This is commonly used in Image Registration by the use of B-Spline functions and in solid mechanics with finite element basis.
2.
In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter " t ".
3.
In Figure 2 the spline function consisting of the two cubic polynomials q _ 1 ( x ) and q _ 2 ( x ) given by ( ) is displayed
4.
Optimal spline functions of degrees 3-7 inclusive, based on symmetric arrangements of 5, 6, and 7 knots, have been computed and the method was applied for smoothing and differentiation of spectroscopic curves.
5.
Finally, in order to achieve tracking quality, the values are in most commercial applications smoothed by a spline smoothing function along the ROI, so the regional measurements are not pure regional, but rather to a degree, spline functions of the global average.
6.
The quadratic spline function used to model the macromelodic component is defined by a sequence of target points, ( couples each pair of which is linked by two monotonic parabolic curves with the spline knot occurring ( by default ) at the midway point between the two targets.
7.
:: : True, the distribution of rainfall recording stations is extremely non-uniform, but those clever blokes at the Met Bureau know a bit of mathematics, and have fitted the observations with a 3-D spline function on a roughly 2.5 km grid, from which they generate the rainfall maps.
8.
In order to achieve sufficient tracking quality when single markers are used, however commercial algorithms very often resort to varieties of spline smoothing using available information from the strongest echoes, very oft the mitral annulus, so the regional measurements are not pure regional, but rather to a degree, spline functions of the global average.
9.
In indirect fourier transformation, a " D max " is defined and an initial distance distribution function p _ i ( r ) is expressed as a sum of " N " cubic spline functions \ phi _ i ( r ) evenly distributed on the interval ( 0, " D max " ):
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