April 8 -
Toronto Convention Center
Geographic Coordinates and the Universal
President, NAC Geographic Products Inc., 1608-45 Huntingdale Blvd.,
Toronto, ON, Canada M1W 2N8 Phone: (416) 496-6110, Email: email@example.com
properties of traditional addresses and postal codes have been
discussed. A new system - the
Natural Area Coding System has
been developed which has
unified the concepts of points and areas
by introducing a unified representation for both points and areas
called Natural Area Codes (NACs).
or ten-character NACs have been called Universal Addresses that will
eliminate all the problems caused by different languages, written
conventions and complicated components in addresses used in the
world. Universal Addresses can be pinpointed on any maps, navigated
with GPS receivers, and processed by GIS applications. They can also
be used as Global Postal Codes to simplify automatic mail sorting
and route optimization for all mail. Moreover, NACs as Universal
Area Codes can significantly improve the efficiency in retrieving
maps from large GIS databases; NAC
be used as
universal map grid system that can be applied onto all kinds of maps
with any scales.
addresses are very complicated. It is not possible to prescribe a
simple, mechanical rule for locating and interpret essential address
the United States, there are more than 50 variations in address
formats  plus
abbreviations and local addressing conventions. In order to
facilitate efficient mail processing, many countries have introduced
postal codes such
9-digit ZIP can
area known as a “segment” such as a side of a street between
intersections . With 9-digit ZIP codes, domestic mail can be
automatically sorted to the mailbags
with significant improvement in efficiency.
service hierarchies inherit many limitations,
and useless in
sorting international mail. Any
changes in mail delivery hierarchies result in the changes of postal
codes that create many
both residents (remembering
new codes, informing
people of the changes,
and post offices (settling complains, paying compensations,
rerouting mail). Therefore,
a global postal code system
independent from any mail delivery hierarchies is demanded for fully
automating mail sorting.
physical addresses is
travellers, taxi drivers, and emergency services
addresses is not
results in complete failure no matter how emergent you feel.
can’t directly pinpoint these addresses on maps or figure out the
distance and direction from them.
been widely used
in many areas such as highway snow removing , efficient
, driver assessment , driving speed review , and even in
irrelevance between addresses and geographic coordinates and
addresses into GPS
receivers make GPS useless to average consumers looking for
constituted the most time-consuming and expensive part in many GIS
is difficult to design a standard form for inputting all
in GIS. Even when an input form for limited formats of addresses is
created, inputting addresses into such a form is still very time
for mail automation, locating and GIS applications
substantial study of
addresses and geographic coordinates has led
the birth of
the Natural Area Coding System.
the Natural Area Coding System, we use highly efficient unified
codes to represent both points and areas with 30 most popular
characters in the world (ten digits and 20 capital consonants).
These codes are called Natural Area Codes (NACs) defined by a series
of NAC grids. The first level NAC grid is formed by dividing the
full range of longitude and latitude in the WGS-84 datum into thirty
equal divisions respectively with one character representing each of
these divisions as shown in Figure 1.
cell on this grid is represented by two characters such as NAC: D H
the black cell in Figure 1. To further divide each of these
cells into thirty equal divisions, we get the second level NAC grid.
A cell in the second level NAC grid is represented with four
characters such as NAC: DK HP. Repeating the same procedure will
make the third, fourth, fifth and even higher level NAC
level NAC Grid
you have a pair of longitude/latitude coordinates, and want to know
which NAC cells containing the point, you can use the following
formulae to calculate:
= (Longitude + 180)/360
= Integer part of(LONG*30)
= Integer part of((LONG*30 -
= Integer part of(((LONG*30 - x1)*30 -
= Integer part of(((...(LONG*30 - x1)*30 -
x2)...)*30 - xn-1)*30)
= (Latitude + 90)/180
= Integer part of(LAT*30 )
= Integer part of((LAT*30 -
= Integer part of(((LAT*30 - y1)*30 -
= Integer part of(((...(LAT*30 - y1)*30 -
with positive for east and negative for west,
latitude with positive in north and negative in south,
is the multiplication sign,
x2, x3, ...xn, y1,
y2, y3, ...yn
are integers ranging from 0 to 29.
