fmesh

Plot 3-D mesh

Syntax

fmesh(f)

fmesh(f,[min max])

fmesh(f,[xmin xmax
ymin ymax])

fmesh(funx,funy,funz)

fmesh(funx,funy,funz,[uvmin
uvmax])

fmesh(funx,funy,funz,[umin
umax vmin vmax])

fmesh(___,LineSpec)

fmesh(___,Name,Value)

fmesh(ax,___)

obj = fmesh(___)

Description

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

example

fmesh(f,[min max]) plots f(x,y) over the interval [min max] for x and y.

fmesh(f,[xmin xmax ymin ymax]) plots f(x,y) over the interval [xmin xmax] for x and [ymin ymax] for y. The fmesh function uses symvar to order the variables and assign intervals.

example

fmesh(funx,funy,funz) plots the parametric mesh x = x(u,v), y = y(u,v), z = z(u,v) over the interval [-5 5] for u and v.

example

fmesh(funx,funy,funz,[uvmin uvmax]) plots the parametric mesh x = x(u,v), y = y(u,v), z = z(u,v) over the interval [uvmin uvmax] for u and v.

fmesh(funx,funy,funz,[umin umax vmin vmax]) plots the parametric mesh x = x(u,v), y = y(u,v), z = z(u,v) over the interval [umin umax] for u and [vmin vmax] for v. The fmesh function uses symvar to order the parametric variables and assign intervals.

fmesh(___,LineSpec) uses the LineSpec to set the line style, marker symbol, and plot color.

fmesh(___,Name,Value) specifies surface properties 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 with the object ax instead of the current axes object gca.

obj = fmesh(___) returns a function surface object or a parameterized function surface object. Use the object to query and modify properties of a specific mesh.

Examples

collapse all

3-D Mesh Plot of Symbolic Expression

Open Live Script

Plot a mesh of the input $\sin (x) + \cos (y)$ over the default range $- 5 < x < 5$ and $- 5 < y < 5$ .

syms x y
fmesh(sin(x)+cos(y))

Figure contains an axes object. The axes object contains an object of type functionsurface.

3-D Mesh Plot of Symbolic Function

Open Live Script

Plot a 3-D mesh of the real part of ${t a n}^{- 1} (x + i y)$ over the default range $- 5 < x < 5$ and $- 5 < y < 5$ .

syms f(x,y)
f(x,y) = real(atan(x + i*y));
fmesh(f)

Figure contains an axes object. The axes object contains an object of type functionsurface.

Specify Plotting Interval of Mesh Plot

Open Live Script

Plot $\sin (x) + \cos (y)$ over $- π < x < π$ and $- 5 < y < 5$ by specifying the plotting interval as the second argument of fmesh.

syms x y
f = sin(x) + cos(y);
fmesh(f, [-pi pi -5 5])

Figure contains an axes object. The axes object contains an object of type functionsurface.

Parameterized Mesh Plot

Open Live Script

Plot the parameterized mesh

$\begin{array}{c} x = r \cos (s) \sin (t) \\ y = r \sin (s) \sin (t) \\ z = r \cos (t) \\ w h e r e r = 8 + \sin (7 s + 5 t) \end{array}$

for $0 < s < 2 π$ and $0 < t < π$ . Make the aspect ratio of the axes equal using axis equal. See the entire mesh by making the mesh partially transparent using alpha.

syms s t
r = 8 + sin(7*s + 5*t);
x = r*cos(s)*sin(t);
y = r*sin(s)*sin(t);
z = r*cos(t);
fmesh(x, y, z, [0 2*pi 0 pi], 'Linewidth', 2)
axis equal
alpha(0.8)

Figure contains an axes object. The axes object contains an object of type parameterizedfunctionsurface.

Input Arguments

collapse all

`f` — 3-D expression or function to be plotted
symbolic expression | symbolic function

Expression or function to be plotted, specified as a symbolic expression or function.

