9781334013768 - generalized map makers problem: optimal flattening of polyhedral surfaces (classic reprint) de l. schwartz, eric (3 resultados)
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Librería: Forgotten Books, London, Reino UnidoForgotten Books
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Paperback. Condición: New. Print on Demand. This book addresses a fundamental challenge in mapmaking: accurately representing curved surfaces in a flat format. While traditional mapmaking focuses on the relatively simple spherical surface of the Earth, the author tackles the much more complex problem of mapping convoluted, non-c…onvex surfaces, such as the human brain. This is no mere academic exercise; it has direct implications for various fields, including computer-aided neuroanatomy, where visualizing the intricate neural maps of the brain is crucial for understanding its functionality. The author introduces a novel numerical solution to this "generalized map-makers problem," which involves optimizing the distances between points on a curved surface and their corresponding points on a flat representation. This is achieved through a variational algorithm that minimizes the "stress" or deviation between the original distance matrix and the flattened representation. This innovative approach offers a practical solution for mapping complex surfaces in a way that preserves the essential metric relationships. The book delves into the technical details of the algorithm, including its implementation and challenges. The author explores the limitations of using only short-range distances for mapping and demonstrates the effectiveness of incorporating longer-range distances. Furthermore, the book presents examples of the algorithm's successful application to mapping the surface of the visual cortex, a particularly complex example. The book's insights contribute significantly to the understanding of how to represent complex three-dimensional surfaces in a flat, two-dimensional format, with practical implications for diverse disciplines, such as computer science and neuroanatomy. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.
