Data gridding and hypersurface fitting (dimension ≥ 2)

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

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

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

`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 string | Description | Continuity |
---|---|---|

`'linear'` | Triangulation-based linear interpolation (default). | C^{0} |

`'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.

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