In Coordinates in Geodesy definitions and transformations are treated based on the general principles of differential geometry for surfaces and three-dimensional Euclidean space, strictly using the tensor calculus. The broad approach applying general concepts of constructing and transforming coordinates allows clearly arranged solutions for all geodetic applications. Moreover, the great number of examples given in this book explain in detail the principles of coordinates in geodetic surveying using ellipsoids of revolution as reference surfaces.
In Coordinates in Geodesy definitions and transformations are treated based on the general principles of differential geometry for surfaces and three-dimensional Euclidean space, strictly using the tensor calculus. The broad approach applying general concepts of constructing and transforming coordinates allows clearly arranged solutions for all geodetic applications. Moreover, the great number of examples given in this book explain in detail the principles of coordinates in geodetic surveying using ellipsoids of revolution as reference surfaces.
1. Introduction.- 2. General Fundamentals of Surface Coordinates.- 2.1 Fundamentals of the Theory of Surfaces.- 2.2 Fundamentals of Complex Analysis.- 3. Representing the Transformation Equations Between Surface Coordinates by Power Series.- 3.1 Constructing Surface Coordinates.- 3.2 Representing Power Series.- 3.3 Transformations Between Geodesic Polar Coordinates and Arbitrary Surface Coordinates.- 3.4 Transformations Between Geodesic Parallel Coordinates and Arbitrary Surface Coordinates.- 3.5 Transformations Between Isothermal Surface Coordinates and Arbitrary Surface Coordinates.- 4. Surface Coordinates on Ellipsoids of Revolution.- 4.1 Preliminary Remarks.- 4.2 Ellipsoids of Revolution and Their Representation Using Geographic Coordinates.- 4.3 Transformations Between Geodesic Polar Coordinates and Geographic Coordinates.- 4.4 Transformations Between Soldner's Parallel Coordinates and Geographic Coordinates.- 4.5 Defining Isothermal Surface Coordinates in the Geographic Coordinate System.- 4.6 Transformations Between Isothermal Geographic Coordinates and Geographic Coordinates.- 4.7 Transformations Between Gaussian Isothermal Coordinates and Geographic Coordinates.- 4.8 Transformations Between Gaussian Isothermal Coordinates and Geodesic Polar Coordinates.- 4.9 Transformations Between Two Systems of Gaussian Isothermal Coordinates.- 4.10 Transformations Between Isothermal Stereographic Coordinates and Geographic Coordinates.- 5. Three-Dimensional Coordinates.- 5.1 Preliminary Remarks.- 5.2 Fundamentals of Three-Dimensional Euclidean Geometry.- 5.3 Surface-Normal Coordinates.- 5.4 Geodetic Coordinates.- 5.5 Transformations Between Geographically Geodetic Coordinates.
1. Introduction.- 2. General Fundamentals of Surface Coordinates.- 2.1 Fundamentals of the Theory of Surfaces.- 2.2 Fundamentals of Complex Analysis.- 3. Representing the Transformation Equations Between Surface Coordinates by Power Series.- 3.1 Constructing Surface Coordinates.- 3.2 Representing Power Series.- 3.3 Transformations Between Geodesic Polar Coordinates and Arbitrary Surface Coordinates.- 3.4 Transformations Between Geodesic Parallel Coordinates and Arbitrary Surface Coordinates.- 3.5 Transformations Between Isothermal Surface Coordinates and Arbitrary Surface Coordinates.- 4. Surface Coordinates on Ellipsoids of Revolution.- 4.1 Preliminary Remarks.- 4.2 Ellipsoids of Revolution and Their Representation Using Geographic Coordinates.- 4.3 Transformations Between Geodesic Polar Coordinates and Geographic Coordinates.- 4.4 Transformations Between Soldner's Parallel Coordinates and Geographic Coordinates.- 4.5 Defining Isothermal Surface Coordinates in the Geographic Coordinate System.- 4.6 Transformations Between Isothermal Geographic Coordinates and Geographic Coordinates.- 4.7 Transformations Between Gaussian Isothermal Coordinates and Geographic Coordinates.- 4.8 Transformations Between Gaussian Isothermal Coordinates and Geodesic Polar Coordinates.- 4.9 Transformations Between Two Systems of Gaussian Isothermal Coordinates.- 4.10 Transformations Between Isothermal Stereographic Coordinates and Geographic Coordinates.- 5. Three-Dimensional Coordinates.- 5.1 Preliminary Remarks.- 5.2 Fundamentals of Three-Dimensional Euclidean Geometry.- 5.3 Surface-Normal Coordinates.- 5.4 Geodetic Coordinates.- 5.5 Transformations Between Geographically Geodetic Coordinates.
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