Appendix A: Glossary of Terms

Introduction

The purpose of this appendix is to provide a list of common terms used in this material along with a more detailed explanation of the terms. Often, we get conditioned to $50 words when other simpler forms would serve as well. This glossary will attempt to get back to simpler usage.

azimuth

The angle between geographic North and the tangent to a line at a particular point, measured clockwise, ranging 0 to 360 degrees.

bisector

Geometrically, a line drawn at 90 degrees across another line at a point exactly in the middle of the other line.

cadastral

Having to do with political, jurisdictional or land ownership boundaries.

canonical

Conforming to specified rules.

cartography

The mathematics and process of making maps.

cell

A Voronoi cell, being one of a specific structure of cells selected for use in a particular end-use application. See also: Voronoi cell, Voronoi cell structure, Voronoi polygon.

cell center point

The point determining the geometry of a cell with respect to its neighbors, only rarely coincident with the centroid. The choice of points to be used for cell centers can be based on the spatial distribution of your location-referenced information.

concise direction cosines

An abbreviated form of direction cosines in which one of the cosines is dropped but may be reconstructed later using the two other cosines plus the sign and identity of the dropped cosine.

conformal

A mathematical term suggesting adherence to known form or rules. In mapping, it suggests that there is a preservation of infinitesimally small shapes.

data domain

A data analysis term used to classify data according to its broad type or use.

DBMS

Acronym for database management system. A piece of specialized software used for the management of data on external storage devices such as a disk.

direction angle

The angle between a vector and a reference axis.

direction cosine

The cosine of a direction angle, a measure of direction which can be used in conjunction with the description of an ellipsoid or sphere to specify the location of a point on the surface.

dodecahedron

The symmetrical solid figure having 12 identical pentagonal plane faces.

ellipsoid

A flattened sphere, such as the Earth, whose meridian cross-sections are elliptical, rather than circular.

entity

A set of points, lines or areas having some common attribute. See also: spatial object.

FIFO

First In, First Out. A term describing the operation of a particular type of queue.

fragment

See line fragment, ring fragment.

geopositioning model

A plan for recording and working with the position of things relative to the Earth's surface.

geodesic

An imaginary line describing the shortest surface distance between any two points on the Earth's surface.

geodesy

The measurement of angles and distances on the Earth's surface (or any other complex mathematical surface for that matter). More generally, the science of numerical exploration of the size and shape of the planetary surface, and of the spatial relationships between objects on or near the surface or in near space.

geoid

an ultra-precise model of the physical Earth that takes into account local concentrations of mass such as the Himalayan mountains.

geo-spatial relationship

Spatial relationship relative to the Earth's surface, subsurface, atmosphere or surrounding near space. See also: spatial relationship.

great circle

The arc traced on the surface of a sphere when travelling the shortest distance between two points.

GUI

Acronym standing for Graphics User Interface, such as Windows.

Hipparchus

Perhaps the greatest of the Greek mathematicians and astronomers who lived in the second century BC. Hipparchus invented the stereographic projection. He is credited with the idea of representing locations on the surface of the Earth by spherical measurements of latitude and longitude. He is also credited with developing a method for performing distance calculations using these angles.

Hipparchus Frame

See Hipparchus sphere, below.

Hipparchus sphere

A near-conformal (with respect to an ellipsoid of rotation) coordinate reference system used to advantage in the Hipparchus Geopositioning System. Point locations are expressed in normalized direction cosine form and common distance measurements consist of the square of the spatial chord on the co-central unit sphere. Synonymous with Hipparchus Frame.

The Hipparchus sphere avoids locality restrictions and geometry imprecisions typically imposed on systems based on "Flat Earth" geometry. On the other hand, it affords the analysis of spatial relationships with sub-millimetric precision sufficient for most practical applications, while avoiding the expense of more rigorous ellipsoidal calculations when processing large volumes of data.

