Map ProjectionsTheory and Applications

Abstract

INTRODUCTION. Introduction to the Problem. Basic Geometric Shapes. Distortion. Scale. Feature Preserved in Projections. Projection Surface. Orientation of the Azimuthal Plane. Orientation of a Cone of Cylinder. Tangency or Secancy. Projection Technique. Plotting Equations. Plotting Tables. MATHEMATICAL FUNDAMENTALS. Coordinate Systems and Azimuth. Grid Systems. Differential Geometry of Space Curves. Differential Geometry of a General Surface. First Fundamental Form. Second Fundamental Form. Surfaces of Revolution. Developable Surfaces. Transformation Matrices. Definition of Equality of Area and Conformality. Rotation of Coordinate Systems. Convergency of the Meridians. Constant of the Cone and Slant Height. FIGURE OF THE EARTH. Geodetic Considerations. Geometry of the Elipse. The Spheroid as a Model of the Earth. The Spherical Model of the Earth. The Triaxial Ellipsoid. EQUAL AREA PROJECTIONS. General Procedures. The Authalic Sphere. Albers, One Standard Parallel. Albers, Two Standard Parallels. Bonne. Azimuthal. Cylindrical. Sinusoidal. Mollweide. Parabolic. Hammer-Aitoff. Boggs Eumorphic. Eckert IV. Interrupted Projections. CONFORMAL PROJECTIONS. General Procedures. Conformal Sphere. Lambert Conformal, One Standard Parallel. Lambert Conformal, Two Standard Parallels. Stereographic. Mercator. State Plane Coordinates. Military Grid Systems. CONVENTIONAL PROJECTIONS. Summary of Procedures. Gnomonic. Azimuthal Equidistant. Orthographic. Simple Conic, One Standard Parallel. Simple Conic, Two Standard Parallels. Conical Perspective. Polyconic. Perspective Cylindrical. Plate Carree'. Carte Parallelogrammatique. Miller. Globular. Aerial Perspective. Van der Grinten. Cassini. Robinson. THEORY OF DISTORTIONS. Qualitative View of Distortion. Quantization of Distortion. Distortions from Euclidean Geometry. Distortions from Different Geometry. Distortions in Equal Area Projections. Distortions in Conventional Projections. MAPPING APPLICATIONS. Map Projections in the Southern Hemisphere. Distortion in the Transformation from the Spheroid to the Authalic Sphere. Distances on the Loxodrome. Tracking System Displays. Differential Distances about a Position. COMPUTER APPLICATIONS. Direct Transformation Subroutines. Inverse Transformation Subroutines. Calling Program for Subroutines. State Plane Coordinates. UTM Grids. Computer Graphics. USES OF MAP PROJECTIONS. Fidelity to Features on the Earth. Characteristics of Parallels and Meridians. Considerations in the Choice of a Projection. Recommended Areas of Coverage. Recommended Set of Map Projections. Conclusion.