Plane Networks and their Applications

"This concise book renders an advanced exposition of the theory of error propagation in geodetic networks that are comprised of up to a few hundred nodes... The reviewed book constitutes a timely and valuable contribution to the theory of plane geodetic network analysis and design. An outstanding feature of this book is the extensive use it makes of the nowadays easy availability of sophisticated automatic computing tools." - Mathematical Reviews

• 1 Introduction.- 1.1 Description of the Discrete Model.- 1.2 Description of the Continuous Model.- 1.3 Variance Propagation.- 2 Discrete Approach.- 2.1 Motivation for the Study.- 2.2 Basic Matrix of Leveling.- 2.3 Regular Traverse.- 2.4 Varying the Boundary Conditions.- 2.5 Variance Propagation.- 2.6 Asymptotic Behavior of the Node Variance.- 2.7 On the Smoothness and Roughness of the Eigenvectors.- 2.8 Green’s Formula for Plane Trigonometric Networks.- 3 Continuous Approach.- 3.1 Leveling Networks.- 3.2 Advanced Error Analysis.- 3.3 Plane Elastic Continuous Networks: A Heuristic Exposition.- 3.4 Distance Networks.- 3.5 Estimates of the Weighted Square Sum of Residuals: the Korn Inequality.- 4 Networks with Relative Observations.- 4.1 Dealing with Relative Observations.- 4.2 Fundamental Solution.- 4.3 Solution of the Boundary Value Problem.- 5 Spectrum.- 5.1 Spectral Density of the Discrete Laplacian.- 5.2 Spectral Distribution Function N(?).- 5.3 Additional Remarks on the Spectral Properties of Geodetic Networks.- 6 Simple Applications.- 6.1 Stiffness Matrix in Practice.- 6.2 Displacement Functions given a Priori.- 6.3 Merging of Digitized Maps.- 6.4 Interpolation of Discrete Vector Field: Cubic Splines.- Author Index.