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This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry.Examines topology of recent compact su

Algebraic topology. --- Surfaces. --- Curved surfaces --- Geometry --- Shapes --- Topology

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This work summarizes the valuable investigations of the authors in the fields of geological and geotechnical engineering, structural engineering, reliability, durability and rehabilitation of structures, monitoring and control of structures, tunnel, subway and underground facilities, road and railway engineering, bridge engineering, seismic engineering, hydraulic engineering, water supply and drainage engineering, heating, gas supply, ventilation and air conditioning works, natural and technogenic disaster prevention and mitigation, survey engineering, cartography and geographic information sy

Structural engineering. --- Surfaces. --- Curved surfaces --- Geometry --- Shapes --- Engineering, Structural --- Structures, Engineering of --- Architecture --- Engineering

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Algebraic topology --- Surfaces --- Topologie algébrique --- 515.1 --- Curved surfaces --- Geometry --- Shapes --- Topology --- 515.1 Topology --- Topologie algébrique --- Variétés topologiques

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Three-manifolds (Topology) --- Surfaces --- 514 --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Curved surfaces --- Geometry --- Shapes --- 514 Geometry

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Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.

Curves on surfaces --- Surfaces --- Surfaces, Models of. --- Models of surfaces --- Models and modelmaking --- Curved surfaces --- Geometry --- Shapes --- Surfaces, Curves on --- Mathematical models.