`[min max]` — Plotting interval for x- and y-axes
[–5 5] (default) | vector of two numbers

Plotting interval for x- and y-axes, specified as a vector of two numbers. The default is [-5 5].

`[xmin xmax ymin ymax]` — Plotting interval for x- and y-axes
[–5 5 –5 5] (default) | vector of four numbers

Plotting interval for x- and y-axes, specified as a vector of four numbers. The default is [-5 5 -5 5].

`funx,funy,funz` — Parametric functions of `u` and `v`
symbolic expressions | symbolic functions

Parametric functions of u and v, specified as a symbolic expression or function.

`[uvmin uvmax]` — Plotting interval for `u` and `v`
[–5 5] (default) | vector of two numbers

Plotting interval for u and v axes, specified as a vector of two numbers. The default is [-5 5].

`[umin umax vmin vmax]` — Plotting interval for `u` and `v`
[–5 5 –5 5] (default) | vector of four numbers

Plotting interval for u and v, specified as a vector of four numbers. The default is [-5 5 -5 5].

`ax` — Axes object
axes object

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

`LineSpec` — Line style, marker, and color
string scalar | character vector

Line style, marker, and color, specified as a string scalar or character vector containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics (line style, marker, and color). For example, if you omit the line style and specify the marker, then the plot shows only the marker and no line.

Example: "--or" is a red dashed line with circle markers.

Line Style	Description	Resulting Line
`"-"`	Solid line
`"--"`	Dashed line
`":"`	Dotted line
`"-."`	Dash-dotted line

Marker	Description	Resulting Marker
`"o"`	Circle
`"+"`	Plus sign
`"*"`	Asterisk
`"."`	Point
`"x"`	Cross
`"_"`	Horizontal line
`"\|"`	Vertical line
`"square"`	Square
`"diamond"`	Diamond
`"^"`	Upward-pointing triangle
`"v"`	Downward-pointing triangle
`">"`	Right-pointing triangle
`"<"`	Left-pointing triangle
`"pentagram"`	Pentagram
`"hexagram"`	Hexagram

Color Name	Short Name	RGB Triplet
`"red"`	`"r"`	`[1 0 0]`
`"green"`	`"g"`	`[0 1 0]`
`"blue"`	`"b"`	`[0 0 1]`
`"cyan"`	`"c"`	`[0 1 1]`
`"magenta"`	`"m"`	`[1 0 1]`
`"yellow"`	`"y"`	`[1 1 0]`
`"black"`	`"k"`	`[0 0 0]`
`"white"`	`"w"`	`[1 1 1]`

Name-Value Arguments

collapse all

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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

`MeshDensity` — Number of evaluation points per direction
35 (default) | number

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

`ShowContours` — Display contour plot under plot
`'off'` (default) | on/off logical value

Display contour plot under plot, specified as 'on' or 'off', or as numeric or logical 1 (true) or 0 (false). A value of 'on' is equivalent to true, and 'off' is equivalent to false. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.

`EdgeColor` — Line color
`'interp'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

Line color, specified as 'interp', an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of 'interp' colors the edges based on the ZData property values.

For a custom color, specify an RGB triplet or a hexadecimal color code.

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].
A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and the hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
`"red"`	`"r"`	`[1 0 0]`	`"#FF0000"`
`"green"`	`"g"`	`[0 1 0]`	`"#00FF00"`
`"blue"`	`"b"`	`[0 0 1]`	`"#0000FF"`
`"cyan"`	`"c"`	`[0 1 1]`	`"#00FFFF"`
`"magenta"`	`"m"`	`[1 0 1]`	`"#FF00FF"`
`"yellow"`	`"y"`	`[1 1 0]`	`"#FFFF00"`
`"black"`	`"k"`	`[0 0 0]`	`"#000000"`
`"white"`	`"w"`	`[1 1 1]`	`"#FFFFFF"`
`"none"`	Not applicable	Not applicable	Not applicable	No color

This table lists the default color palettes for plots in the light and dark themes.

