Parametric Geometry of Curves and Surfaces: Architectural Form-Finding

Parametric Geometry of Curves and Surfaces is a textbook that introduces the differential geometry of parametrized curves and surfaces, with applications to architectural elements. It is suitable for lecture courses, engineering, architecture, and mathematics students, and researchers interested in the mathematics of architecture or computer-aided design.

Format: Hardback
Length: 276 pages
Publication date: 07 September 2021
Publisher: Springer Nature Switzerland AG

Geometric elements in architecture play a crucial role in responding to practical, physical, and aesthetic needs. A deep understanding of the mathematics underlying the geometry is essential for controlling the construction process. This book establishes a connection between the classical mathematical theory of parametrized curves and surfaces and its numerous applications in architecture. The presentation is comprehensive, featuring numerous figures and animations to illustrate the theory, with a special emphasis on recent trends in the field. Solved exercises are included to facilitate practical application of the theory.

Designed as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically inclined students in engineering, architecture, and related fields. It can also serve as a textbook for traditional differential geometry courses for mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will find great value in this book, as it combines precise mathematics with architectural examples.

Parametrized curves and surfaces are fundamental mathematical concepts that describe the shape and geometry of curves and surfaces in terms of parameters. These parameters can vary continuously or discretely, allowing for a wide range of shapes and forms. Parametric geometry provides a powerful tool for analyzing and designing these geometric elements, as it allows for the representation and manipulation of complex shapes in a concise and efficient manner.

One of the key applications of parametric geometry in architecture is in the design of buildings and structures. By parametrizing the shape of a building or structure, architects can create designs that are both functional and aesthetically pleasing. For example, parametric surfaces can be used to create curved roofs or walls, while parametric curves can be used to define the shape of windows or doors. Parametric modeling also allows architects to create complex designs that are not feasible with traditional construction methods, such as curved surfaces or asymmetrical shapes.

Parametric geometry is also used in the analysis and optimization of architectural designs. By parametrizing the shape of a building or structure, architects can analyze the structural behavior of the design and optimize it for efficiency and cost-effectiveness. For example, parametric modeling can be used to analyze the wind loads on a building and optimize the design to reduce wind resistance and increase energy efficiency.

In addition to its applications in architecture, parametric geometry has numerous other applications in fields such as engineering, computer graphics, and mathematics. Parametric surfaces, for example, are used in computer graphics to create realistic 3D models of objects, while parametric curves are used in engineering to model the behavior of mechanical systems. Parametric modeling is also used in mathematics to study the properties of complex systems and to develop new mathematical models and theories.

Parametric geometry is a versatile and powerful tool that has numerous applications in architecture and other fields. Its ability to represent and manipulate complex shapes in a concise and efficient manner allows for the creation of innovative and beautiful designs that meet the practical, physical, and aesthetic needs of users. As technology continues to advance, we can expect to see even more exciting applications of parametric geometry in the future.

In conclusion, this book provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical, and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice.

Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture, and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.

Weight: 617g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030813161
Edition number: 1st ed. 2021