Parametric Geometry of Curves and Surfaces

Architectural Form-Finding

verfasst von: Dr. Alberto Lastra

Verlag: Springer International Publishing

Buchreihe : Mathematics and the Built Environment

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This textbook 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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Parametrizations and Plane Curves

Abstract

The chapter is devoted to the study of plane curves from the point of view of differential geometry. We focus our attention to classical curves and also on conics, and provide examples and other applications in architectural elements of the mathematical theory.

Alberto Lastra

Chapter 2. Parametrizations and Space Curves

Abstract

The chapter describes the mathematical theory of space curves from differential geometry, and its application to specific architectural elements. We focus on the study of helices and some transformations on them.

Alberto Lastra

Chapter 3. Parametrizations and Regular Surfaces

Abstract

The theory of the previous chapters is applied on surfaces and parametrizations. Elements involved in the study of regular surfaces are shown and illustrated with examples. Some classical surfaces in architecture are analyzed from the point of view of the theory described previously in the chapter.

Alberto Lastra

Chapter 4. Special Families of Surfaces

Abstract

The chapter is devoted to the study of special families of surfaces which are of common use in architecture such as ruled surfaces and some of their subfamilies. The technique followed for achieving a parametrization is also described in detail. Quadrics, minimal and developable surfaces are also considered.

Alberto Lastra

Backmatter

Titel: Parametric Geometry of Curves and Surfaces
verfasst von: Dr. Alberto Lastra
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-81317-8
Print ISBN: 978-3-030-81316-1
DOI: https://doi.org/10.1007/978-3-030-81317-8