Differential Geometry Applied To Curve And Surface Design Foundations
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Differential Geometry Applied To Curve And Surface Design Foundations
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Author : Anthony William Nutbourne
language : en
Publisher: Ellis Horwood
Release Date : 1988
Differential Geometry Applied To Curve And Surface Design Foundations written by Anthony William Nutbourne and has been published by Ellis Horwood this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Differential Geometry Applied To Curve And Surface Design
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Author : Anthony W. Nutbourne
language : en
Publisher:
Release Date : 1984
Differential Geometry Applied To Curve And Surface Design written by Anthony W. Nutbourne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Differential Geometry Applied To Curve And Surface Design
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Author : Anthony William Nutbourne
language : en
Publisher:
Release Date : 1988
Differential Geometry Applied To Curve And Surface Design written by Anthony William Nutbourne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Differential Geometry Applied To Curve And Surface Design
DOWNLOAD
Author : Anthony W. Nutbourne
language : en
Publisher:
Release Date : 1988
Differential Geometry Applied To Curve And Surface Design written by Anthony W. Nutbourne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Parametric Geometry Of Curves And Surfaces
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Author : Alberto Lastra
language : en
Publisher: Springer Nature
Release Date : 2021-09-06
Parametric Geometry Of Curves And Surfaces written by Alberto Lastra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-06 with Mathematics categories.
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.
Designing Fair Curves And Surfaces
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Author : Nickolas S. Sapidis
language : en
Publisher: SIAM
Release Date : 1994-01-01
Designing Fair Curves And Surfaces written by Nickolas S. Sapidis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Computers categories.
This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.
Basics Of Computer Aided Geometric Design
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Author : M. Ganesh
language : en
Publisher: I. K. International Pvt Ltd
Release Date : 2011-10-06
Basics Of Computer Aided Geometric Design written by M. Ganesh and has been published by I. K. International Pvt Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-06 with categories.
The aim of the book is to provide a good foundation of Computer-Aided Geometric Design to students who are doing under-graduate courses in engineering, especially Mechanical Engineering, Computer Science, Geometric Modeling and CAD/CAM. This book is organized in two parts. Part-I deals with the basics of differential geometry of curves and surface, a good understanding of which is essential prerequisite to what follows in the Part-II. Part-II is devoted entirely to the geometric designs of curves and surfaces, which are used in the development of computer graphics and profiles and hulls of ships, aircraft wings, satellites (to name a few large scale products) as also telephones, mobile phones, fancy flower vases (to name a few small-scale products). Concepts introduced are illustrated with examples, which are completely worked out. A list of problems is also given at the end of each chapter
Differential Geometry Of Curves And Surfaces
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Author : Kristopher Tapp
language : en
Publisher: Springer
Release Date : 2016-09-30
Differential Geometry Of Curves And Surfaces written by Kristopher Tapp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-30 with Mathematics categories.
This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
Differential Geometry Of Curves And Surfaces
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Author : Manfredo P. do Carmo
language : en
Publisher: Courier Dover Publications
Release Date : 2016-12-14
Differential Geometry Of Curves And Surfaces written by Manfredo P. do Carmo and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-14 with Mathematics categories.
One of the most widely used texts in its field, this volume's clear, well-written exposition is enhanced by many examples and exercises, some with hints and answers. 1976 edition.
Differential Geometry Of Curves And Surfaces
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Author : Shoshichi Kobayashi
language : en
Publisher: Springer Nature
Release Date : 2019-11-13
Differential Geometry Of Curves And Surfaces written by Shoshichi Kobayashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-13 with Mathematics categories.
This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.
