Architectural Geometry and Design Guide

Learning with Bentley
Books by Bentley Institute Press

Architectural Geometry

Helmut Pottmann (Author), Andreas Asperl (Author), Michael Hofer (Author), Axel Kilian (Author)
ISBN: 9781934493045

Architectural Geometry is the first book to introduce a revolutionary new approach to design.

Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture.

Written for students, architects, construction engineers, and industrial designers – Architectural Geometry is a source of inspiration for scientists interested in applications of geometry processing in architecture and art.

With over 700 pages, including 2,100 full-color images of built architecture, architectural projects, and artwork, Architectural Geometry takes readers from basic to advanced geometry then leads them to the cutting-edge of research in the architectural geometry field.

Meet the Authors

Helmut Pottman is a Mathematics Professor at the Vienna University of Technology, with research interests in the fields of industrial, architectural, and discrete differential geometry. He has held faculty positions at the University of Hamburg, University of Kaiserlautern, Purdue University, University of California at Davis, and Tsinghua University in Beijing. In addition to Architectural Geometry, Pottmann co-authored Computational Line Geometry in November 2009.

Michael Hofer is a post-doctoral researcher at the Vienna University of Technology where he also received his doctoral degree in Applied Geometry. Hofer’s current research focuses on the solution of current geometric problems in applications such as computer-aided design, computer graphics, and image processing.

Andreas Asperl studied Mathematics and Descriptive Geometry at the Vienna University of Technology, where he has held a faculty position since 1983. He is the author of several textbooks for use in Austrian schools, and an advocate of the use of three-dimensional CAD systems in geometry education.

Axel Kilian received his Master’s of Science and Ph.D. in Computation and Design from the Massachusetts Institute of Technology. He has lectured on the topic of generative design in the US, Central America, and Europe, and teaches courses and workshops on the subject in collaboration with the SmartGeometry group in the United Kingdom.


Read an excerpt from Architectural Geometry or order the book online today!

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Architectural Geometry is perfect for students and teachers of architecture, practicing architects, and other professionals seeking an in-depth understanding of geometric principles and their integral relationship to the world of design. Clearly, its content is fundamental and will be not only relevant but essential for many years to come...”

Gary Hack, University of Pennsylvania School of Design

Architectural Geometry is a superior, comprehensive survey of geometric modeling for architecture filled with stunning illustrations of unparalleled precision and clarity. The authors are at the forefront of research into advanced modeling technologies and the underlying geometrical principles upon which they are based…” 

Miles Ritter, Princeton University School of Architecture

“This book is a carefully considered, well-structured, balanced, and informative book on constructive geometry and its application to design for the built environment in a contemporary setting. It mixes theoretical ideas, how-to advice, and real-world examples, and will appeal to a wide range of potential users, from students to educators and practitioners.” 

Andre Brown, Liverpool University

"It is full of beautiful pictures and illustrations as well as theoretical explanations. I believe that this book would be needed by many architects who are practicing BIM approaches."

Ryota Leiri, Nikkei Business Publications, Inc.,

“The scope of Architectural Geometry is as expansive as its size... there’s an incredible wealth of information to be learnt. In fact the more I delve into the book, the more value I see for the non-geometrician.” 

Nigel Davies, Evolve Consultancy,

"I think Bentley has now come up with the goods. Three mathematicians and an architect have come up with Architectural Geometry a lavish publication that succeeds in bringing together all the essential geometrical concepts that power our cad tools ... I would recommend this book to anyone with a desire to understand and exploit geometry in the production of better architecture."

Marc Thomas, Architects Design Partnership, Building Design Magazine

Featured topics  

This book incorporates several themes that build in educational level— from basics to research.

  • freeform curves and surfaces
  • differential geometry
  • kinematic geometry
  • mesh processing
  • shape optimization
  • digital reconstruction


Note from the authors:

These days we are facing dramatic changes, the tools at our disposal becoming seemingly unlimited. However, the increase in possibilities did not go along with an increase in the depth of geometry education. In fact, the opposite is true. Thus, it is the most important task of this book to close the gap between the technical possibilities and an effective working knowledge of the new methods of geometric design.

Modern architecture takes advantage of the greatly increasing design possibilities, yet architects are not just a new group of CAD users. Scale and construction technologies pose new challenges to engineering and design. We are convinced that such challenges can be met more effectively with a solid understanding of geometry.

Geometric computing is a broad area with many branches. An interdisciplinary field such as architecture benefits from such variety. We have tried to provide views into this larger scientific context. In fact, we believe that a new research area—which might be termed architectural geometry—is currently evolving and we hope that our book will help to promote its future development.

To advance this emerging field, a close cooperation between geometers and architects is of highest importance. This book may be seen as an example. The stimulating cooperation of three geometers and an architect (Axel Kilian) developed the book’s geometric content, the discussion of its marriage with modern architecture, and the presentation of both. Moreover, it led to the identification of challenging research problems—some of which are described in the later chapters of the book.