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E-grāmata: Parametric Geometry of Curves and Surfaces: Architectural Form-Finding

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Parametric Geometry of Curves and Surfaces: Architectural Form-FindingPalielināt
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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.

Recenzijas

This book is the result of the authors 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)

1 Parametrizations and Plane Curves
1(58)
1.1 Plane Curves and Parametrizations
2(7)
1.2 Some Classic Curves in Architecture
9(6)
1.3 Some Elements of Regular Plane Curves
15(11)
1.4 Conies
26(12)
1.5 Some Conies in Architecture
38(3)
1.6 On the Implicitation and Parametrization of Curves
41(10)
1.7 Approximation and Interpolation of Curves
51(4)
1.8 Suggested Exercises
55(4)
2 Parametrizations and Space Curves
59(44)
2.1 Space Curves and Parametrizations
59(7)
2.2 Some Elements of Regular Space Curves
66(21)
2.3 Some Classic Space Curves in Architecture
87(3)
2.4 Rigid Transformations in R3
90(6)
2.5 Some Transformations on a Helix
96(5)
2.6 Suggested Exercises
101(2)
3 Parametrizations and Regular Surfaces
103(36)
3.1 Surfaces and Parametrizations
103(13)
3.2 Some Classic Surfaces in Architecture
116(7)
3.3 Projections of Surfaces onto Planes
123(3)
3.4 Curves in Surfaces and Intersection of Surfaces
126(10)
3.5 Suggested Exercises
136(3)
4 Special Families of Surfaces
139(128)
4.1 Ruled Surfaces
139(9)
4.2 Some Subfamilies of Ruled Surfaces
148(6)
4.3 Parametrization of Some Ruled Surfaces
154(6)
4.4 Surfaces of Revolution
160(9)
4.5 Quadric Surfaces
169(18)
4.6 Quadrics Revisited: Some Examples in Architecture
187(3)
4.7 Curvature: Minimal and Developable Surfaces
190(11)
4.7.1 Final Comments
200(1)
4.8 Suggested Exercises
201(4)
A Coordinate Systems
205(8)
B Mathematical Tool Kit
213(10)
B.1 Introduction to Linear Algebra
213(1)
B.1.1 Systems of Linear Equations
213(1)
B.1.2 Vector Spaces
214(1)
B.1.3 Euclidean Vector Spaces
215(1)
B.1.4 Diagonalization: Eigenvalues and Eigenvectors
215(1)
B.2 Real Functions of One Variable
216(3)
B.3 Functions of Several Real Variables
219(2)
B.4 Differential Equations and Systems of Differential Equations
221(2)
C Solution to the Suggested Exercises
223(44)
C.1
Chapter 1
223(12)
C.2
Chapter 2
235(10)
C.3
Chapter 3
245(4)
C.4
Chapter 4
249(18)
References 267(6)
Index 273
Alberto Lastra is associate professor at University of Alcalį (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.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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