Parametric Geometry of Curves and Surfaces Architectural Form-Finding

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...

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Bibliographic Details
Main Author: Lastra, Alberto
Format: eBook
Language:English
Published: Cham Birkhäuser 2021, 2021
Edition:1st ed. 2021
Series:Mathematics and the Built Environment
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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100 1 |a Lastra, Alberto 
245 0 0 |a Parametric Geometry of Curves and Surfaces  |h Elektronische Ressource  |b Architectural Form-Finding  |c by Alberto Lastra 
250 |a 1st ed. 2021 
260 |a Cham  |b Birkhäuser  |c 2021, 2021 
300 |a XXIII, 276 p. 189 illus., 165 illus. in color  |b online resource 
505 0 |a 1 Parametrizations and Plane Curves -- 2 Parametrizations and Space Curves -- 3 Parametrizations and Regular Surfaces -- 4 Special Families of Surfaces -- A Coordinate Systems -- B Mathematical Tool Kit -- C Solutions to the Suggested Exercises -- References -- Photograph Credits -- List of Symbols -- Index 
653 |a Geometry, Differential 
653 |a Mathematics in Art and Architecture 
653 |a Architecture / Mathematics 
653 |a Arts 
653 |a Differential Geometry 
653 |a Mathematics 
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490 0 |a Mathematics and the Built Environment 
028 5 0 |a 10.1007/978-3-030-81317-8 
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520 |a 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