
Shape And Energies Of Geometric Objects
World Scientific Publishing Co Pte Ltd
Published on 13. April 2026
Book
Hardback
260 pages
978-981-98-1945-4 (ISBN)
Description
In this book, we study the shape of different geometric objects (curves, surfaces, and knots) through small deformation: infinitesimal bending. The shape of geometric objects is determined by their geometric curvature as well as curvature-based functionals, which are referred to as energies. Different kinds of curvatures, their properties, and their influence on shape and energy are discussed. For the investigation of shape and energy, we use our own software visualization tools.We aim to offer a mathematical way of considering shape. That is, all the geometrical information that is invariant to translations, rotations, and size changes. A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality. By allowing also isometric (or near-isometric) deformations, such as infinitesimal bending, the intrinsic geometry of the object will stay the same, while sub-parts might be located at very different positions in space.A special part of the book presents the construction of examples of unknots, as well as knots that can resist simplification by energy gradient and force evolution methods in programming models.
More details
Series
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Product notice
Laminated cover
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 21 mm
Weight
582 gr
ISBN-13
978-981-98-1945-4 (9789819819454)
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Schweitzer Classification
Persons
Author
Univ Of Illinois At Chicago, Usa
University Of Nis, Serbia
University Of Pristina In Kosovska Mitrovica, Serbia
University Of Nis, Serbia