Palette Palette Colors

Palette	Palette Colors
`"gem"` — Light theme default Before R2025a: Most plots use these colors by default.
`"glow"` — Dark theme default

"gem" — Light theme default

Before R2025a: Most plots use these colors by default.

"glow" — Dark theme default

You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Example: 'blue'

Example: [0 0 1]

Example: '#0000FF'

`LineStyle` — Line style
`"-"` (default) | `"--"` | `":"` | `"-."` | `"none"`

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

Line Style	Description	Resulting Line
`"-"`	Solid line
`"--"`	Dashed line
`":"`	Dotted line
`"-."`	Dash-dotted line
`"none"`	No line	No line

`LineWidth` — Line width
`0.5` (default) | positive value

Line width, specified as a positive value in points, where 1 point = 1/72 of an inch. If the line has markers, then the line width also affects the marker edges.

The line width cannot be thinner than the width of a pixel. If you set the line width to a value that is less than the width of a pixel on your system, the line displays as one pixel wide.

`Marker` — Marker symbol
`"none"` (default) | `"o"` | `"+"` | `"*"` | `"."` | ...

Marker symbol, specified as one of the values listed in this table. By default, the object does not display markers. Specifying a marker symbol adds markers at each data point or vertex.

Marker	Description	Resulting Marker
`"o"`	Circle
`"+"`	Plus sign
`"*"`	Asterisk
`"."`	Point
`"x"`	Cross
`"_"`	Horizontal line
`"\|"`	Vertical line
`"square"`	Square
`"diamond"`	Diamond
`"^"`	Upward-pointing triangle
`"v"`	Downward-pointing triangle
`">"`	Right-pointing triangle
`"<"`	Left-pointing triangle
`"pentagram"`	Pentagram
`"hexagram"`	Hexagram
`"none"`	No markers	Not applicable

`MarkerEdgeColor` — Marker outline color
`'auto'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

Marker outline color, specified as 'auto', an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of 'auto' uses the same color as the EdgeColor property.

For a custom color, specify an RGB triplet or a hexadecimal color code.

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].
A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and the hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
`"red"`	`"r"`	`[1 0 0]`	`"#FF0000"`
`"green"`	`"g"`	`[0 1 0]`	`"#00FF00"`
`"blue"`	`"b"`	`[0 0 1]`	`"#0000FF"`
`"cyan"`	`"c"`	`[0 1 1]`	`"#00FFFF"`
`"magenta"`	`"m"`	`[1 0 1]`	`"#FF00FF"`
`"yellow"`	`"y"`	`[1 1 0]`	`"#FFFF00"`
`"black"`	`"k"`	`[0 0 0]`	`"#000000"`
`"white"`	`"w"`	`[1 1 1]`	`"#FFFFFF"`
`"none"`	Not applicable	Not applicable	Not applicable	No color

This table lists the default color palettes for plots in the light and dark themes.

Palette Palette Colors

Palette	Palette Colors
`"gem"` — Light theme default Before R2025a: Most plots use these colors by default.
`"glow"` — Dark theme default

"gem" — Light theme default

Before R2025a: Most plots use these colors by default.

"glow" — Dark theme default

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Example: [0.5 0.5 0.5]

Example: 'blue'

Example: '#D2F9A7'

`MarkerFaceColor` — Marker fill color
`"none"` (default) | `"auto"` | RGB triplet | hexadecimal color code | `"r"` | `"g"` | `"b"` | ...

Marker fill color, specified as "auto", an RGB triplet, a hexadecimal color code, a color name, or a short name. The "auto" value uses the same color as the MarkerEdgeColor property.

For a custom color, specify an RGB triplet or a hexadecimal color code.

