ANALYSIS OF A CONTOUR MAP ON A CLOSED SURFACE.

Abstract

The various components of a contour map are defined, and a point of view is introduced that aids in developing insight into the properties of contour maps. Contour lines are the lines of intersection of a surface with reference surfaces. The contour lines can be classified into four classes: positive, negative, maximum, and minimum. If the surface is closed, such as the Earth's surface, positive and negative contour lines are always closed curves. Where the surface is perpendicular to the reference surfaces, a cliff is formed. A cliff line on a contour map is characterized by a merger of different contour lines. There is a graphical technique for determining where the various contour lines enter and leave a cliff line. A method exists for truncating the contour map so that it covers only a portion of a closed surface and still maintains the closed-curve property of contour lines. By defining an outer boundary, one is able to talk about the interior and exterior of those contour lines that are closed curves. Lines of slope are lines that are everywhere perpendicular to the contour lines. Slope contour lines are contour lines for the slope of the surface. The former is concerned with the direction of the gradient, the latter with its magnitude. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1965
Accession Number
AD0631670

Entities

People

  • Stephen P. Morse

Organizations

  • New York University

Tags

Readers

  • Calculus or Mathematical Analysis
  • Geodesy