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The Handbook and Atlas of Curves describes available analytic and visual properties of plane and spatial curves. Information is presented in a unique format, with one half of the book detailing investigation tools and the other devoted to the Atlas of Plane Curves. Main definitions, formulas, and facts from curve theory (plane and spatial) are discussed.
Contains more than 1400 curves, almost three times as many as in the 1987 edition. The curves are normalized in appearance to aid making comparisons among materials. All diagrams include metric units, and many also include U.S. customary units
Broad appeal to undergraduate teachers, students, and engineers; Concise descriptions of properties of basic planar curves from different perspectives; useful handbook for software engineers; A special chapter---"Geometry on the Web"---will further enhance the usefulness of this book as an informal tutorial resource.; Good mathematical notation, descriptions of properties of lines and curves, and the illustration of geometric concepts facilitate the design of computer graphics tools and computer animation.; Video game designers, for example, will find a clear discussion and illustration of hard-to-understand trajectory design concepts.; Good supplementary text for geometry courses at the undergraduate and advanced high school levels
Practical Handbook of Curve Fitting is a reference work assembled by Arlinghaus and a set of editors with well over a century of combined experience in various disciplines and activities related to curve fitting. The book demonstrates how to analyze World data bases and graph and map the results. Default settings in software packages can produce attractive graphs of data imported into the software. Often, however, the default graph has no equation associated with it and cannot therefore be used as a tool for further analysis or projection of the data. The same software can often be used to generate curves from equations. The reader is shown directly, and in a series of steps, how to fit curves to data using Lotus 1-2-3. There are traditional unbounded curve fitting techniques-lines of least squares, exponentials, logistic curves, and Gompertz curves. There is the bounded curve fitting technique of cubic spline interpolation. Beyond these, there is a detailed application of Feigenbaum's graphical analysis from chaos theory, and there is a hint as to how fractal geometry might come into play. Curve fitting algorithms take on new life when they are actually used on real-world data. They are used in numerous worked examples drawn from electronic data bases of public domain information from the Stars data base of The World Bank and from the WRD data base of the World Resources Institute. The applications are current and reflect a state-of-the-art interest in the human dimensions of global change.
Contains more than 500 fatigue curves for industrial ferrous and nonferrous alloys. Also includes an explanation of fatigue testing and interpretation of test results. Each curve is presented independently and includes an explanation of its particular importance.
Computers are now being used virtually everywhere in arts, drafting, and design to generate curves and surfaces ranging from the elementary to the intricate. Practical Handbook of Curve Design and Generation is a ready reference that presents the basic mathematics of curves in a complete, clear manner that enables you to apply the material to your own work with minimum effort. By knowing how curves are mathematically generated and how their shape is controlled, you can more fully exploit available computer tools, modify these tools themselves, and provide input for others to modify them. It will also help you to identify mathematical equations required to produce specific curves. The book does not require a heavy mathematical background-if you understand elementary algebra and trigonometry, you can fully apply the material presented. Essential mathematical concepts are repeated in the book to reinforce your knowledge of those topics. Featuring some 300 graphic examples, the book is organized so that early chapters cover fundamental polynomial, trigonometric, and exponential forms. The mathematical transformation of curves is then treated in order to give you a general approach for modifying known curves. Later chapters introduce complex curves that can be composed from the building blocks presented in earlier chapters. The final chapters cover interesting ideas in space curves and in surfaces.