Methods of Shape-Preserving Spline Approximation

Non-uniform exponential tension splines

“…, l. In many applications tension splines of class C 1 [19,20] or C 2 [19,21] are used. C 2 exponential tension splines also belong to the class of generalized tension B-splines as defined in [17]. Next to these two spline spaces, we will also observe tension splines that are of class C 1 , and have continuous second generalized derivative at the joining points x i instead of the second ordinary derivative.…”

“…Fort = t i we just taket → t + i , whenever it appears in the algorithm (17). For f ∈ S(4, dσ , T) andt ∈ (t i , t i+1 ), the algorithm becomes (see [5]):…”

“…to remove extraneous inflections, find monotone or convex interpolant to monotone or convex data etc. ; see [17] for recent references. There is some arbitrariness in the choice of tension parameters, and typically these applications do not require extra precision, some not even making use of the B-spline representation.…”

“…The same is true for CAGD applications, which exploit the fact that tension curve approaches control polygon by adding some tension to a cubic spline curve. The words Tension spline and Tension methods are today used in broader sense for any system of functions allowing interpolation problem to be solved, and possessing some parameters which can be determined to obtain desired approximation properties; see [17] for a list of references. Here, we consider the classical case, and the word 'tension spline' will be henceforth used for exponential (sometimes also called hyperbolic) tension spline only.…”

Development of vector-parametric fifth-degree B-spline with control points incident the surface

“…Работа является логическим продолжением иссле-дований [4][5][6][7][8][9][10][11][12][13][14][15]. Автор статьи планирует продолжить данные исследования, ввиду их очевидной полезности потребителям.…”