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Although there are still practitioners of the traditional art of manual fairing of ship lines, the geometry of most hull forms ranging from small yachts to the largest commercial and naval ships are now almost invariably developed using one of the commercially available hull modeling software packages. Such software normally includes, in addition to the hull modeling and display functions, routines for the computation of hydrostatics, stability and other hull properties. It may form a part of a comprehensive computer-based design and manufacturing system or it may be included in a shipboard computer-based operational system used for cargo load monitoring and damage control. The present volume presents first, the theoretical basis for these hull modeling systems and second, the procedures for computing hull geometric, buoyancy and other properties by mathematical methods utilizing such models. The emphasis is upon the nomenclature and fundamentals underlying several different methods of hull geometrical modeling with the intention of providing the understanding needed to use intelligently both existing and future tools. Some topics included in the volume are continuity and fairness of surfaces, B-spline and NURBS representation, ruled and developable surfaces, subdivision surfaces, and classic computational topics such as hydrostatic properties and initial stability. This is a subject area characterized by a continuing stream of innovation and new software products so the objective here is to present the basis needed to understand and keep abreast of new developments in the field. * Replaces Chapter 1 in PNA Volume I: Stability and Strength