HP-GL/2

Hewlett-Packard Graphics Language. A proprietary protocol for communicating information to graphic devices such as plotters or laser printers.

icosahedron

The symmetrical solid figure having 20 identical plane triangular faces.

isometric

Having the same dimensional measure in all directions.

latitude

An angular measurement of North/South distance from the Equator. By convention, latitudes measured northward from the Equator are positive while those measured southward are negative. High latitudes are those approaching either pole.

LIFO

Last In, First Out. A term describing the operation of a particular type of queue. This is the way that a classic stack operates.

line

An ordered set of two or more points on the surface of the Earth that if connected together would form a line. The points are said to be vertices of the line and successive pairs of vertices define line segments. Each segment is a geodesic, the shortest distance on the surface of an ellipsoidal planet. The directional sense of a line can be significant.

line fragment

That part of a line that starts in a cell and then exits that cell, or that enters a cell and then ends in that cell, or that enters a cell and then exits that cell.

line set

An unordered set of zero, one or multiple lines having some common attribute. The lines of a set may intersect or be tangent to themselves or one another. The external representation of a line set consists of ordered sequences of global ellipsoid coordinates defining the position of each vertex for each line. The Hipparchus internal representation is a specific cell local coordinate form in which the individual vertices defining each segment of each line are related to the cells visited by the lines. In addition, the internal representation lists those cells visited (or overflown) by the segments of the line(s).

In Hipparchus documentation, a line set is sometimes referred to as an "Lset".

longitude

An angular measurement of East/West distance from the prime meridian. By convention, longitudes measured Eastward are positive while those measured Westward are negative.

meridian

A great circle on the surface of the Earth, passing through the poles and a particular place. The prime meridian is the one passing through London (Greenwich) commonly used as the zero reference for measurements of longitude.

model

A general plan or way of thinking about things. See also: paradigm.

near space

That small part of space that immediately surrounds the Earth, extending so far out as to include Earth's satellites.

object

A set of points, lines or areas having some common attribute. See also: entity, spatial object.

orbital

Having to do with the path of orbiting satellites.

paradigm

The central idea, method or way of thinking about things. See also: model.

point

A single position or location on the surface of the Earth.

point set

An unordered set of zero, one or multiple points having some common attribute. Its external form consists of an aggregate of points defined by global ellipsoidal coordinates. The Hipparchus internal representation is a specific cell local coordinate form in which each point is related to its containing cell. In addition, the internal representation lists those cells occupied by the point(s) of the set.

In Hipparchus documentation, a point set is sometimes referred to as a "Pset".

polygon

A plane figure of many angles and sides; usually one whose perimeter consists of more than four straight lines.

plane

A flat surface, such as a table-top, map sheet or video display (conceptually, at least!).

planar

Being flat.

platform

A computing platform is the combination of computer hardware and operating system software that defines a particular computing environment.

projection

A particular view of an object, usually presented on some flat surface such as a display or map sheet.

radian

a unit of angular measure which divides a complete revolution into 2 parts so that 360 degrees = 2 times 3.1415926... radians. This is the usual representation of angular measurements in mathematical calculations.

region

An area or areas of the Earth's surface containing all those surface points that possess some common attribute. A region is defined by an unordered set of zero, one or multiple rings defining the boundaries of the area(s). A region is non-simply connected if it is defined by more than one ring. Multiple rings within a set may not cross or be tangent to one another. Rings may wholly contain other rings of the same set, to any level of nesting, for example defining islands in lakes on islands, etc.

The external representation of a region consists of sequences of ordered global ellipsoidal coordinates defining the location of each vertex of each segment of each bounding ring of the set.

The Hipparchus internal representation is a specific cell local coordinate form in which the individual vertices defining each segment of the bounding rings are related to the cells visited by the rings. In addition, the internal representation lists those cells wholly contained within each bounded area as well as those cells visited by the segments of the bounding ring(s).