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].
A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and the hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
`"red"`	`"r"`	`[1 0 0]`	`"#FF0000"`
`"green"`	`"g"`	`[0 1 0]`	`"#00FF00"`
`"blue"`	`"b"`	`[0 0 1]`	`"#0000FF"`
`"cyan"`	`"c"`	`[0 1 1]`	`"#00FFFF"`
`"magenta"`	`"m"`	`[1 0 1]`	`"#FF00FF"`
`"yellow"`	`"y"`	`[1 1 0]`	`"#FFFF00"`
`"black"`	`"k"`	`[0 0 0]`	`"#000000"`
`"white"`	`"w"`	`[1 1 1]`	`"#FFFFFF"`
`"none"`	Not applicable	Not applicable	Not applicable	No color

This table lists the default color palettes for plots in the light and dark themes.

Palette Palette Colors

Palette	Palette Colors
`"gem"` — Light theme default Before R2025a: Most plots use these colors by default.
`"glow"` — Dark theme default

"gem" — Light theme default

Before R2025a: Most plots use these colors by default.

"glow" — Dark theme default

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Example: [0.3 0.2 0.1]

Example: "green"

Example: "#D2F9A7"

`MarkerSize` — Marker size
`6` (default) | positive value

Marker size, specified as a positive value in points, where 1 point = 1/72 of an inch.

Output Arguments

collapse all

`obj` — One or more objects
scalar | vector

One or more objects, returned as a scalar or a vector. The object is either a function surface object or parameterized mesh object, depending on the type of plot. You can use these objects to query and modify properties of a specific line. For details, see FunctionSurface Properties and ParameterizedFunctionSurface Properties.

Tips

For additional examples, follow the fsurf page because fmesh and fsurf share the same syntax. All examples on the fsurf page apply to fmesh.

Algorithms

fmesh assigns the symbolic variables in f to the x-axis, then the y-axis, and symvar determines the order of the variables to be assigned. Therefore, variable and axis names might not correspond. To force fmesh to assign x or y to its corresponding axis, create the symbolic function to plot, then pass the symbolic function to fmesh.

For example, the following code plots the mesh of f(x,y) = sin(y) in two ways. The first way forces the waves to oscillate with respect to the y-axis. In other words, the first plot assigns the y variable to the corresponding y-axis. The second plot assigns y to the x-axis because it is the first (and only) variable in the symbolic function.

syms x y;
f(x,y) = sin(y);

figure;
subplot(2,1,1)
fmesh(f);
subplot(2,1,2)
fmesh(f(x,y)); % Or fmesh(sin(y));

Two mesh plots showing f(x,y) = sin(y), one plot with respect to the y-axis and the other plot with respect to the x-axis

Version History

Introduced in R2016a

fmesh

Syntax

Description

Examples

3-D Mesh Plot of Symbolic Expression

3-D Mesh Plot of Symbolic Function

Specify Plotting Interval of Mesh Plot

Parameterized Mesh Plot

Input Arguments

`f` — 3-D expression or function to be plotted
symbolic expression | symbolic function

`[min max]` — Plotting interval for x- and y-axes
[–5 5] (default) | vector of two numbers

`[xmin xmax ymin ymax]` — Plotting interval for x- and y-axes
[–5 5 –5 5] (default) | vector of four numbers

`funx,funy,funz` — Parametric functions of `u` and `v`
symbolic expressions | symbolic functions

`[uvmin uvmax]` — Plotting interval for `u` and `v`
[–5 5] (default) | vector of two numbers

`[umin umax vmin vmax]` — Plotting interval for `u` and `v`
[–5 5 –5 5] (default) | vector of four numbers

`ax` — Axes object
axes object

`LineSpec` — Line style, marker, and color
string scalar | character vector

Name-Value Arguments

`MeshDensity` — Number of evaluation points per direction
35 (default) | number

`ShowContours` — Display contour plot under plot
`'off'` (default) | on/off logical value

`EdgeColor` — Line color
`'interp'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

`LineStyle` — Line style
`"-"` (default) | `"--"` | `":"` | `"-."` | `"none"`

`LineWidth` — Line width
`0.5` (default) | positive value

`Marker` — Marker symbol
`"none"` (default) | `"o"` | `"+"` | `"*"` | `"."` | ...

