Custom cover image
Modeling of Curves and Surfaces with MATLAB® / by Vladimir Rovenski
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Undergraduate Texts in Mathematics and Technology ; 7 | SpringerLink BücherPublisher: New York, NY : Springer Science+Business Media, LLC, 2010Description: Online-Ressource (XV, 452p. 156 illus, digital)ISBN:- 9780387712789
- 1280390891
- 9781280390890
- 516
- 516.36 23
- 516.00285/53 23
- QA440-699
- QA448.D38
Contents:
Summary: Functions and Transformations -- Functions and Graphs -- Rigid Motions (Isometries) -- Affine and Projective Transformations -- Möbius Transformations -- Curves and Surfaces -- Examples of Curves -- Geometry of Curves -- Geometry of Surfaces -- Examples of Surfaces -- Piecewise Curves and Surfaces.Summary: This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors, transformations using matrices, and then studies more complex geometrical modeling problems related to analysis of curves and surfaces. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text greatly extends the author’s previous title, Geometry of Curves and Surfaces with Maple (Birkhäuser, © 2000), and has a different focus. In addition to being applications driven and motivated by numerous examples and exercises from real-world fields, the book also contains over 60 percent new material, including new sections with complex numbers, quaternions, matrices and transformations, hyperbolic geometry, fractals, and surface-splines and over 300 figures reproducible using MATLAB® programs. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines, engineers, computer scientists, and instructors of applied mathematics.PPN: PPN: 1649889763Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Modeling of Curves and Surfaces with MATLAB ""; ""Dedication ""; ""Foreword""; ""Preface""; ""Contents ""; ""Part I Functions and Transformations""; ""1 Functions and Graphs""; ""1.1 Numbers""; ""1.1.1 Integers, rationals, and reals""; ""1.1.2 Complex numbers""; ""1.1.3 Quaternions""; ""1.2 Elementary and Special Functions""; ""1.2.1 Plotting in two dimensions""; ""1.2.2 Plotting graphs""; ""1.2.3 Elementary functions""; ""1.2.4 Special functions""; ""1.3 Piecewise Functions""; ""1.3.1 Piecewise constant and linear functions""; ""1.3.2 The functions max and min""
""1.3.3 Functions containing the operation abs""""1.3.4 Functions that are defined using limit""; ""1.3.5 Statistical functions""; ""1.4 Graphs in Polar Coordinates""; ""1.4.1 Basic plots in polar coordinates""; ""1.4.2 Remarkable curves""; ""1.4.3 Spirals""; ""1.4.4 Roses and crosses""; ""1.5 Polynomial Interpolation of Functions""; ""1.5.1 Representation of polynomials""; ""1.5.2 Lagrange polynomials""; ""1.5.3 Hermite polynomial""; ""1.5.4 Least-squares analysis""; ""1.6 Spline Interpolation of Functions""; ""1.6.1 Cubic spline""; ""1.6.2 Construction of curves using splines""
""1.6.3 Extremal property of a cubic spline""""1.7 Two-Dimensional Interpolation and Smoothing""; ""1.7.1 Two-dimensional interpolation""; ""1.7.2 Two-dimensional smoothing""; ""1.7.3 Extremal property of a bicubic spline""; ""1.8 Exercises""; ""2 Rigid Motions (Isometries)""; ""2.1 Vectors""; ""2.1.1 Vectors in bold0mu mumu RRdottedRRRR3""; ""2.1.2 Lines and conics""; ""2.2 Rigid Motions in Rn""; ""2.2.1 Rigid motions in two dimensions""; ""2.2.2 Rotations and reflections in planes of R3""; ""2.2.3 Rotations and reflections using quaternions""; ""2.3 Sphere""
""2.3.1 Spherical transformations""""2.3.2 Stereographic projection""; ""2.4 Polyhedra""; ""2.4.1 What is a polyhedron?""; ""2.4.2 Platonic solids""; ""2.4.3 Symmetries of regular polygons and polyhedra""; ""2.4.4 Star-shaped polyhedra""; ""2.4.5 Archimedean solids""; ""2.5 Appendix: Matrices and Groups""; ""2.5.1 Permutations and group actions""; ""2.5.2 Matrices and linear transformations""; ""2.6 Exercises""; ""3 Affine and Projective Transformations""; ""3.1 Affine Transformations""; ""3.1.1 Affine transformations in two and three dimensions""; ""3.1.2 Parallel projections""
""3.1.3 Convex hull and Delaunay triangulation""""3.2 Projective Transformations""; ""3.2.1 Homogeneous coordinates""; ""3.2.2 Duality and cross-ratio""; ""3.2.3 Projective transformations of RP2""; ""3.3 Transformations in Homogeneous Coordinates""; ""3.3.1 Transformations in two dimensions""; ""3.3.2 Transformations in three dimensions""; ""3.4 Exercises""; ""4 Möbius Transformations""; ""4.1 Inversive Geometry""; ""4.1.1 Reflection in a sphere""; ""4.1.2 Inversive geometry of a plane""; ""4.2 Möbius Transformations""; ""4.2.1 Möbius transformations in two dimensions""
""4.2.2 Möbius transformations in three dimensions""
No physical items for this record