Geometry is to the fore in this textbook. Inspired by the work of Thom and Arnol'd on Singularity Theory, topics such as umbilics, ridges and subparabolic lines, all robust features of a smooth surface, which are rarely treated in elementary courses on differential geometry, are here considered in detail. These features are of immediate relevance in modern areas of application including pattern recognition, computer vision, electronic scanning and remote sensing. Central to the exposition is the role of certain cubic forms associated with a surface; using this theory many interesting results are proved and illustrative examples explored. The text is based on extensive teaching at Liverpool University to audiences of advanced undergraduate and beginning postgraduate students in mathematics, but its wide applicability will mean that it will also appeal to scientists and engineers from a variety of other disciplines.
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"This book will be a source of inspiration for research mathematicians and students of visual geometry for years to come." Thomas F. Banchoff, American Scientist
Book Description
In this book elementary differential geometry is approached from a new standpoint, one inspired by Thom's work on singularity theory. This textbook provides a unique exposition of surface theory.
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Inside This Book
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First Sentence:
St Paul's Cathedral was designed following the Great Fire of London in 1666. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ordinary cuspidal edge, geodesic inflection, rhamphoid cusp, principal tangent lines, normal focal surface, regular space curve, nowhere linear, stationary curvature, ordinary undulation, surjective criterion, regular smooth surface, real cubic forms, ordinary inflection, umbilical centre, inflection circle, ordinary kink, bumpy cube, bumpy spheres, ordinary turning point, flat umbilic, regular smooth curve, regular plane curve, tangent developable, ordinary vertex, bumpy circle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Proof Exercise, Proof Let, Stelios Markatis, Proof There, Proof All, Prove Corollary, Taylor's Theorem, Wilkinson's Theorem New!
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Front Cover | First Pages | Index | Back Cover | Surprise Me!
St Paul's Cathedral was designed following the Great Fire of London in 1666. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
ordinary cuspidal edge, geodesic inflection, rhamphoid cusp, principal tangent lines, normal focal surface, regular space curve, nowhere linear, stationary curvature, ordinary undulation, surjective criterion, regular smooth surface, real cubic forms, ordinary inflection, umbilical centre, inflection circle, ordinary kink, bumpy cube, bumpy spheres, ordinary turning point, flat umbilic, regular smooth curve, regular plane curve, tangent developable, ordinary vertex, bumpy circle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Prove Proposition, Proof Exercise, Proof Let, Stelios Markatis, Proof There, Proof All, Prove Corollary, Taylor's Theorem, Wilkinson's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
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cites this book:
- Studies on Christiaan Huygens by Symposium on the Life and Work of Christiaan Huygens in Back Matter
- Vision Geometry IX (Proceedings of Spie) by Longin J. Latecki in Back Matter
- Vision Geometry (Proceedings of Spie) by Ronert A. Melter in Back Matter
- MULTIMEDIA MODELING (Modeling Multimedia Information and Systems) by Shuji Hashimoto on page 489
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