONG><A HREF="msg00035.html">Re: Just a bit of musing</A></STRONG>
</LI>
<LI>Prev by thread:
<STRONG><A HREF="msg00030.html">Re: Quadtrees?</A></STRONG>
</LI>
<LI>Next by thread:
<STRONG><A HREF="msg00040.html">Re: Quadtrees?</A></STRONG>
</LI>
<LI>Index(es):
<UL>
<LI><A HREF="index.html#00034"><STRONG>Date</STRONG></A></LI>
<LI><A HREF="thread.html#00034"><STRONG>Thread</STRONG></A></LI>
</UL>
</LI>
</UL>
<!--X-BotPNI-End-->
<!--X-User-Footer-->
<!--X-User-Footer-End-->
<ul><li>Thread context:
<BLOCKQUOTE><UL>
<LI><STRONG>Re: Quadtrees?</STRONG>, <EM>(continued)</EM>
<ul compact>
<LI><strong><A NAME="00023" HREF="msg00023.html">Re: Quadtrees?</A></strong>,
S001GMU <a href="mailto:S001GMU#nova,wright.edu">S001GMU#nova,wright.edu</a>, Sat 01 Mar 1997, 04:11 GMT
</LI>
<LI><strong><A NAME="00025" HREF="msg00025.html">Re: Quadtrees?</A></strong>,
Carter T Shock <a href="mailto:ctso#umiacs,umd.edu">ctso#umiacs,umd.edu</a>, Sat 01 Mar 1997, 05:12 GMT
</LI>
<LI><strong><A NAME="00026" HREF="msg00026.html">Re: Quadtrees?</A></strong>,
S001GMU <a href="mailto:S001GMU#nova,wright.edu">S001GMU#nova,wright.edu</a>, Sat 01 Mar 1997, 05:38 GMT
</LI>
<LI><strong><A NAME="00030" HREF="msg00030.html">Re: Quadtrees?</A></strong>,
Chris Gray <a href="mailto:cg#ami-cg,GraySage.Edmonton.AB.CA">cg#ami-cg,GraySage.Edmonton.AB.CA</a>, Sat 01 Mar 1997, 17:34 GMT
</LI>
<LI><strong><A NAME="00034" HREF="msg00034.html">Re: Quadtrees?</A></strong>,
Carter T Shock <a href="mailto:ctso#umiacs,umd.edu">ctso#umiacs,umd.edu</a>, Sun 02 Mar 1997, 21:41 GMT
</LI>
<LI><strong><A NAME="00040" HREF="msg00040.html">Re: Quadtrees?</A></strong>,
coder <a href="mailto:coder#ibm,net">coder#ibm,net</a>, Mon 03 Mar 1997, 03:26 GMT
</LI>
<LI><strong><A NAME="00048" HREF="msg00048.html">Re: Quadtrees?</A></strong>,
coder <a href="mailto:coder#ibm,net">coder#ibm,net</a>, Tue 04 Mar 1997, 14:53 GMT
</LI>
</ul>
</LI>
<LI><strong><A NAME="00009" HREF="msg00009.html">Just a bit of musing</A></strong>,
Nathan Yospe <a href="mailto:yospe#hawaii,edu">yospe#hawaii,edu</a>, Thu 27 Feb 1997, 08:49 GMT
<UL>
<li><Possible follow-up(s)><br>
<LI><strong><A NAME="00010" HREF="msg00010.html">Re: Just a bit of musing</A></strong>,
Adam Wiggins <a href="mailto:nightfall#inficad,com">nightfall#inficad,com</a>, Thu 27 Feb 1997, 12:24 GMT
</LI>
</UL>
</LI>
</UL></BLOCKQUOTE>
</ul>
<hr>
<center>
[ <a href="../">Other Periods</a>
| <a href="../../">Other mailing lists</a>
| <a href="/search.php3">Search</a>
]
</center>
<hr>
</body>
</html>