`MarkerEdgeColor` — Marker outline color
`'auto'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

`MarkerFaceColor` — Marker fill color
`"none"` (default) | `"auto"` | RGB triplet | hexadecimal color code | `"r"` | `"g"` | `"b"` | ...

`MarkerSize` — Marker size
`6` (default) | positive value

Output Arguments

`obj` — One or more objects
scalar | vector

Tips

Algorithms

Version History

See Also

Functions

Properties

Topics

fmesh

Syntax

Description

Examples

3-D Mesh Plot of Symbolic Expression

3-D Mesh Plot of Symbolic Function

Specify Plotting Interval of Mesh Plot

Parameterized Mesh Plot

Input Arguments

f — 3-D expression or function to be plotted symbolic expression | symbolic function

[min max] — Plotting interval for x- and y-axes [–5 5] (default) | vector of two numbers

[xmin xmax ymin ymax] — Plotting interval for x- and y-axes [–5 5 –5 5] (default) | vector of four numbers

funx,funy,funz — Parametric functions of u and v symbolic expressions | symbolic functions

[uvmin uvmax] — Plotting interval for u and v [–5 5] (default) | vector of two numbers

[umin umax vmin vmax] — Plotting interval for u and v [–5 5 –5 5] (default) | vector of four numbers

ax — Axes object axes object

LineSpec — Line style, marker, and color string scalar | character vector

Name-Value Arguments

MeshDensity — Number of evaluation points per direction 35 (default) | number

ShowContours — Display contour plot under plot 'off' (default) | on/off logical value

EdgeColor — Line color 'interp' (default) | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

LineStyle — Line style "-" (default) | "--" | ":" | "-." | "none"

LineWidth — Line width 0.5 (default) | positive value

Marker — Marker symbol "none" (default) | "o" | "+" | "*" | "." | ...

MarkerEdgeColor — Marker outline color 'auto' (default) | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

MarkerFaceColor — Marker fill color "none" (default) | "auto" | RGB triplet | hexadecimal color code | "r" | "g" | "b" | ...

MarkerSize — Marker size 6 (default) | positive value

Output Arguments

obj — One or more objects scalar | vector

Tips

Algorithms

Version History

See Also

Functions

Properties

Topics

`f` — 3-D expression or function to be plotted
symbolic expression | symbolic function

`[min max]` — Plotting interval for x- and y-axes
[–5 5] (default) | vector of two numbers

`[xmin xmax ymin ymax]` — Plotting interval for x- and y-axes
[–5 5 –5 5] (default) | vector of four numbers

`funx,funy,funz` — Parametric functions of `u` and `v`
symbolic expressions | symbolic functions

`[uvmin uvmax]` — Plotting interval for `u` and `v`
[–5 5] (default) | vector of two numbers

`[umin umax vmin vmax]` — Plotting interval for `u` and `v`
[–5 5 –5 5] (default) | vector of four numbers

`ax` — Axes object
axes object

`LineSpec` — Line style, marker, and color
string scalar | character vector

`MeshDensity` — Number of evaluation points per direction
35 (default) | number

`ShowContours` — Display contour plot under plot
`'off'` (default) | on/off logical value

`EdgeColor` — Line color
`'interp'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

`LineStyle` — Line style
`"-"` (default) | `"--"` | `":"` | `"-."` | `"none"`

`LineWidth` — Line width
`0.5` (default) | positive value

`Marker` — Marker symbol
`"none"` (default) | `"o"` | `"+"` | `"*"` | `"."` | ...

`MarkerEdgeColor` — Marker outline color
`'auto'` (default) | RGB triplet | hexadecimal color code | `'r'` | `'g'` | `'b'` | ...

`MarkerFaceColor` — Marker fill color
`"none"` (default) | `"auto"` | RGB triplet | hexadecimal color code | `"r"` | `"g"` | `"b"` | ...

`MarkerSize` — Marker size
`6` (default) | positive value

`obj` — One or more objects
scalar | vector