MATLAB Function Reference |

**Syntax**

surf(Z) surf(X,Y,Z) surf(X,Y,Z,C) surf(...,'

*PropertyName*',PropertyValue) surfc(...) h = surf(...) h = surfc(...)

**Description**

Use `surf`

and `surfc`

to view mathematical functions over a rectangular region. `surf`

and `surfc`

create colored parametric surfaces specified by `X`

, `Y`

, and `Z`

, with color specified by `Z`

or `C`

.

```
surf(Z)
```

creates a a three-dimensional shaded surface from the *z* components in matrix `Z`

, using `x`

`=`

`1:n`

and `y`

`=`

`1:m`

, where `[m,n] = size(Z)`

. The height, `Z`

, is a single-valued function defined over a geometrically rectangular grid. `Z`

specifies the color data as well as surface height, so color is proportional to surface height.

```
surf(X,Y,Z)
```

creates a shaded surface using `Z`

for the color data as well as surface height. `X`

and `Y`

are vectors or matrices defining the *x* and *y* components of a surface. If `X`

and `Y`

are vectors, `length(X)`

`=`

`n`

and `length(Y)`

`=`

`m`

, where `[m,n]`

`=`

`size(Z)`

. In this case, the vertices of the surface faces are `triples. `

```
surf(X,Y,Z,C)
```

creates a shaded surface, with color defined by `C`

. MATLAB performs a linear transformation on this data to obtain colors from the current colormap.

specifies surface properties along with the data.`surf(...,'`

PropertyName```
',PropertyValue)
```

```
surfc(...)
```

draws a contour plot beneath the surface.

```
h = surf(...) and h = surfc(...)
```

return a handle to a surface graphics object.

**Algorithm**

Abstractly, a parametric surface is parametrized by two independent variables, `i`

and `j`

, which vary continuously over a rectangle; for example, `1`

`i`

`m`

and `1`

`j`

`n`

. The three functions, `x(i,j)`

, `y(i,j)`

, and `z(i,j),`

specify the surface. When `i`

and `j`

are integer values, they define a rectangular grid with integer grid points. The functions `x(i,j)`

, `y(i,j)`

, and `z(i,j)`

become three `m`

-by-`n`

matrices, `X`

, `Y`

and `Z`

. surface color is a fourth function, `c(i,j)`

, denoted by matrix `C`

.

Each point in the rectangular grid can be thought of as connected to its four nearest neighbors.

This underlying rectangular grid induces four-sided patches on the surface. To express this another way, `[X(:)`

`Y(:)`

`Z(:)]`

returns a list of triples specifying points in 3-space. Each interior point is connected to the four neighbors inherited from the matrix indexing. Points on the edge of the surface have three neighbors; the four points at the corners of the grid have only two neighbors. This defines a mesh of quadrilaterals or a *quad-mesh*.

Surface color can be specified in two different ways - at the vertices or at the centers of each patch. In this general setting, the surface need not be a single-valued function of `x`

and `y`

. Moreover, the four-sided surface patches need not be planar. For example, you can have surfaces defined in polar, cylindrical, and spherical coordinate systems.

The `shading`

function sets the shading. If the shading is `interp`

, `C`

must be the same size as `X`

, `Y`

, and `Z`

; it specifies the colors at the vertices. The color within a surface patch is a bilinear function of the local coordinates. If the shading is `faceted`

(the default) or `flat`

, `C(i,j) `

specifies the constant color in the surface patch:

In this case, `C`

can be the same size as `X`

, `Y`

, and `Z`

and its last row and column are ignored, Alternatively, its row and column dimensions can be one less than those of `X`

, `Y`

, and `Z`

.

The `surf`

and `surfc`

functions specify the view point using `view(3)`

.

The range of `X`

, `Y`

, and `Z`

, or the current setting of the axes `XLimMode`

, `YLimMode`

, and `ZLimMode`

properties (also set by the `axis`

function) determine the axis labels.

The range of `C`

, or the current setting of the axes `CLim`

and `ClimMode`

properties (also set by the `caxis`

function) determine the color scaling. The scaled color values are used as indices into the current colormap.

**Examples**

Display a surface and contour plot of the `peaks`

surface.

Color a sphere with the pattern of +1s and -1s in a Hadamard matrix.

k = 5; n = 2^k-1; [x

`,`

y`,`

z] =`sphere`

(n); c =`hadamard`

(2^k); surf(x`,`

y`,`

z`,`

c); colormap([1 1 0; 0 1 1]) axis equal

**See Also**

`axis`

, `caxis`

, `colormap`

, `contour`

, `delaunay`

, `mesh`

, `pcolor`

, `shading`

, `trisurf`

, `view`

Properties for surface graphics objects

Creating Surfaces and Meshes for related functions

Representing a Matrix as a Surface for more examples

Coloring Mesh and Surface Plots for information about how to control the coloring of surfaces

support | surf2patch |