Modeling of Curves and Surfaces with MATLAB®
R The textbookModeling of Curvesand Surfaceswith MATLAB by ProfessorVladimir Rovenski contains interesting geometrical topics with examples and exercises which illustrate solution techniques in numeric and symbolic computing and visualizing the objects. Covering many aspects of geometry and algebra, this book exposes readers to R geometrical concepts through the use of a modern computing tool — MATLAB. This work is based on the author’s previous book Geometry of Curves and Surfaces with MAPLE, but it is a greatly expanded version with new chapters and excellent chosen themes. Thebookis organizedin twoparts. The rst part coversbasictopics:graphsof fu- tions and transformations of space, classical polyhedra and non-Euclidean geometries. The second part treats curves and surfaces from the discrete avor of the rst part to the area of classical analysis including approximation and tting problems. This new edition is aimed at advanced undergraduate and postgraduate students, and can be recommended to engineers and applied mathematicians who are interested in mathematical modeling and visualization. Irina Albinsky, Ph.D. Computer Sciences and Modeling Specialist vii Preface Thistext on geometrymodelingis devotedto a numberof central geometricaltopics — graphs of functions, transformations, (non-)Euclidean geometries, curves and sur- ces — andpresentssomeelementarymethodsforanalyticalmodelingandvisualization of them. In 1872 F. Klein proposed his Erlangen Programme in which he suggested that d- ferent geometries can be studied by the properties of the groups of transformations a- ing on the geometry. The following geometries are represented in this way: Euclidean, af ne, projective, inversive, spherical, and hyperbolic.
Covers basic MATLAB® and complex geometrical modeling problems related to analysis and differential equationsProvides more than 150 stimulating exercises and problems and over 300 figures reproducible using MATLAB®Includes applications including numerous examples and exercises from a variety of real-world fields such as physics, engineering, biology, computer science, and IT