Spatial Relationships

Objectives

• Brief introduction to topics covered in book
• Some demonstrations

Basic geometric relationships

(They deal with relationship between two objects - lines or points)

• Direction
• Distance

Applications that created mapping technology: navigation (sea, land, air), land surveying, military operations (eventually artillery)... Each deals with distance and direction.

Direction

amount of a turn required from one bearing (azimuth) to another.

Three "Norths" on the map

• "True" North - towards polar axis (Polaris almost)
• Magnetic North (where the magnetic compass points- it varies)
• Grid North (where the planar reference system - a projection - points)

shown on a declination diagram.

Direction on a sphere:

Great circle (shortest path, on a plane that cuts through center of Earth)

Constant compass bearing (rhumb line or loxodrome) easier to navigate

Distance

Scale relationship to ground (may vary, due to projecion)

may calculate from coordinates (Phythagorean theorem for planar, spherical formula - see book p. 264-265)

Modifications of "as-the-crow-flies" distance: time, difficulty, etc.

Resources in Text

• Chapter 14: Orienteering methods, basic navigation
• Chapter 15: Using GPS
• Appendix D: Navigational Instruments (a lot of obsolete stuff and some details on GPS)

What is one of the most persistent technologies of the past 40 Centuries?

Triangles

• Know two angles, you know the other.
• Know one distance (and some angles) get the other distances.
• Know the distances, get all the angles

From these SIMPLE rules (apologies to Euclid) you can build great spatial relationships.

• Networks of triangles that covered the Earth (geodetic surveying)
• Artificial satellites that send out timing signals, measure distances (delay) infer location (GPS)

Version of 28 January 2000