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Geometry lies at the core of the architectural design process. It is omnipresent, from the initial determination of form to the final construction. Modern geometric computing provides a variety of tools for the efficient design, analysis, and manufacturing of complex shapes. On the one hand this opens up new horizons for architecture. On the other, the architectural context also poses new problems for geometry. The research area of architectural geometry, situated at the border of applied geometry and architecture, is emerging to address these problems. This volume, presenting the papers accepted at the 2010 Advances in Architectural Geometry conference in Vienna, reflects the substantial progress made in this field. The interdisciplinary nature of architectural geometry is reflected in the diversity of backgrounds of the contributing authors. Renowned architects, engineers, mathematicians, and computer scientists present novel research ideas and cutting-edge solutions at the interface of geometry processing and architectural design.

Architecture --- Architectural design --- Geometry in architecture --- Composition, proportion, etc.

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Advances in Architectural Geometry 2023 is a comprehensive collection of 34 technical papers from the biennial conference that explores cutting-edge developments in architectural geometry. The book bridges the gap between theoretical research and practical applications, highlighting innovative approaches and emerging trends in the field. It covers a wide array of topics, including parametric design strategies, advanced computational methods, and the application of artificial intelligence in construction. The work serves as a valuable resource for architects, engineers, computer scientists, and industry professionals, offering insights into the integration of geometry in modern architectural design and fostering interdisciplinary collaboration.

Geometry in architecture. --- Architectural design. --- Geometry in architecture --- Architectural design

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This textbook is a comprehensive and yet accessible introduction to non-Euclidean Laguerre geometry, for which there exists no previous systematic presentation in the literature. Moreover, we present new results by demonstrating all essential features of Laguerre geometry on the example of checkerboard incircular nets. Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic and elliptic space, and study the corresponding groups of Laguerre transformations. We give an introduction to Lie geometry and describe how these Laguerre geometries can be obtained as subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the properties of checkerboard incircular nets.

Geometry --- Mathematics --- geometrie