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Further Examples: ListInterpolation

ListInterpolation is similar to Interpolation, but provides a more convenient interface for data that does not include coordinates and for multidimensional data.

Here is a table of values of a function on a regular three dimensional grid.

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This constructs an approximate function that represents these values. There is not enough data in the z direction (only z = 0 and z = 1) for a higher order approximation, so the order in that direction is reduced automatically. (The order can be reduced manually; in this case by setting the option InterpolationOrder to {3,3,1}.)

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The approximation reproduces the values at each of the points in the table.

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You can get approximate values at other points. In this case, the interpolation is a fairly good approximation to the function.

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Here values and derivatives specified at the points , , and . There is not enough data to construct a third order (cubic) polynomial in either the x or the y direction, so the (default) interpolation order of is reduced automatically.

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Again, the given values are represented by the approximate function.

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The given derivatives are also represented.

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Where the derivative was given by Automatic, it is computed automatically by the interpolation.

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You can also get approximate values at other points.

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Let's clean up by getting rid of the symbols defined in these examples.

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