Parametric Geometry of Curves and Surfaces

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.

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

Auteur

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.

Résumé
"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)

Contenu
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.