Reading Assignment Geography 12: Maps and Mapping Lecture 10: Map Projections I Monmonier, Drawing the Line, The Peters Projection Controversy (handout) No Battersby and Montello article But an interesting read. It will be posted on the course website. Today s topics Quiz Contour Interpretation Activity Different types of maps Map Projections A few key terms Reasons for map projections How to make a projection Properties of projections The Peters Projection Controversy Types of projections Review Session for latter part of class on Tuesday Map Projections Making a 3D world appear flat Resulting differences from projection 1
Map Projections: Key Terms The graticule shows increments of latitude and longitude Projection A systematic rendering of a graticule of lines of latitude and longitude on a flat sheet of paper. Graticule The pattern of latitude and longitude lines. Not always a grid. Perspective View A view from a single point Orthographic View Directly overhead at all points Why Do We Need Projections? Every view of the earth is a compromise Globe is an accurate picture but: Not much detail Expensive Difficult to store Can only see part of the world at once So We Need Maps, But Why Projections? No single projection does the job Projections maximize different qualities: shape, size, direction As a result, there is no single best projection Each projection is suited to specific tasks Thinking about projections As analogs: Developable form Globe-and-Shadow Analogy Imagine a light source at the center of a transparent globe with lines of latitude and longitude drawn in The light projects the graticule on the sides of the room By changing the position of the light source, and the shape of the room, and the orientation of the globe, we will get different patterns on the walls Projections aren t really done this way (though many could be), but it s a useful way to think of it 2
How do we make projections? Project on to different surfaces Vary the location of the light source Vary orientation and tangency of the surface Keep in mind, it s just an analogy Mathematical (and digital) Input is long/lat pair (λ, φ) Output is (x, y) coordinates on paper Changing the Surface Surfaces Plane (Azimuthal) Developable Surface Cone Cylinder But others possible Lets see some examples Surface: Plane (Azimuthal) Surface: Cone 3
Surface: Cylinder Changing the Origin of the Light Source Gnomonic Light projected from the center of the globe Stereographic Light projected a point on the globe exactly opposite to the point of tangency (the antipode) Orthographic Light projected from a point infinitely removed from the globe Antipodes Light Source: In Pictures Tangent and Secant Secant vs. Tangent Tangency is where the projection surface contacts the globe Secant Projection in which the projection surface intersects the globe 4
Changing Orientation and Tangency of the Surface (Aspect) When you change tangency, you also change orientation, or the direction the surface is facing Three Types Regular or Normal Aligned with poles Transverse Turned 90 degrees from regular Oblique Any other orientation Secant cylindrical map projections Tangent Properties of Maps and Globes Major Properties Conformality Generally shape is preserved Technically retention of correct angles Equivalence Area remains the same throughout the map Requires scale compression Properties of Maps and Globes Minor Properties Distance A line drawn on the map between two points on a map is also the shortest distance between two points on a globe Direction A straight line drawn between two points on the map shows the great-circle route and azimuth between the points. Straight Lines and Great Circle Distances 5
Azimuthal Equidistant Distance from a single point preserved All Properties Cannot Be Preserved On a Map This is the root of why we have more than one projection No one map is best But some are objectively better for some tasks Question: What makes one map projection better than another for the purpose of a general reference world map? Midterm results 6