In Hipparchus documentation, a region is sometimes referred to as an "Rset".

ring

an ordered set of points on the surface of the Earth which, if connected, would define a bounded area. The points are said to be vertices of the ring. By convention, the area defined lies to the left of the line formed by the vertices taken in order. Also by convention, the last vertex is not specified explicitly but is taken to be identical with the first vertex of the ring. Also, by definition, the segments of a ring may not intersect or be tangent one to another.

ring fragment

That part of a ring that starts in a cell and then exits that cell, or that enters a cell and then ends in that cell or that enters a cell and then exits that cell.

ring set

The set of bounding rings defining a region.

segment

The portion of a line or bounding ring that connects two successive vertices. Hipparchus considers such segments to be true geodesics.

sexagesimal

Measurement of angles in units of degrees, minutes and seconds of arc. This is the usual external representation of angular measurements.

space

The entirety of everything that's out there, to infinity.

spatial

Having to do with what's where.

spatial frame of reference

A particular coordinate system in which canonical numeric models of spatial objects are constructed and manipulated.

spatial index

A directory for finding where location-related data is stored in a computer's memory or attached or networked disk storage device.

spatial object

A point set, line set or ring set (region) defining the location of things, conditions or events on the surface of the Earth, below the surface, in the atmosphere or in near space surrounding the Earth.

spatial relationship

Where is this with respect to that? Is this point near that one? Do these lines cross each other? Do these regions have places in common?

sphere

A ball-shaped object whose cross-sections are circular, any way you cut them.

tangent plane

A plane which meets the Earth's surface at a single point without intersecting it.

tangency point

The single point where the tangent plane touches the ellipsoid.

terrestrial

On or about the Earth.

tessellation

The division of a surface into a mesh or network (reticulation).

Voronoi, M.G.

Nineteenth century Russian mathematician who described the construction and properties of Voronoi polygon structures on the plane.

Voronoi cell

An area of the Earth's surface having boundaries with neighboring cells defined by the geodesic distances between its center point and the center points of its neighbors. Although imaginary, the boundaries themselves are considered to be geodesics. See also: cell, Voronoi cell structure, Voronoi polygon structure.

Voronoi cell structure

A subdivision of the Earth's surface having properties corresponding to those of a Voronoi polygon subdivision of the plane, notably that every point contained within a particular cell is closer to the center point of that cell than the center point of any other cell. This cell structure forms the basis for spatial indexing within Hipparchus. See also: cell, Voronoi cell, Voronoi polygon structure.

Voronoi polygon structure

A subdivision of the plane into polygons such that points on the plane within a particular polygon are closer to the center point of that polygon than the center point of any other polygon. See also: cell, Voronoi cell, Voronoi cell structure.

Summary

Appendix B: Galileo and Georama

Introduction

Galileo is fully documented by the Galileo Guide. An executable for Windows is available for download from the web at www.geodyssey.com. The download includes numerous sample data files and demo scripts.

By contrast, Georama for Windows is an end-user Atlas viewer that permits seamless browsing of World Atlas material, and includes a number of world place-name gazetteers. Georama processing includes mouse-directed inspection of geographical features or events. Georama accepts real-time inputs from a GPS receiver, providing notebook computer users with a GPS trace log and a moving-map display. Although directly executable from the CD-ROM, Georama may be set up for partial or exclusive operation from a hard disk.

Georama is fully documented by the Georama Guide. A fully functional Georama executable is available for download from the web at www.geodyssey.com. The data provided with this download provides multi-thematic coverage of New Zealand only.

Summary

Appendix C: Bibliography

Introduction

The purpose of this appendix is to provide a list of other sources of reading material that might be helpful for developers interested in expanding their understanding of some of the subject matter.

Bibliography

1. Surveying Theory and Practice, Davis, Foote, Anderson, Mikhail, McGraw-Hill, 1981.

   This exceedingly practical book provides a basic overview of the mathematics of surveying and mapping. The material provides detailed explanations of practical geopositional surveying problems and techniques.

