# NAME

**cxLookupInterp**- interpolate lattice data at one coordinate location

**#include <cx/Lookup.h>**

int cxLookupInterp(cxLookup *lut, float *loc, void *val)

integer function cxLookupInterp(lut, loc, val)integer lutreal loc(*)<type> val

- lut
- Input lookup table structure.
- loc
- Input vector of the point location at which to look up data.
- val
- Output vector of data interpolated at location loc.

`cxLookupInterp`should take care to allocate sufficient space in val and interpret the results in the right type.

For curvilinear lattices with nCoordVar > nDim (scattered data) NAG routines are used for interpolation within the bounding box, while an error exit is returned outside the bounding box. Strictly speaking this is a combination of interpolation (for points inside the lattice domain) and extrapolation (for points outside the lattice domain but inside the bounding box). The nearest neighbor method is faster, but less accurate than, the linear method.

When using this method the function returns zero to indicate success and one if a domain error is encountered, meaning that the sample point was outside the bounding box of the lattice. The returned vals are set to zero in this case.

For curvilinear lattices with nDim = nCoordVar (structured meshes), as well as all uniform and perimeter lattices, `cxLookupInterp` interpolates data by a three step process. First, it calculates which lattice cell contains the point loc. The cell is numbered according to the zero-based default uniform coordinate system for lattices. Second, `cxLookupInterp` calculates the fractional indices of the coordinate point within the cell. These fractional indices lie between zero and one in each index dimension of the lattice. Third, `cxLookupInterp` interpolates the corner values of the chosen cell according to the fractional indices found in step two. For uniform and perimeter lattices, steps one and two are performed at the same time and step three is inexpensive.

For curvilinear lattices in this category, a k-D tree is used to partition the k-dimensional coordinate space of the lattice so that the cell identification of step one runs quickly. A Newton iteration is performed in step two to discover the fractional lattice indices which, when interpolated in the lattice's coordinate space, yield the input coordinate location loc. Finally, the fractional indices are interpolated in data space to yield the data val. Both steps one and two are more expensive for curvilinear lattices than for uniform or perimeter lattices.

When using this method, the function returns zero to indicate success and one if a domain error is encountered, meaning that the sample point was outside the coordinate space of the lattice. For domains errors in uniform and perimeter lattices, the sample point is clamped to the domain and the interpolation is performed at that clamped value. For domains errors in curvilinear lattices, the returned vals are set to zero.

Lookup tables are used to preprocess colormap information for later color lookup, for example in the `Contour` module. Lookup tables are also used in the `Interpolate` and `PickLat` modules for data interpolation, and in modules that calculate particle trajectories, such as `NAGAdvectSimple` and `NAGAdvectAnimate`.

*cxLookupCreate(3E), cxLookupInterpV(3E), cxLookupIndex(3E)*

*Last modified: Mon Nov 6 16:33:28 GMT 2000*

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