BE Magazine - Volume 5, Issue 1 - (Page 41) TECH NOTES understanding have increased significantly with many freeform projects being realized. Our book covers the whole range of levels, from the elementary freshman level to results of cutting-edge research. geometry is aiming at applications in architecture and industrial design. Geometry has not been taught much at architecture schools in recent years and we hope this work will provide a starting point for teaching it again in a contemporary context. Axel Kilian studied architecture and specialized in design and computation for a master’s, Ph.D., and post-doctorate at Massachusetts Institute of Technology It may well be the first book written jointly by geometers (researchers and teachers) and an architect (with a very solid background in geometric computing). Look into a typical geometry book or a typical architecture book and you will see the difference. The collaboration started in 2005 at Bentley’s BE Conference in Baltimore, Md., when Helmut Pottmann spoke at the research seminar and was intrigued by the work of the SmartGeometry research group. For us, it was great to work in an interdisciplinary team and to include the mutual feedback in the text and illustrations of the book. What are some of the most challenging research problems that were uncovered by this collaboration? v HOT OFF THE PRESS! Providing more than 700 pages of color images, Architectural Geometry is the first textbook to successfully integrate the disciplines of geometry and architecture. Read more about one of the newest titles from Bentley Institute Press. >>more How do you define architectural geometry and how is this new research area evolving? How is this book different than typical geometry books written for architects? Architectural geometry solves geometric problems arising in the architectural design or construction. Increasingly complicated shapes require more research. So far, CAD and geometric modeling have been largely driven by the demands in other industries. Architects are using some of these methods, but the design tools have not always kept up with these developments. Architectural geometry should be a multidisciplinary research area, mixing expertise from architecture, geometric modeling and processing, mathematics, and building technology. Why is it so important to have a close cooperation between geometers and architects? The development of freeform meshing with planarity constraints is one such challenging research problem. Chapter 19 provides a good overview of the state of the art. In general, each construction technology comes with its own research challenge. How can we adjust a given shape (freeform shape) in such a way that the adapted geometry optimally matches the practical requirements of the construction method? Moreover, what are good design strategies for automatically generating these construction-specific shape representations? Our book illustrates this problem area in various ways by means of multilayer freeform structures formed by planar quadrilateral panels. Neither does a geometer understand the needs in architecture nor does a typical architect master the methods and theories necessary to solve the really challenging problems in architectural geometry. Both domains have a high degree of specialization and collaboration allows for synergy effects that are beneficial for both partners. Architects may find design inspiration and novel aesthetics within advanced geometry, and geometers may benefit from identifying new areas of research that are unique to the geometric demands of architecture. What is so significant about Architectural Geometry’s authors being comprised of three geometers and an architect? Helmut Pottmann is a professor of geometry at Vienna University of Technology, where he directs a research group at the Institute of Discrete Mathematics and Geometry How is Architectural Geometry applicable to both students and professionals? It is both a text book for students and teachers and a reference book for professionals who want to get more deeply involved with geometry. The demands for geometric Most geometry books for architects focus on geometry as a representation tool. In other words, they deal with the elementary rules of descriptive geometry, perspective projection in particular. While this material is also covered in our book, the main focus is on the use of CAD systems and other digital media such as 3D scanning and rapid prototyping. Architectural Geometry addresses topics in generative design taking into account constraints from construction and manufacturing. These processes are used in practice and the understanding of the geometric components is crucial for building. Architectural Geometry also includes many contemporary topics in geometry such as freeform surfaces, otherwise mostly found in advanced geometry books. The book also provides the basic math needed for scripting and for the implementation of research ideas. To our best knowledge, no book exists to date that covers the entire range—from elementary geometry to cutting-edge research with a focus on architectural needs. We hope this book will stimulate a more thorough teaching of geometry at architectural schools and it will help to make architectural geometry a growing and flourishing research area. Architectural geometry fascinates us for its many aspects ranging from aesthetics to functionality and continuously generates new and challenging research problems. v Volume 5, Issue 1 | BE MAGAZINE 41 http://www.bentley.com/en-US/Training/Bentley+Institute+Press/Architectural+Geometry.htm
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