2. Geodesy, Henry D. Bomford, Oxford University Press, Third Edition, 1973.

   This is a well known textbook on the subject of the measurement of all manner of things on the Earth's surface. This could be a valuable complement to the library of material for the serious Hipparchus developer. However, recognize that this is a theoretical source of "last resort" for only the ambitious. This will not likely be your first book.

3. Geodesy, W. M. Tobey, 1928, Government of Canada Queen's Printers.

   This is a classic on the subject of the basic geometry of the surface of an ellipsoid. This small book provides the classical approach to the angular latitude/longitude computational geodesy in contrast to the direction cosine vector approach. If you are a collector of material on the subject, you will want to add this little gem.

4. Manual of Remote Sensing, Second Edition, 1983, American Society of Photogrammetry, Volumes 1 and 2.

   Specifically, Chapter 6 on "Orbital Mechanics for Remote Sensing" by Kenneth I. Duech and Joseph C. King contains a comprehensive treatment of the subject.

5. The Shape of the World, The Mapping and Discovery of the Earth, Simon Berthon, Andrew Robinson, Rand McNally, 1991.

   Following the immensely successful PBS television series on this subject hosted by Patrick Stewart (second generation Captain Jean Luc Picard of the "Starship Enterprise"), the authors captured the series content in book form. This easily digestible material follows the evolution of knowledge and awareness of the shape if the world since earliest time. The book is an easy read and a great coffee table item.

6. The C Programming Language, Second Edition, Ritchie and Kernighan

   This is the classic definition of the C programming language by the C language creators themselves.

7. Learning to Program in C, Thomas Plum, Plum Hall, 1989.

   This tutorial assumes that readers have absolutely no knowledge of C, and therefore is the classic introduction to the language. Well written and loaded with helpful examples, it is a great assist for C novices who are trying to learn the language.

8. Reliable Data Structures in C, Thomas Plum, Prentice-Hall, 1985.

   Hipparchus operates on many data structures. Your application will use these structures for location information. The text develops the concepts of structures, dynamic memory management, queues, stacks, doubly linked lists and so on. The book is particulary helpful for programmers who are learning C as a second programming language and where their first language does not have these capabilities.

9. C Traps & Pitfalls, Andrew Koenig, AT&T Laboratories, 1989.

   A great source of information on debugging techniques. Along with the power and flexibility that the C language provides, come the risks of incredibly complex code and the ensuing challenge of making it work and keeping it working. Koenig's work has been a blessing to many.

Previous Appendix | Table of Contents

Appendix D: Geocuriosa

Introduction

The purpose of this Appendix is to provide some facts and figures about the planet Earth. And just for fun, we have also included a few historical notes.

This material is provided as a possible source of assistance or amusement to developers working on applications involving objects on or near the surface of the planet.

Much of the material is drawn from Isaac Asimov's Book of Facts, Bell Publishing Co., 1981, ISBN 0-517-38111-6.

Facts

AREA

The surface area of Earth is 196,950,000 square miles. 57,500,000 square miles is land mass and the balance of 139,450,000 square miles is covered by water (71%).

Asia covers 17,139,000 square miles.

Africa covers 11,702,000 square miles.

North America covers 9,360,000 square miles.

South America covers 6,894,000 square miles.

Antarctica covers 5,100,000 square miles.

Europe covers 4,023,000 square miles.

Australia (with Tasmania) covers 2,975,000 square miles.

The Pacific Ocean covers 64,000,000 square miles.

The Atlantic Ocean covers 31,814,600 square miles.

The Indian Ocean covers 25,298,000 square miles.

The Arctic Ocean covers 5,400,000 square miles.

The ancient Egyptians first developed a method for calculating area. We are sure it will be no surprise to learn that the purpose of this was to provide a basis for taxation. They first learned how to calculate the areas of rectangles and triangles. They also learned how to approximate the areas of fields with curved borders (the creativity and genius of the taxperson knows no limits!). They learned how to measure angles and took the first faltering steps in the development of trigonometry.

