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An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulati...
This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.
Explores the beautifully intricate dynamics of pop-up cards using high school mathematics, making tangible what is often dry and abstract.
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.
Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.
Original essays on the metaphysics of time, identity, and the self, written by distinguished scholars and important rising philosophers.The concepts of time and identity seem at once unproblematic and frustratingly difficult. Time is an intricate part of our experience—it would seem that the passage of time is a prerequisite for having any experience at all—and yet recalcitrant questions about time remain. Is time real? Does time flow? Do past and future moments exist? Philosophers face similarly stubborn questions about identity, particularly about the persistence of identical entities through change. Indeed, questions about the metaphysics of persistence take on many of the complexitie...
'A powerful and gripping piece of writing from a born storyteller.' Joseph O'Connor 'The narrative is just like his singing voice, full of powerful strength and compassion.' Michael Harding 'Lucid, lovingly-written and lyrical.' Professor Christine Kinealy 1846. County Cork. On the barren outskirts of Macroom, Pádraig and Cáit ua Buachalla face a perilous winter after the comprehensive failure of their blighted crop – the final episode in a whole history threatening to push them over the edge. From his shop at the centre of town, pawnbroker Cornelius Creed sees the poor in their darkest hour, his premises often being their last stop on the way to the workhouse. Perfectly placed at the ju...
Reflections on the metaphysics and epistemology of classification from a distinguished group of philosophers. Contemporary discussions of the success of science often invoke an ancient metaphor from Plato's Phaedrus: successful theories should "carve nature at its joints." But is nature really "jointed"? Are there natural kinds of things around which our theories cut? The essays in this volume offer reflections by a distinguished group of philosophers on a series of intertwined issues in the metaphysics and epistemology of classification. The contributors consider such topics as the relevance of natural kinds in inductive inference; the role of natural kinds in natural laws; the nature of fundamental properties; the naturalness of boundaries; the metaphysics and epistemology of biological kinds; and the relevance of biological kinds to certain questions in ethics. Carving Nature at Its Joints offers both breadth and thematic unity, providing a sampling of state-of-the-art work in contemporary analytic philosophy that will be of interest to a wide audience of scholars and students concerned with classification.
A state-of-the-art collection of previously unpublished essays on the topics of determinism, free will, moral responsibility, and action theory, written by some of the most important figures in these fields of study.
Laws and norms that focus on women's lives in conflict have proliferated across the regimes of international humanitarian law, international criminal law, international human rights law and the United Nations Security Council. While separate institutions, with differing powers of monitoring and enforcement, implement these laws and norms, the activities of regimes overlap. Women's Rights in Armed Conflict under International Law is the first book to account for this pluralism and institutional diversity. This book identifies key aspects of how different regimes regulate women's rights in conflict, and how they interact. Using country case studies to reveal the practical implications of the fragmented protection of women's rights in conflict, this book offers a dynamic account of how regimes and institutions interact, the extent to which they reinforce each other, and the tensions and gaps in regulation that emerge.