Discovering Curves and Surfaces with Maple(r)

ISBN-13: 9780387948904 / Angielski / Twarda / 1997 / 217 str.

G. Klimek; Grazyna Klimek; Maciej Klimek

Opis

Despite the fact that Maple V has become one of the most popular computer algebra systems on the market, surprisingly few users realize its potential in the field of scientific visualization. The purpose of this book is to equip the reader with a variety of graphics tools needed on the voyage of discovery into the complex and often beautiful world of curves and surfaces. A comprehensive treatment of Maple's graphics commands and structures is combined with an introduction to the main aspects of visual perception. Top priority is given to the use of light, color, perspective, and geometric transformations. Numerous examples, accompanied by pictures (many in color), cover all aspects of Maple graphics. The examples can be easily customized to suit the individual needs of the reader. The approach is context independent, and as such will appeal to students, educators, and researchers in a broad spectrum of scientific disciplines. For the general user at any level of experience, this book can serve as a comprehensive reference manual. For the beginner, it offers a user- friendly elementary introduction to the subject, with mathematical requirements kept to a minimum. For those interested in advanced mathematical visualization, it explains how to maximize Maple's graphical capabilities. In particular, this book shows how to turn Maple into an excellent modeling tool capable of generating elaborate surfaces that conventional modelers cannot produce. These surfaces can be exported to an external ray tracer (e.g. POV-ray) for sophisticated photo-realistic rendering. All of the Maple code segments which are presented in the book, as well as high-resolution pictures showing alternative renderings of some of the book's color plates, are included on the accompanying DOS diskette.

Spis treści

1. Maple Preliminaries.- 1.1 General Comments.- 1.2 Basic Plots.- 1.3 Accessing Plotting Structures.- 2. Two-Dimensional Plots.- 2.1 Basic Graphs.- 2.2 Additional Options.- 2.3 Maps of Surfaces.- 3. Geometric Manipulation.- 3.1 Affine Transformations in Two Dimensions.- 3.2 Affine Transformations in Three Dimensions.- 3.3 Coordinate Systems.- 3.4 Perspective.- 3.5 Shadow and Radial Projections.- 3.6 Matrix Notation.- 3.7 General Transformations of Plots.- 4. Three-Dimensional Plots.- 4.1 Basic Three-Dimensional Plots.- 4.2 Overview of Plotting Options.- 4.3 Color.- 4.4 Lighting.- 4.5 PLOT and PLOT3D Data Structures.- 4.6 Examples.- 5. Functions and Procedures.- 5.1 Elementary Functions.- 5.2 Graphics and Functions.- 5.3 Procedures.- 5.4 Interpolation.- 5.5 Iteration and Fractals.- 5.6 Mixing Curves and Surfaces.- 6. Animations.- 6.1 Overview of Animation Commands.- 6.2 Animations in Two-Dimensions.- 6.3 Animations in Three-Dimensions.- 7. The plottools Package.- 7.1 The plottools Objects.- 7.2 Plot Transformations.- 8. Specialized Graphics.- 8.1 Graphing Complex Functions.- 8.2 Differential Equations.- 8.3 Miscellaneous Commands.- 9. Saving and Exporting Maple Graphics.- 9.1 Saving, Editing, and Printing.- 9.2 External Rendering and Ray Tracing.