FIGURE 5.1. Latitude and longitude lines. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.2. Great circle path between Minneapolis, USA, and Frankfurt, Germany. The great circle distance is 4,392 miles. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.3. Reference ellipsoid showing major parameters. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.4. In this schematic drawing, an ellipsoid and a geoid represent the earth’s surface. The ellipsoid is less accurate than the geoid, but both may not properly align with actual locations distant from their geospatial optimizations. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.5. Basic geometric shapes (cone, cylinder, and plane) serve as developable surfaces, shown here with a reference globe. The resulting projections of latitude and longitude lines are shown in the rightmost column. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.6. Some possible aspects for conical, cylindrical, and planar projections. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.7. Examples of tangent and secant projection surfaces. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.8. These six different projections show the countries of the world. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE 5.9. A transverse Mercator projection. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE Tissot’s indicatrix circle indicating no areal and no angular distortion. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE Two Tissot indicatrix circles shown on a Mercator projection with the standard line of the equator. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.

FIGURE An example of an obvious error resulting from using data sources for the same area (Minnesota) but with different projections. Diagnosing the causes of such errors and resolving them can be very time-consuming if information about the choices made regarding the respective projections is unavailable. From A Primer of GIS, 2nd edition, by Francis Harvey. Copyright 2016 by The Guilford Press.