The ancient Greeks collected the wisdom of many civilizations including the Egyptians. Thales of Miteus (640? - 546 B.C.) adapted the tax assessors' ideas and discovered some of the fundamental propositions of plane geometry. One of his students, Anaximander (611 - 547 B.C.) prepared a map of the world based on data from the sailors who frequented the city of Mileteus where he lived.

CIRCUMFERENCE

The circumference of the Earth is 24,888 miles. Eratosthenes of Alexandria first compared the length of the Sun's shadow at the same time at Alexandria and at Syene, about 500 miles away. Assuming the Earth to be a sphere, he obtained an estimate of the Earth's circumference to be 250,000 stadia or about 28,740 miles. He then drew up a map of the known world and suggested one could sail from Spain to India "along the same parallel".

CITIES

There are approximately 5000 cities in the world of population in excess of 100,000 people.

DESERT

The largest desert in the world - the Sahara - is as large as the US. Although certain valleys in Antarctica are the driest spots on Earth, they have more water than does any place on or above the surface of Mars.

DIAMETER

The equatorial diameter of the Earth is 7922 miles. The distance between the poles is 7895 miles. The difference results from the bulge of the Equator induced by centrifugal force (of rotation).

ECCENTRICITY

The ellipsoidal eccentricity of the Earth is about 0.34%. (See diameter above).

FLAT EARTH

An absurd fiction of history is that when Columbus said that the world was round, everybody else thought that it was flat. During the debates at the court of Queen Isabella, the true shape of the Earth was never the issue; its size was! The opponents of Columbus said he was underestimating the size, and that he could never sail due west from Europe to the Orient. They were probably right. Except for his accidental discovery of an unknown continent in between, Columbus would either have turned back or starved at sea.

GAS

Almost every bit of Helium that exists in the world today is a product of natural gas wells in the United States.

HIGHEST POINT

The highest point in the world is the peak of Mount Everest at 29,028 feet above sea level. Mount Everest is a foot higher than it was a century ago, and it may be growing at an accelerating rate.

ICE

About 3,900,000 square miles of the Earth's land surface (10% of the whole) is under a permanent ice cover. 80% of all of the world's ice is in Antarctica; 12% more is in Greenland. The remaining 8% is distributed among various polar islands and mountain glaciers.

LOWEST POINT

The lowest land point in the world is where the Jordan River enters the Dead Sea, at 1290 feet below sea level. Another interpretation could be the ocean floor in the Mariana Trench in the western Pacific Ocean which is 35,810 feet below sea level.

MAPS

An ambitious plan for an international map of the world on a uniform scale has been proposed, but only a part of the plan has been completed. Designed by the German Albrecht Penck, and presented to several meetings of the International Geographical Congress (in 1891, 1909, 1913), the map would consist of about 1500 sheets each covering four degrees of latitude and six degrees of longitude in a modified conic projection, on a scale of 1:1,000,000.

PARALLELS AND MERIDIANS

Hipparchus of Nicaea was one of the great mathematicians of Rhodes in the Aegean Sea. He built an observatory there and painstakingly performed brilliant research with the best instruments of his time. He is said to have been the first to describe a position on the surface of the Earth in terms of latitude and longitude. Hipparchus was also the first to observe that the equinoxes fall a little later each year.

PEOPLE AND PLACES

Frigid, ruggedly beautiful Patagonia, the narrowing tip of South America, is the only populated continental land area south of 45 degrees South Latitude. By comparison, most of Europe, Asia and two-thirds of North America are north of 40 degrees North Latitude.

Berlin and Warsaw are farther north than parts of Alaska. The southern-most Aleutian Island, Amchitka, is at a latitude of about 51.7 degrees North, which is about the latitude of London and Calgary. Both are farther south than Berlin or Warsaw.

