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David Greenhood, Mapping,
Chapter 6
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Side Notes |
Links |
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Linear measure
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These are the key concepts in this lesson. You should be able to define or describe them after you have read this lesson, finished the assigned reading and explored the links. You should also be able to do the exercises and answer the questions at the end of the lesson.
The flat map problemCircles are round and lines are straight. Yet distances on a circle can be interpreted immediately and directly in terms of linear distances. For example, a tape measure, normally coiled for storage, is used to measure distance along a straight path or around a curved path. As an example of that, one can determine the circumference of a tree by wrapping the tape around the tree and reading at the appropriate place. Equivalently, the measure can be taken by wrapping a rope around the tree, and then measuring it afterwards when it is laid out straight. That is, circles map easily to line segments. And arc length on a circle is directly analogous to length of a line segment. Spheres are round and planes are flat. As we associate length with line segments, we associate area with portions of a plane. And we associate concepts of line and angle with both spheres and planes. But using a flat surface to represent a sphere, or portion of it, involves risks not present in the circle-line relationship. The desire to view the surface of Earth on a planar surface probably arises from both historical and pragmatic reasons. Regardless of the shape of an object, illustration of it has been on planar media through many stages, from drawing on sand and walls of caves to drawing and writing on papyrus and animal skins, to printing on paper, to display on electronic screens that are essentially flat. Reasons include ease of execution, tradition, limitations of technology, economy, portability. Accurate illustration of three-dimensional objects has been through sculpture and various forms of model-building. Another reason for use of flat surfaces is the desire for comprehensive view. Simultaneous viewing of all sides of a three-dimensional object is at best difficult, impossible without mirrors or similar assistance. But in times when Earth was believed to be flat, a comprehensive view representing the knowledge of the time was possible. |
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ProjectionsMuch of the visual sense that we make of maps is in terms of several attributes: distance, area, shape, betweenness and connectivity of the land masses. Transforming Earth's shape to a plane involves some sacrifice of these. Of these aspects, moderate errors in distance and area are most tolerable. Errors in betweenness and connectivity are intolerable. Projection of a sphere, e.g. a spherical map of Earth, to a plane is
achieved just as film is projected from a light source to a screen. A
point of focus and points on the sphere are aligned with points on the
plane. The traces on the plane comprise a projection of the sphere.
Location of the point, or points, of focus, i.e. center(s) of projection,
determines the degree to which the various attributes are distorted. The
purpose of a projection determines the degree to which sacrifices can be
tolerated. Common ProjectionsFor making maps of Earth, there are three common strategies for projecting Earth's surface, or portions of it, from a point to a plane:
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Rhumb lines
UTM projection |
Historically
the most common projection is the Mercator projection. It is a cylindrical
projection, the cylinder tangent to Earth at the equator. As is the case
with cylindrical projections, there is substantial distortion of shape and
distance in the temperate, arctic and antarctic zones. Best accuracy is
near the Equator.
One reason for the durability of the Mercator projection is its representation of rhumb lines. In this projection, they appear as line segments. Thus, in times of primitive navigation tools, one could use a Mercator map to draw a line from point of origin to destination, set sail and maintain the direction indicated by the rhumb line. Such a path is not necessarily the shortest path and is therefore not on a great circle. But a good degree of certainty of finding the destination was probably often more attractive than the prospect of saving some time, especially given the variety of possible reasons for delay, anyway. The Universal Transversal Mercator (UTM) projection is comprised of sixty portions of Mercator projections, those tangent to Earth at meridians where longitude is a multiple of six, i.e. 0, 6, 12, … Location on the projection image is entirely in terms of meters and is based on the equator and certain meridians. No latitude-longitude is used. A primary advantage of the UTM system is uniformity of accuracy of measure throughout the Torrid Zone, the Temperate Zones and part of the Arctic and Antarctic zones. |
Description of Mercator projection.
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Links List of map projections. Classification of map projections. Fundamentals of cartography, Earth projections
Exercises
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