Interpolating Cubic Splines

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Gary D. Knott

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Approximation theory computer-aided design

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"Spline functions arise in a number of fields: statistics, computer graphics, programming, computer-aided design technology, numerical analysis, and other areas of applied mathematics. Much work has focused on approximating splines such as B-splines and Bezier splines. In contrast, this book emphasizes interpolating splines. Almost always, the cubic polynomial form is treated in depth. Interpolating Cubic Splines covers a wide variety of explicit approaches to designing splines for the interpolation of points in the plane by curves, and the interpolation of points in 3-space by surfaces. These splines include various estimated-tangent Hermite splines and double-tangent splines, as well as classical natural splines and geometrically-continuous splines such as beta-splines and n-splines. A variety of special topics are covered, including monotonic splines, optimal smoothing splines, basis representations, and exact energy-minimizing physical splines. An in-depth review of the differential geometry of curves and a broad range of exercises, with selected solutions, and complete computer programs for several forms of splines and smoothing splines, make this book useful for a broad audience: students, applied mathematicians, statisticians, engineers, and practicing programmers involved in software development in computer graphics, CAD, and various engineering applications."--Zentralblatt Math
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