POPULATION

The current population of the world is estimated at 5.2 billion (January 1, 1990 estimate). Half of the world's population live in just four countries: China, India, the former Soviet Union and the United States (China alone counts for about 25% of the total). The other half live in over 160 countries.

RADIUS

Eratosthenes, a Greek scholar and astronomer is credited with measuring the circumference and the tilt of the Earth. When he needed to know the distance from Alexandria to Syene, men were engaged who were trained to walk in uniform steps and count them - the distance was about 500 miles! We use 6,371,007.1808 meters for the radius of the Earth.

RAINFALL

The driest place on Earth is Calama, in the Atacama Desert in Chile. Not a drop of rain has been seen there, ever!

ROTATION AROUND THE SUN

The Earth revolves around the sun, its axis inclined at an angle of about 23 degrees to the plane of rotation. It remains inclined at almost the same angle throughout the revolution; thus the direct rays of the sun fall on different parts of the Earth at different times, resulting in our change of seasons.

ROTATION OF EARTH

In 1851, Jean Bernard Leon Foucault set up an experiment in which a pendulum seemed to change its plane of swing slowly. Actually, the pendulum continued to oscillate in a single plane; the Earth carrying the observer was slowly rotating beneath it!

The spinning of the Earth has an effect on moving objects: it causes them to deflect slightly to the right in the Northern Hemisphere, or to the left in the Southern hemisphere. The "Coriolis effect" applies equally well to a river or a ballistic missile. But don't be fooled; its because of this deflection to the right that bath water goes down the drain in a counter-clockwise rotation (North of the Equator).

In addition, the slow precession of the axis of the Earth's rotation has advanced the December solstice to Sagittarius. The Tropic of Capricorn is used to describe the geographic latitude where the sun appears overhead because two millennia ago the December solstice was located in Capricornus and the reference has stuck. The same is true of the Tropic of Cancer, for the summer solstice is now in Gemini, not in Cancer.

SHAPE

Although we have spent much time talking about various mathematical models of the Earth, the "real thing" is quite complex. One of the best analogies used to describe the exact shape of the Earth is that of a thick-skinned balloon filled with water. As the balloon rotates around an its axis pulled by forces of gravity and rotation, the equatorial points bulge out to give us something of the "pumpkin" shape we talked about (except that the top of our balloon looks just like the bottom, unlike a real pumpkin). To complicate our model, we add an uneven, brittle crust to our balloon (the land mass variations of the globe).

TIME

Immanuel Kant suggested, in the eighteenth century, that tidal friction slowed the rotation of the Earth. He was correct, but it could not be demonstrated for another century. As the tidal bulge travels about the planet, it scrapes against shallow sea bottom - especially the Bering Sea and the Irish Sea - and the energy of the Earth's rotation is dissipated in frictional heat enough to slow rotation and lengthen the day by one second every 100,000 years.

To go on the lunar day, merely adjust your watch to lose two minutes and five seconds every hour.

Time Zones were invented and introduced in 1884 by Sir Sanford Fleming, engineer and surveyor of the Canadian Pacific Railway.

The former Soviet Union was so wide that it encompassed eleven time zones.

The most exciting cartographic discovery in this century turned out to be a forgery - the infamous Vinland Map, "proof" that the Vikings had explored the New World.

WATER AREAS

Approximately 71% of the surface of the Earth is covered by water. The Pacific Ocean fills nearly a complete hemisphere of the Earth's surface. The oceans of the world are so vast and deep that if the Earth had an absolutely level crust, the seas would form an envelope over 8,800 feet deep around the globe.

Summary

We think that the planet Earth is a fascinating place. Since most of us are destined to spend our lives here, learning more about the place seems to be a prudent objective. Some of the facts about our planet are truly interesting. We would be pleased to hear from the reader regarding other pertinent facts that we might include in this Appendix.

For more fun, be sure to visit www.geocuriosa.com.