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Parametric Geometry of Curves and Surfaces

Architectural Form-Finding

  • Textbook
  • © 2021

Overview

Authors:
  1. Alberto Lastra

    1. Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain

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  • Provides an illustrated, self-contained introduction to the differential geometry of curves and surfaces
  • Connects abstract mathematical theory with real architectural objects
  • Richly illustrated with over 150 figures as well as 20 QR Codes linked to animations
  • Many solved exercises to go beyond the theory

Part of the book series: Mathematics and the Built Environment (MABE, volume 5)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xxiii
    Download chapter PDF

  2. Parametrizations and Plane Curves

    • Alberto Lastra
    Pages 1-57

  3. Parametrizations and Space Curves

    • Alberto Lastra
    Pages 59-102

  4. Parametrizations and Regular Surfaces

    • Alberto Lastra
    Pages 103-137

  5. Special Families of Surfaces

    • Alberto Lastra
    Pages 139-204

  6. Back Matter

    Pages 205-276
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Keywords

About this book

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.

Reviews

“This book is the result of the author’s years long experience lecturing parametric geometry of curves and surfaces in architectural studies … . In fact it will give a mathematics student a fresh approach to the subject. The book shows many examples of curves and surfaces that can usually be found in classical books, showing its use in architecture. … Indeed a very interesting book on parametric curves and surfaces.” (Ana Pereira Do Vale, zbMATH 1486.53010, 2022)

Authors and Affiliations

  • Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Spain

    Alberto Lastra

About the author

Alberto Lastra is associate professor at University of Alcalá (Spain). He has been teaching mathematics in the degree courses Architecture and Fundamentals of Architecture and Urbanism there since 2011, with a particular focus on innovation and interdisciplinarity. He is author of more than 40 journal publications in asymptotic analysis, functional equations, symbolic computation and orthogonal polynomials, as well as the mathematics of architecture.

Bibliographic Information

  • Book Title: Parametric Geometry of Curves and Surfaces

  • Book Subtitle: Architectural Form-Finding

  • Authors: Alberto Lastra

  • Series Title: Mathematics and the Built Environment

  • DOI: https://doi.org/10.1007/978-3-030-81317-8

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-81316-1Published: 07 September 2021

  • Softcover ISBN: 978-3-030-81319-2Published: 08 September 2022

  • eBook ISBN: 978-3-030-81317-8Published: 06 September 2021

  • Series ISSN: 2512-157X

  • Series E-ISSN: 2512-1561

  • Edition Number: 1

  • Number of Pages: XXIII, 276

  • Number of Illustrations: 24 b/w illustrations, 165 illustrations in colour

  • Topics: Differential Geometry, Mathematics in Art and Architecture

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