182
two or more known values of a function. The function in this case may be known,
but in a complex form for computation. Also, the function may be unknown, but
some other information about it is known, i.e. function values on a given set of
points. It is this second case that is common in solving engineering problems and
scientific and technical tasks. For example, when measurements yield only a certain
number of function values, the so-called discrete set of points, it is necessary to
determine the approximate values of a given function at other points. Estimation,
i.e. interpolation, can be performed in one, two or three dimensions. The estimation
can be performed on the basis of known values of the observed primary variable
(autocorrelation) or with the help of the values of one or more other secondary variables in the same area. The condition is that the secondary variables are strongly
correlated with the primary variable. Also, there are several methods that include
bilinear and bicubic interpolation in two dimensions and trilinear interpolation in
three dimensions (Li et al. 2005; de Smith et al. 2009).
Many interpolation procedures and methods are used in various fields of science
and research. All these methods, i.e. interpolators, can be divided into several
categories:
• Global/local interpolators
• Exact/approximate (approximate) interpolators
• Continuous (gradual, gradual)/intermittent (unconnected, sharp) interpolators
• Stochastic/deterministic interpolators
Global interpolators define a single function that determines values for the entire
interpolation area. The change in one of the entered values is reflected in the total
display area or interpolation area. Local interpolators use an algorithm that repeats
the values of a smaller set of points relative to the whole set of point values. A
change in one of the entered values only affects the results within the local area.
Exact interpolators treat all points equally with which the interpolation is entered.
Namely, the interpolation surface passes through all points whose values are known,
i.e. advance date. Approximation interpolators are applied when there are indeterminate or unknown values of a given surface. They are applied in data sets where
there are global trends that vary slowly, overshadowed by local fluctuations, and
that vary sharply and produce certain errors (deviations) in given values. For these
reasons, the smoothing effect reduces the effect of defects on the obtained (interpolated) surface. Gradual interpolators are methods with sufficiently small elements
that are interconnected in continuity and that deviate minimally from given points.
A typical example of gradual interpolators is the moving surface method (de Smith
et al. 2009).
Intermittent approach methods involve sharp transitions and relatively rough
barriers in the interpolation process. Interpolators (methods) are based on the
concept of random variables. The interpolation surface is projected (imagined) as
one of many that have been observed, that is, which can be obtained on the basis of
known points with high probability. When it comes to deterministic methods, it
should be borne in mind that they do not use probability theory and statistics or
models of random processes (de Smith et al. 2009).
R. Šajn et al.
two or more known values of a function. The function in this case may be known,
but in a complex form for computation. Also, the function may be unknown, but
some other information about it is known, i.e. function values on a given set of
points. It is this second case that is common in solving engineering problems and
scientific and technical tasks. For example, when measurements yield only a certain
number of function values, the so-called discrete set of points, it is necessary to
determine the approximate values of a given function at other points. Estimation,
i.e. interpolation, can be performed in one, two or three dimensions. The estimation
can be performed on the basis of known values of the observed primary variable
(autocorrelation) or with the help of the values of one or more other secondary variables in the same area. The condition is that the secondary variables are strongly
correlated with the primary variable. Also, there are several methods that include
bilinear and bicubic interpolation in two dimensions and trilinear interpolation in
three dimensions (Li et al. 2005; de Smith et al. 2009).
Many interpolation procedures and methods are used in various fields of science
and research. All these methods, i.e. interpolators, can be divided into several
categories:
• Global/local interpolators
• Exact/approximate (approximate) interpolators
• Continuous (gradual, gradual)/intermittent (unconnected, sharp) interpolators
• Stochastic/deterministic interpolators
Global interpolators define a single function that determines values for the entire
interpolation area. The change in one of the entered values is reflected in the total
display area or interpolation area. Local interpolators use an algorithm that repeats
the values of a smaller set of points relative to the whole set of point values. A
change in one of the entered values only affects the results within the local area.
Exact interpolators treat all points equally with which the interpolation is entered.
Namely, the interpolation surface passes through all points whose values are known,
i.e. advance date. Approximation interpolators are applied when there are indeterminate or unknown values of a given surface. They are applied in data sets where
there are global trends that vary slowly, overshadowed by local fluctuations, and
that vary sharply and produce certain errors (deviations) in given values. For these
reasons, the smoothing effect reduces the effect of defects on the obtained (interpolated) surface. Gradual interpolators are methods with sufficiently small elements
that are interconnected in continuity and that deviate minimally from given points.
A typical example of gradual interpolators is the moving surface method (de Smith
et al. 2009).
Intermittent approach methods involve sharp transitions and relatively rough
barriers in the interpolation process. Interpolators (methods) are based on the
concept of random variables. The interpolation surface is projected (imagined) as
one of many that have been observed, that is, which can be obtained on the basis of
known points with high probability. When it comes to deterministic methods, it
should be borne in mind that they do not use probability theory and statistics or
models of random processes (de Smith et al. 2009).
R. Šajn et al.