DQUAD returns a double quadratic interpolated value in two or more dimensions
Arguments
The function y is defined as
y = DQUAD(1, 2, "XC", "YC", x, 1)
With the following Telitab set in the Data slot:
For x = 2.5, this relation returns
y=6.25
NOTE: In case you apply the symbolic addressing of the columns for the description of the point on the curve or surface to compute the differential for, e.g. "Par_x" and "Par_y", please make sure that your Telitab set contains these names. If not, an error message is generated and the calculation is stopped.
Interpolation in more dimensions
In addition to traditional two-dimensional interpolation it is also possible to perform matrix (n-dimensional) interpolation. In that case, a special Telitab set definition format can be applied, clarified by the following example which is an interpolation in a matrix of draft and speed:
The interpolation of resistance "R-TOT" is in a sense performed in the 'inward out' direction: first R-TOT on VS, then R-TOT for fixed VS on DRAFT.
The expression is the following:
R_TOT=DQUAD(1, 3, "DRAFT", "VS", "R-TOT", Draft, Vs)
And the dataslot containing:
For Draft=5.6 m and Vs=11.8 m/s, the function returns
R-TOT=12400 N
The matrix interpolation can be applied in all except Method 2, obviously not in Method 2 since only x,y data points are provided in that case.
In direct definition, the points needed for interpolation are stated in the Relation itself. This method can only be used for 2D interpolation. The syntax is
DQUAD( Pno%, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, Xint, [DirivNo%=1])
If Pno%=0 then all x_i and y_i values should be numeric expressions. The minimum number of x,y data points Npoints% in the list is 2 in which case the interpolation (and differentiation) is performed linear. Let y be a function defined by
y = DIFF(0, 4, 1, 1, 2, 4, 3, 9, 4, 16, x, 1)
For x=2.5, this equation returns
y=6.25
These methods are similar to syntax 1, for information on how to acces the TeLiTab data with those methods see: TeLiTab access.
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