x1, x2, x3, ..., xn,
y1, y2, y3, ..., yn
have been calculated, you can use the following table:
1 The Values of NAC Characters
find their corresponding characters:
then combine these characters to form a standard NAC：
followed by the string of characters for longitude, a blank
string of characters for latitude. Here n represents
the level of NAC grid and can
be any positive
you can say that the point is within this NAC. For example,
point at longitude
west 79.39222 and latitude north 43.65145 is within NAC:
Q, also within NAC: 8C Q8, NAC: 8CH
series of neighbouring NAC cells
can be represented by
a single complex NAC. For
WGB + NAC：HJL
WGB = NAC：HJK-L
WGB + NAC：HJK
WGC + NAC：HJK
WGD = NAC：HJK
QP + NAC：GJ
QP + NAC：GH
QQ + NAC：GJ
QQ = NAC：GH-J
as the end of a string in a NAC can be dropped for simplification,
WKS = NAC：HJ
is, any neighbouring NAC cells forming a rectangular area can be
represented by a single complex NAC.
important application is Universal Addresses defined by eight- or
ten-character NACs that uniquely represents an address or a square
meter area in the world. The major advantages of a Universal Address
and culture independent.
handled by computers and electronic devices because of only most
popular characters and standard format
to remember because of short strings and clear spatial
through many channels: maps, GPS receivers, and other surveying
needs to be assigned and maintained by government or companies.
be pinpointed on maps, and navigated with GPS
for all locations in the world: every address, tree, parking
meter, fire hydrant,
universal addresses, no matter from where and speaking what
language, people can easily find their destinations with NAC
enhanced maps or GPS receivers. If a city has marked all its street
signs and house number plates with universal addresses, people can
find their destinations efficiently in the city even without any
helps, that will greatly benefit residents, tourists, taxi drivers,
delivery companies, and especially emergency services.
universal address can also be used as a global postal code with
accuracy than any other postal codes, even 9 digits ZIP
changes no matter how post offices adjust their mail delivery
needs to be assigned, maintained and modified by
the automation for mail sorting and route optimization.
checking capability. More than 80% of the area in the world is
covered by water or deserts where no people live. If a universal
address is written incorrectly, it will have more than 80% chance
falling into these areas and will be easily found by mail sorting
standard for including a universal address with a traditional
address is to place the NAC on a new line after the end of the
address no matter in which language. For example, our address can be
Geographic Products Inc.
the universal addresses can be used immediately. If a post office
has installed a NAC enhanced mail sorting program in their
computers, they can take the advantages of the universal addresses,
otherwise just use the old address without interference.
Natural Area Coding System has many other applications too. The NAC
grids can be used as a standard Universal Map Grid System that can
be applied onto all kinds of maps with any scales and projections
and lead to map independent universal grid
used as Universal Area Codes have filled the vacuum of standard
codes for all areas in the world for retrieving maps and geographic
data from large GIS databases. It just requires very few keys
instead of typing many keys to specify the longitude, latitude,
width and length of an area. If you want to retrieve a map of
Ontario, from a world GIS, you need to type only two characters 8 Q.
NACs can be used to improve all location related
Natural Area Coding System is a very useful geographic technology.
It makes human brains easy to remember and use high resolution
geographic coordinates in their daily life. It has removed the
obstacles in addresses caused by different languages and traditions
and eased the exchanging of geographic information among different
countries by providing efficient standard universal addresses,
global postal codes, universal area codes and universal map grids.
Royce Kneece, R.,
Jr. and Randall, D.
L. February 1972.
Precoding of Letter Mail Addresses by Large-Volume
Institute for Defense Analyses System Evaluation Division, IDA Log
No. HQ 72-13942, Paper P-840
Domestic Mail Manual, United States Postal Service, April
Snow removal in the
windy city gets technical.
Grant, M. Nov 2001. Technology for crops.
(Production). Successful Farming
v99 i12 p50 (1)
Porter, M.M. and Whitton, M.J. Oct 15, 2001.
USING THE GLOBAL POSITIONING SYSTEM
(GPS). The Gerontologist
Fox, R. Oct 2001. Wile E. Coyote Doesn't Stand a Chance.
Communications of the ACM v44 i10
News & World Report
Showing What You
Know. Appraisal Journal
v69 i4 p431.
Shen is the founder and CEO of NAC Geographic Products Inc. – a
Toronto based Canadian company specialized in the development of GIS
and mapping software and web GIS applications.