MATLAB Function Reference |

Data gridding and hypersurface fitting (dimension >= 2)

**Syntax**

**Description**

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

fits a hyper-surface of the form 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`

-D space. `y`

is of dimension `m`

-by-`1`

, representing `m`

values of the hyper-surface (`X`

). `xi`

is a vector of size `p`

-by-`n`

, representing `p`

points in the `n`

-D space whose surface value is to be fitted. `yi`

is a vector of length `p`

approximating the values (`xi`

). The hypersurface always goes through the data points (`X`

,`y`

). `xi`

is usually a uniform grid (as produced by `meshgrid`

).

```
[...] = griddatan(...,'method')
```

defines the type of surface fit to the data, where `'method'`

is one of:

`'linear'` |
Tessellation-based linear interpolation (default) |

`'nearest'` |
Nearest neighbor interpolation |

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

**Algorithm**

The `griddatan`

methods are based on a Delaunay triangulation of the data that uses Qhull [2]. This triangulation uses the Qhull joggle option (`'QJ'`

). For information about Qhull, see http://www.geom.umn.edu/software/qhull/. For copyright information, see http://www.geom.umn.edu/software/download/COPYING.html.

**See Also**

`delaunayn`

, `griddata`

, `griddata3`

, `meshgrid`

**Reference**

[1] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for
Convex Hulls," *ACM Transactions on Mathematical Software*, Vol. 22, No. 4,
Dec. 1996, p. 469-483. Available in HTML format at
http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
and in PostScript format at ftp://geom.umn.edu/pub/software/qhull-96.ps.

[2] National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.

griddata3 | gsvd |