Interpolating Cubic Splines

ยท Progress in Computer Science and Applied Logic แƒฌแƒ˜แƒ’แƒœแƒ˜ 18 ยท Springer Science & Business Media
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2 แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ
แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜
244
แƒ’แƒ•แƒ”แƒ แƒ“แƒ˜
แƒ แƒ”แƒ˜แƒขแƒ˜แƒœแƒ’แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜ แƒ“แƒแƒฃแƒ“แƒแƒกแƒขแƒฃแƒ แƒ”แƒ‘แƒ”แƒšแƒ˜แƒ ย แƒจแƒ”แƒ˜แƒขแƒงแƒ•แƒ”แƒ— แƒ›แƒ”แƒขแƒ˜

แƒแƒ› แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

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 construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

แƒจแƒ”แƒคแƒแƒกแƒ”แƒ‘แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜

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2 แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ

แƒจแƒ”แƒแƒคแƒแƒกแƒ”แƒ— แƒ”แƒก แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜

แƒ’แƒ•แƒ˜แƒ—แƒฎแƒแƒ แƒ˜แƒ— แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒแƒ–แƒ แƒ˜.

แƒ˜แƒœแƒคแƒแƒ แƒ›แƒแƒชแƒ˜แƒ แƒฌแƒแƒ™แƒ˜แƒ—แƒฎแƒ•แƒแƒกแƒ—แƒแƒœ แƒ“แƒแƒ™แƒแƒ•แƒจแƒ˜แƒ แƒ”แƒ‘แƒ˜แƒ—

แƒกแƒ›แƒแƒ แƒขแƒคแƒแƒœแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒขแƒแƒ‘แƒšแƒ”แƒขแƒ”แƒ‘แƒ˜
แƒ“แƒแƒแƒ˜แƒœแƒกแƒขแƒแƒšแƒ˜แƒ แƒ”แƒ— Google Play Books แƒแƒžแƒ˜ Android แƒ“แƒ iPad/iPhone แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜แƒกแƒ—แƒ•แƒ˜แƒก. แƒ˜แƒก แƒแƒ•แƒขแƒแƒ›แƒแƒขแƒฃแƒ แƒแƒ“ แƒ’แƒแƒœแƒแƒฎแƒแƒ แƒชแƒ˜แƒ”แƒšแƒ”แƒ‘แƒก แƒกแƒ˜แƒœแƒฅแƒ แƒแƒœแƒ˜แƒ–แƒแƒชแƒ˜แƒแƒก แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒแƒœแƒ’แƒแƒ แƒ˜แƒจแƒ—แƒแƒœ แƒ“แƒ แƒกแƒแƒจแƒฃแƒแƒšแƒ”แƒ‘แƒแƒก แƒ›แƒแƒ’แƒชแƒ”แƒ›แƒ—, แƒฌแƒแƒ˜แƒ™แƒ˜แƒ—แƒฎแƒแƒ— แƒกแƒแƒกแƒฃแƒ แƒ•แƒ”แƒšแƒ˜ แƒ™แƒแƒœแƒขแƒ”แƒœแƒขแƒ˜ แƒœแƒ”แƒ‘แƒ˜แƒกแƒ›แƒ˜แƒ”แƒ  แƒแƒ“แƒ’แƒ˜แƒšแƒแƒก, แƒ แƒแƒ’แƒแƒ แƒช แƒแƒœแƒšแƒแƒ˜แƒœ, แƒ˜แƒกแƒ” แƒฎแƒแƒ–แƒ’แƒแƒ แƒ”แƒจแƒ” แƒ แƒ”แƒŸแƒ˜แƒ›แƒจแƒ˜.
แƒšแƒ”แƒžแƒขแƒแƒžแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ”แƒ‘แƒ˜
Google Play-แƒจแƒ˜ แƒจแƒ”แƒซแƒ”แƒœแƒ˜แƒšแƒ˜ แƒแƒฃแƒ“แƒ˜แƒแƒฌแƒ˜แƒ’แƒœแƒ”แƒ‘แƒ˜แƒก แƒ›แƒแƒกแƒ›แƒ”แƒœแƒ แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ˜แƒก แƒ•แƒ”แƒ‘-แƒ‘แƒ แƒแƒฃแƒ–แƒ”แƒ แƒ˜แƒก แƒ’แƒแƒ›แƒแƒงแƒ”แƒœแƒ”แƒ‘แƒ˜แƒ— แƒจแƒ”แƒ’แƒ˜แƒซแƒšแƒ˜แƒแƒ—.
แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒกแƒฎแƒ•แƒ แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜
แƒ”แƒšแƒ”แƒฅแƒขแƒ แƒแƒœแƒฃแƒšแƒ˜ แƒ›แƒ”แƒšแƒœแƒ˜แƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ–แƒ” แƒฌแƒแƒกแƒแƒ™แƒ˜แƒ—แƒฎแƒแƒ“, แƒ แƒแƒ’แƒแƒ แƒ˜แƒชแƒแƒ Kobo eReaders, แƒ—แƒฅแƒ•แƒ”แƒœ แƒฃแƒœแƒ“แƒ แƒฉแƒแƒ›แƒแƒขแƒ•แƒ˜แƒ แƒ—แƒแƒ— แƒคแƒแƒ˜แƒšแƒ˜ แƒ“แƒ แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒแƒ— แƒ˜แƒ’แƒ˜ แƒ—แƒฅแƒ•แƒ”แƒœแƒก แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒแƒจแƒ˜. แƒ“แƒแƒฎแƒ›แƒแƒ แƒ”แƒ‘แƒ˜แƒก แƒชแƒ”แƒœแƒขแƒ แƒ˜แƒก แƒ“แƒ”แƒขแƒแƒšแƒฃแƒ แƒ˜ แƒ˜แƒœแƒกแƒขแƒ แƒฃแƒฅแƒชแƒ˜แƒ”แƒ‘แƒ˜แƒก แƒ›แƒ˜แƒฎแƒ”แƒ“แƒ•แƒ˜แƒ— แƒ’แƒแƒ“แƒแƒ˜แƒขแƒแƒœแƒ”แƒ— แƒคแƒแƒ˜แƒšแƒ”แƒ‘แƒ˜ แƒ›แƒฎแƒแƒ แƒ“แƒแƒญแƒ”แƒ แƒ˜แƒš แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ–แƒ”.

แƒกแƒ”แƒ แƒ˜แƒ˜แƒก แƒ’แƒแƒ’แƒ แƒซแƒ”แƒšแƒ”แƒ‘แƒ

แƒ›แƒกแƒ’แƒแƒ•แƒกแƒ˜ แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ”แƒ‘แƒ˜