# Documentation

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# griddatan

Data gridding and hypersurface fitting (dimension ≥ 2)

## Syntax

`yi = griddatan(x,y,xi)yi = griddatan(x,y,xi,method)yi = griddatan(x,y,xi,method,options)`

## Description

`yi = griddatan(x,y,xi)` fits a hyper-surface of the form y = f(x) to the data in the (usually) nonuniformly-spaced vectors (`x`, `y`). `griddatan` interpolates this hyper-surface at the points specified by `xi` to produce `yi`. `xi` can be nonuniform.

`X` is of dimension `m`-by-`n`, representing `m` points in n-dimensional space. `y` is of dimension `m`-by-`1`, representing `m` values of the hyper-surface f(`X`). `xi` is a vector of size `p`-by-`n`, representing `p` points in the n-dimensional space whose surface value is to be fitted. `yi` is a vector of length `p` approximating the values f(`xi`). The hypersurface always goes through the data points (`X`,`y`). `xi` is usually a uniform grid (as produced by `meshgrid`).

`yi = griddatan(x,y,xi,method)` defines the type of surface fit to the data, where `'method'` is one of:

method stringDescriptionContinuity
`'linear'`Triangulation-based linear interpolation (default).C0
`'nearest'`Nearest neighbor interpolation.Discontinuous

All the methods are based on a Delaunay triangulation of the data.

If `method` is `[]`, the default `'linear'` method is used.

`yi = griddatan(x,y,xi,method,options)` specifies a cell array of strings `options` to be used in Qhull via `delaunayn`.

If `options` is `[]`, the default options are used. If `options` is `{''}`, no options are used, not even the default.

## Examples

collapse all

### Fit a Hypersurface

```X = 2*gallery('uniformdata',[5000 3],0)-1;; Y = sum(X.^2,2); d = -0.8:0.05:0.8; [y0,x0,z0] = ndgrid(d,d,d); XI = [x0(:) y0(:) z0(:)]; YI = griddatan(X,Y,XI); ```

Since it is difficult to visualize 4-D data sets, use isosurface at 0.8:

```YI = reshape(YI, size(x0)); figure p = patch(isosurface(x0,y0,z0,YI,0.8)); isonormals(x0,y0,z0,YI,p) p.FaceColor = 'blue'; p.EdgeColor = 'none'; view(3) axis equal camlight lighting phong ```