fmesh

Plot 3-D mesh

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

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

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].

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.

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

3-D Mesh Plot of Expression

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

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

Parameterized Mesh Plot

Plot the parameterized mesh

$$\begin{array}{c}x=r\cos (s)\sin (t)\\ y=r\sin (s)\sin (t)\\ z=r\cos (t)\\ wherer=2+\sin (7s+5t)\end{array}$$

for $$0<s<2\pi$$ and $$0<t<\pi$$. 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)

Specify Interval of Mesh Plot and Plot Piecewise Input

Plot the piecewise input

$$\begin{array}{cc}erf(x)+\cos (y)& -5<x<0\\ \sin (x)+\cos (y)& 0<x<5\end{array}$$

over the interval $$-5<y<5.$$

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

Specify Mesh Plot Properties

Create a mesh plot using red lines.

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

Input Arguments

f — 3-D function to plot

function handle

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);

xyinterval — Plotting interval for x and y

[-5 5 -5 5] (default) | vector of form [min max] | vector of form [xmin xmax ymin ymax]

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.

funx — Parametric function for x coordinates

function handle

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);

funy — Parametric function for y coordinates

function handle

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);

funz — Parametric function for z coordinates

function handle

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;

uvinterval — Plotting interval for u and v

[-5 5 -5 5] (default) | vector of form [min max] | vector of form [umin umax vmin vmax]

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.

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

character vector | string

Line style, marker, and color, specified as a character vector or string 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
-	Solid line
--	Dashed line
:	Dotted line
-.	Dash-dot line

Marker	Description
'o'	Circle
'+'	Plus sign
'*'	Asterisk
'.'	Point
'x'	Cross
'_'	Horizontal line
'|'	Vertical line
's'	Square
'd'	Diamond
'^'	Upward-pointing triangle
'v'	Downward-pointing triangle
'>'	Right-pointing triangle
'<'	Left-pointing triangle
'p'	Pentagram
'h'	Hexagram

Color	Description
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 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.

'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 character vector or a string scalar 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. Thus, 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 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

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB^® uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	'#0072BD'
[0.8500 0.3250 0.0980]	'#D95319'
[0.9290 0.6940 0.1250]	'#EDB120'
[0.4940 0.1840 0.5560]	'#7E2F8E'
[0.4660 0.6740 0.1880]	'#77AC30'
[0.3010 0.7450 0.9330]	'#4DBEEE'
[0.6350 0.0780 0.1840]	'#A2142F'

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.

Value	Description
'o'	Circle
'+'	Plus sign
'*'	Asterisk
'.'	Point
'x'	Cross
'_'	Horizontal line
'|'	Vertical line
'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

'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 character vector or a string scalar 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. Thus, 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 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

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	'#0072BD'
[0.8500 0.3250 0.0980]	'#D95319'
[0.9290 0.6940 0.1250]	'#EDB120'
[0.4940 0.1840 0.5560]	'#7E2F8E'
[0.4660 0.6740 0.1880]	'#77AC30'
[0.3010 0.7450 0.9330]	'#4DBEEE'
[0.6350 0.0780 0.1840]	'#A2142F'

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 character vector or a string scalar 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. Thus, 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 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

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB uses in many types of plots.

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	'#0072BD'
[0.8500 0.3250 0.0980]	'#D95319'
[0.9290 0.6940 0.1250]	'#EDB120'
[0.4940 0.1840 0.5560]	'#7E2F8E'
[0.4660 0.6740 0.1880]	'#77AC30'
[0.3010 0.7450 0.9330]	'#4DBEEE'
[0.6350 0.0780 0.1840]	'#A2142F'

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

fs — One or more FunctionSurface or ParameterizedFunctionSurface objects

scalar | vector

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.