Space Tessellations

Tackling a topic that has particular appeal in the age of digital design, this well-founded introduction to the subject of parquet deformation fills a gap. These subtle, intricate geometric transformations, best known through the "Metamorphosis" series by M. C. Escher, were introduced to design curricula by American professor William S. Huff in the 1960s. The book brings together scholarly articles by the most important authors in the field and material collected in the archives of the Ulm School of Design in Germany, juxtaposed with extensive illustrations of two- and three-dimensional works created at the Vienna University of Technology. Written for anyone interested in the fields of design and geometry, this book aims to inform and inspire.

This unusual book, richly illustrated with 29 colour illustrations and about 200 line drawings, explores the relationship between classical tessellations and three-manifolds. In his original and entertaining style, the author provides graduate students with a source of geometrical insight into low-dimensional topology. Researchers in this field will find here an account of a theory that is on the one hand known to them but here is "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.

Smart technologies have advanced rapidly throughout our society (e.g. smart energy, smart health, smart living, smart cities, smart environment, and smart society) and across geographic spaces and places. Behind these "smart" developments are a number of seminal drivers, such as social media (e.g. Twitter), sensors (drones, wearables), smartphone apps, and computing infrastructure (e.g. cloud computing). These developments have captured the enthusiasm of the public, while inevitably present unprecedented challenges and opportunities for the geographic research community. When meeting the smart challenges, are there emerging theories, methods, and observations that reveal new spatial phenomena, produce new knowledge, and foster new policies? Smart Spaces and Places addresses questions such as how to make spaces and places "smart", how the "smartness" affects the way we think spaces and places, and what role geographies play in knowledge production and decision-making in a "smart" era. The collection of 21 chapters offers stimulating discussion over the meaning of spaces, places, and smartness; scientific insights into smartness; social-political views of smartness; and policy implications of smartness. The chapters in this book were originally published as a special issue of Annals of the American Association of Geographers.

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.

Advances in Applied Mechanics, Volume 54 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Advanced geometry representations and tools for microstructural and multiscale modelling, Material Point Method: overview and challenges ahead, From Experimental Modeling of Shotcrete to Numerical Simulations of Tunneling, Mechanics of Hydrogel-Based Bioprinting: From 3D to 4D, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Advances in Applied Mechanics series

Will provide a more elementary introduction to these topics than other books available; Gentle is the author of two other Springer books

Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory.