# Documentation

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# fmesh

## Syntax

``fmesh(f)``
``fmesh(f,xyinterval)``
``fmesh(funx,funy,funz)``
``fmesh(funx,funy,funz,uvinterval)``
``fmesh(___,LineSpec)``
``fmesh(___,Name,Value)``
``fmesh(ax,___)``
``fs = fmesh(___)``

## Description

example

````fmesh(f)` creates a mesh plot of the expression `z = f(x,y)` over the default interval `[-5 5]` for `x` and `y`.```

example

````fmesh(f,xyinterval)` plots over the specified interval. To use the same interval for both `x` and `y`, specify `xyinterval` as a two-element vector of the form `[min max]`. To use different intervals, specify a four-element vector of the form ```[xmin xmax ymin ymax]```.```

example

````fmesh(funx,funy,funz)` plots the parametric mesh defined by `x = funx(u,v)`, ```y = funy(u,v)```, `z = funz(u,v)` over the default interval `[-5 5]` for `u` and `v`.```
````fmesh(funx,funy,funz,uvinterval)` plots the parametric mesh over the specified interval. To use the same interval for both `u` and `v`, specify `uvinterval` as a two-element vector of the form `[min max]`. To use different intervals, specify a four-element vector of the form ```[umin umax vmin vmax]```.```
````fmesh(___,LineSpec)` sets the line style, marker symbol, and color of the mesh. For example, `'-r'` specifies red lines. Use this option after any of the previous input argument combinations.```

example

````fmesh(___,Name,Value)` specifies properties of the mesh using one or more name-value pair arguments. Use this option with any of the input argument combinations in the previous syntaxes.```
````fmesh(ax,___)` plots into the axes specified by `ax` instead of the current axes `gca`.```
````fs = fmesh(___)` returns a `FunctionSurface` object or a `ParameterizedFunctionSurface` object, depending on the inputs. Use `fs` to query and modify properties of a specific surface. For a list of properties, see FunctionSurface Properties or ParameterizedFunctionSurface Properties.```

## Examples

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Plot a mesh of the input over the default interval and .

`fmesh(@(x,y) sin(x)+cos(y))`

Plot the parameterized mesh

for and . Make the mesh partially transparent using `alpha`.

```r = @(s,t) 2 + sin(7.*s + 5.*t); x = @(s,t) r(s,t).*cos(s).*sin(t); y = @(s,t) r(s,t).*sin(s).*sin(t); z = @(s,t) r(s,t).*cos(t); fmesh(x,y,z,[0 2*pi 0 pi])```

`alpha(0.8)`

Plot the piecewise input

over the interval

Specify the plotting interval as the second argument of `fmesh`. When you plot multiple inputs over different intervals in the same axes, the axis limits adjust to include all the data.

```fmesh(@(x,y) erf(x)+cos(y),[-5 0 -5 5]) hold on fmesh(@(x,y) sin(x)+cos(y),[0 5 -5 5]) hold off```

Create a mesh plot using red lines.

`fmesh(@(x,y) sin(x)+cos(y),'EdgeColor','red')`

## Input Arguments

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3-D function to plot, specified as a function handle to a named or anonymous function.

Specify a function of the form `z = f(x,y)`. The function must accept two matrix input arguments and return a matrix output argument of the same size. Use array operators instead of matrix operators for the best performance. For example, use `.*` (`times`) instead of * (`mtimes`).

Example: `f = @(x,y) sin(x) + cos(y);`

Plotting interval for `x` and `y`, specified in one of these forms:

• Vector of form `[min max]` — Use the interval `[min max]` for both `x` and `y`

• Vector of form `[xmin xmax ymin ymax]` — Use the interval `[xmin xmax]` for `x` and ```[ymin ymax]``` for `y`.

Parametric function for x coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form `x = funx(u,v)`. The function must accept two matrix input arguments and return a matrix output argument of the same size. Use array operators instead of matrix operators for the best performance. For example, use `.*` (`times`) instead of * (`mtimes`).

Example: `funx = @(u,v) u.*sin(v);`

Parametric function for y coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form `y = funy(u,v)`. The function must accept two matrix input arguments and return a matrix output argument of the same size. Use array operators instead of matrix operators for the best performance. For example, use `.*` (`times`) instead of * (`mtimes`).

Example: `funy = @(t) @(u,v) -u.*cos(v);`

Parametric function for z coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form `z = funz(u,v)`. The function must accept two matrix input arguments and return a matrix output argument of the same size. Use array operators instead of matrix operators for the best performance. For example, use `.*` (`times`) instead of * (`mtimes`).

Example: `funz = @(u,v) v;`

Plotting interval for `u` and `v`, specified in one of these forms:

• Vector of form `[min max]` — Use the interval `[min max]` for both `u` and `v`.

• Vector of form `[umin umax vmin vmax]` — Use the interval `[umin umax]` for `u` and ```[vmin vmax]``` for `v`.

Axes object. If you do not specify an axes object, then `fmesh` uses the current axes.

Line specification, specified as a character vector or string with a line style, marker, and color. The elements can appear in any order, and you can omit one or more options. To show only markers with no connecting lines, specify a marker and omit the line style.

Example: `'r--o'` specifies a red color, a dashed line, and circle markers

Line Style SpecifierDescription
`-`Solid line (default)
`--`Dashed line
`:`Dotted line
`-.`Dash-dot line
Marker SpecifierDescription
`o`Circle
`+`Plus sign
`*`Asterisk
`.`Point
`x`Cross
`s`Square
`d`Diamond
`^`Upward-pointing triangle
`v`Downward-pointing triangle
`>`Right-pointing triangle
`<`Left-pointing triangle
`p`Pentagram
`h`Hexagram
Color SpecifierDescription

`y`

yellow

`m`

magenta

`c`

cyan

`r`

red

`g`

green

`b`

blue

`w`

white

`k`

black

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`' '`). You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `'Marker','o','MarkerFaceColor','red'`

The properties listed here are only a subset. For a full list, see FunctionSurface Properties.

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Number of evaluation points per direction, specified as a number. The default is `35`. Because `fmesh` objects use adaptive evaluation, the actual number of evaluation points is greater.

Example: `100`

Display contour plot under plot, specified as `'off'` (default) or `'on'`.

Line color, specified as `'interp'`, an RGB triplet, or one of the color options listed in the table. The default value of `'interp'` colors the edges based on the `ZData` property values.

For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, `[0.4 0.6 0.7]`. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
`'red'` or `'r'`Red`[1 0 0]`
`'green'` or `'g'`Green`[0 1 0]`
`'blue'` or `'b'`Blue`[0 0 1]`
`'yellow'` or `'y'`Yellow`[1 1 0]`
`'magenta'` or `'m'`Magenta`[1 0 1]`
`'cyan'` or `'c'`Cyan`[0 1 1]`
`'white'` or `'w'`White`[1 1 1]`
`'black'` or `'k'`Black`[0 0 0]`
`'none'`No colorNot applicable

Example: `'blue'`

Example: ```[0 0 1]```

Line style, specified as one of the line styles listed in this table.

Line StyleDescriptionResulting Line
`'-'`Solid line

`'--'`Dashed line

`':'`Dotted line

`'-.'`Dash-dotted line

`'none'`No lineNo line

Line width, specified as a positive value in points. If the line has markers, then the line width also affects the marker edges.

Example: `0.75`

Marker symbol, specified as one of the values in this table. By default, a line does not have markers. Add markers at selected points along the line by specifying a marker.

ValueDescription
`'o'`Circle
`'+'`Plus sign
`'*'`Asterisk
`'.'`Point
`'x'`Cross
`'square'` or `'s'`Square
`'diamond'` or `'d'`Diamond
`'^'`Upward-pointing triangle
`'v'`Downward-pointing triangle
`'>'`Right-pointing triangle
`'<'`Left-pointing triangle
`'pentagram'` or `'p'`Five-pointed star (pentagram)
`'hexagram'` or `'h'`Six-pointed star (hexagram)
`'none'`No markers

Marker outline color, specified as `'auto'`, an RGB triplet, or one of the color options listed in the table. The default value of `'auto'` uses the same color as the `EdgeColor` property.

For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, `[0.4 0.6 0.7]`. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
`'red'` or `'r'`Red`[1 0 0]`
`'green'` or `'g'`Green`[0 1 0]`
`'blue'` or `'b'`Blue`[0 0 1]`
`'yellow'` or `'y'`Yellow`[1 1 0]`
`'magenta'` or `'m'`Magenta`[1 0 1]`
`'cyan'` or `'c'`Cyan`[0 1 1]`
`'white'` or `'w'`White`[1 1 1]`
`'black'` or `'k'`Black`[0 0 0]`
`'none'`No colorNot applicable

Example: `[0.5 0.5 0.5]`

Example: `'blue'`

Marker fill color, specified as `'auto'`, an RGB triplet, or one of the color options listed in the table. The `'auto'` value uses the same color as the `MarkerEdgeColor` property.

For a custom color, specify an RGB triplet. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, `[0.4 0.6 0.7]`. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
`'red'` or `'r'`Red`[1 0 0]`
`'green'` or `'g'`Green`[0 1 0]`
`'blue'` or `'b'`Blue`[0 0 1]`
`'yellow'` or `'y'`Yellow`[1 1 0]`
`'magenta'` or `'m'`Magenta`[1 0 1]`
`'cyan'` or `'c'`Cyan`[0 1 1]`
`'white'` or `'w'`White`[1 1 1]`
`'black'` or `'k'`Black`[0 0 0]`
`'none'`No colorNot applicable

Example: `[0.3 0.2 0.1]`

Example: `'green'`

Marker size, specified as a positive value in points.

Example: `10`

## Output Arguments

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One or more `FunctionSurface` or `ParameterizedFunctionSurface` objects, returned as a scalar or a vector.

• If you use the `fmesh(f)` syntax or a variation of this syntax, then `fmesh` returns `FunctionSurface` objects.

• If you use the `fmesh(funx,funy,funz)` syntax or a variation of this syntax, then `fmesh` returns `ParameterizedFunctionSurface` objects.

You can use these objects to query and modify properties of a specific mesh. For a list of properties, see FunctionSurface Properties and ParameterizedFunctionSurface Properties.