Calculates the coefficients of the bicubic interpolation polynomial for the rectangular grid cell under consideration.
Given arrays dataPoints, derivatives1stDirection,
derivatives2ndDirection and crossDerivatives,
each of length 4 contain the function, gradients parallel to the
grid axis, and the cross derivatives evaluated at the four grid points of a
rectangular grid cell. The first element of the array corresponds the values at the
lower left (when viewed from above) grid point, with the remaining second, third and
fourth elements of the array's consecutively assigned to the other points in
counter clockwise direction.
Given lengthGrid1stDirection and lengthGrid2ndDirection,
the lengths of the grid cell in the 1st and 2nd directions, this method returns a
array of dimension 2 of length 4, where each of the four
arrays also have length 4 (i.e. a 4 by 4 matrix).
The 2 dimensional array coeff[i][j] contains the coefficients
in the bicubic polynomial of the grid cell under consideration in accordance with
the following convention:
f(x,y) = (coeff[3][0] * y3) + (coeff[3][1] * y3 * x) + ... + (coeff[3][3] * y3 * x3) +
.... + coeff[0][0] + (coeff[0][1] * x) + ... + (coeff[0][3] * x3)
where the variable x is the coordinate value in the 1st direction, and the
variable y is the coordinate values in the 2nd direction where the
origin is at the grid point at the lower left corner of the grid cell considered. Recall
that this grid point is also the point at which the first elements of each of the arrays
dataPoints, derivatives1stDirection, derivatives2ndDirection
and crossDerivatives; correspond to.
Inter Class | Interpolation Namespace | BicubicInterpolation(double[],...) evaluates the values and derivatives of a bicubic polynomial taken the bicubic polynomials coefficients are a parameter.