GEOGRAPHY AND THE PROPERTIES OF SURFACES SERIES. DETERMINATION OF GEODESIC AND MINIMUM PATH LINES BY GRAPHICAL METHODS.
HARVARD UNIV CAMBRIDGE MASS LAB FOR COMPUTER GRAPHICS
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The present study proposes a graphical method for the determination of a geodesic line between two points of a surface. A preliminary review is presented on plane curves and space curves with a discussion of the determination of the curvature, osculating circle, tangent lines, tangent planes. Since these curves are graphic not mathematically equated a graphical method is introduced. For space curves, the determination of the tangent, normal, and osculating planes is made by the descriptive method. All constructions thus presented can be expressed analytically. Therefore, it is feasible to digitize the geometric elements involved in those constructions and to write a program for their performance with a computer. The necessity of this becomes very obvious owing to the numerous, however simple, geometric constructions required in the determination of points of the geodesic line. Author