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Titlebook: Interpolating Cubic Splines; Gary D. Knott Book 2000 Springer Science+Business Media New York 2000 Approximation.Approximation theory.Spli

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发表于 2025-3-21 19:19:57 | 显示全部楼层 |阅读模式
书目名称Interpolating Cubic Splines
编辑Gary D. Knott
视频video
概述Includes supplementary material:
丛书名称Progress in Computer Science and Applied Logic
图书封面Titlebook: Interpolating Cubic Splines;  Gary D. Knott Book 2000 Springer Science+Business Media New York 2000 Approximation.Approximation theory.Spli
描述A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi­ cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi­ nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav­ els side-by-side with the art of automobile design, sail construc
出版日期Book 2000
关键词Approximation; Approximation theory; Splines; algorithms; architecture; computer graphics; computer-aided
版次1
doihttps://doi.org/10.1007/978-1-4612-1320-8
isbn_softcover978-1-4612-7092-8
isbn_ebook978-1-4612-1320-8Series ISSN 2297-0576 Series E-ISSN 2297-0584
issn_series 2297-0576
copyrightSpringer Science+Business Media New York 2000
The information of publication is updating

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发表于 2025-3-21 21:30:54 | 显示全部楼层
Quadratic Space Curve Based Cubic Splines,Show that a quadratic space curve .(.) = . + . + . is a planar curve, and thus prove that a cubic is the lowest degree polynomial space curve which has non-zero torsion.
发表于 2025-3-22 00:33:58 | 显示全部楼层
https://doi.org/10.1007/978-1-4612-1320-8Approximation; Approximation theory; Splines; algorithms; architecture; computer graphics; computer-aided
发表于 2025-3-22 05:08:44 | 显示全部楼层
Gary D. KnottIncludes supplementary material:
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发表于 2025-3-22 18:48:01 | 显示全部楼层
Function and Space Curve Interpolation, .,…,. . in . or ., perhaps along given associated directions ., .,…, . ., with |.| ≠ 0 for . = 1, 2,…, .. Indeed, we could elaborate the interpretation of the direction vectors, .…, ., so that . = 0 would be taken to specify a sharp corner or . at ..
发表于 2025-3-22 21:53:17 | 显示全部楼层
2D-Function Interpolation, that of 2D-functional interpolation: given points of the graph of an otherwise unknown 2D-function ., we are interested in constructing another 2D-function which interpolates the given points and which serves as an estimate of the function . .
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发表于 2025-3-23 06:10:28 | 显示全部楼层
Cubic Spline Vector Space Basis Functions,φ. where α.,… , α. ∈ .. For the case of a vector space of cubic spline functions, some basis sets can be developed by focusing on a representation of the cubic polynomial spline segments as component-wise linear combinations of fixed functions.
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