Lecture01

# Lecture01 - Transformations in Mapping T1 True earth to...

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Analytical and Computer Cartography Lecture 1: Review of Geodesy and Scale Transformations in Mapping • T1: True earth to globe – Lengths scaled by the Representative Fraction e.g. 1:1M – Real world objects become symbols (representations) e.g. road to a red line – Need to choose earth model (Datum) • T2: 3D earth to flat map – Map projection transformation – Inherent distortion! Earth models • Plane, Sphere, Ellipsoid, Geoid • Much simple survey assumes flat, then corrects (e.g. Township and Range system) • Sphere assumed since Pythagoras. Aristotle introduced logic proofs • Ellipsoid since discrepancies in lengths of degrees of latitude discovered • Geoid involves detailed spherical harmonic model based on gravimetry Aristotle (384–322 BC) Arguments for a spherical earth • Every portion of the Earth tends toward the center until by compression and convergence they form a sphere. ( De caelo , 297a9–21) • Travelers going south see southern constellations rise higher above the horizon; and • The shadow of Earth on the Moon during a lunar eclipse is round. ( De caelo , 297b31–298a10)

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By observation Oblate vs. Prolate ellipsoid French Academy of Sciences sent expeditions to Peru (now Ecuador) in1735 and Sweden (1736-37) Proved along with Cassini’s meridian at Paris that the length of a degree became longer at higher latitudes Geodetic latitude More consequences… • Chandler’s wobble
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Lecture01 - Transformations in Mapping T1 True earth to...

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