fcontour

Plot contours

Syntax

fcontour(f)

fcontour(f,xyinterval)

fcontour(___,LineSpec)

fcontour(___,Name,Value)

fcontour(ax,___)

fc = fcontour(___)

Description

fcontour(f) plots the contour lines of the function z = f(x,y) for constant levels of z over the default interval [-5 5] for x and y.

fcontour(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].

fcontour(___,LineSpec) sets the line style and color for the contour lines. For example, '-r' specifies red lines. Use this option after any of the previous input argument combinations.

fcontour(___,Name,Value) specifies line properties using one or more name-value pair arguments.

fcontour(ax,___) plots into the axes specified by ax instead of the current axes.

fc = fcontour(___) returns a FunctionContour object. Use fc to query and modify properties of a specific FunctionContour object. For a list of properties, see FunctionContour Properties.

Examples

Plot Contours of Function

Plot the contours of $$f(x,y)=\sin (x)+\cos (y)$$ over the default interval of $$-5<x<5$$ and $$-5<y<5$$.

f = @(x,y) sin(x) + cos(y);
fcontour(f)

Specify Plotting Interval and Plot Piecewise Contour Plot

Specify the plotting interval as the second argument of fcontour. When you plot multiple inputs over different intervals in the same axes, the axis limits adjust to display all the data. This behavior lets you plot piecewise inputs.

Plot the piecewise input

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

over $$-5<y<5$$.

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

Change Line Style and Width

Plot the contours of $$x^2-y^2$$ as dashed lines with a line width of 2.

f = @(x,y) x.^2 - y.^2;
fcontour(f,'--','LineWidth',2)

Plot Multiple Contour Plots

Plot $$\sin (x)+\cos (y)$$ and $$x-y$$ on the same axes by using hold on.

fcontour(@(x,y) sin(x)+cos(y))
hold on
fcontour(@(x,y) x-y)
hold off

Modify Contour Plot After Creation

Plot the contours of $$e^{-(x/3{)}^2-(y/3{)}^2}+e^{-(x+2{)}^2-(y+2{)}^2}$$. Assign the function contour object to a variable.

f = @(x,y) exp(-(x/3).^2-(y/3).^2) + exp(-(x+2).^2-(y+2).^2);
fc = fcontour(f)

fc = 
  FunctionContour with properties:

     Function: @(x,y)exp(-(x/3).^2-(y/3).^2)+exp(-(x+2).^2-(y+2).^2)
    LineColor: 'flat'
    LineStyle: '-'
    LineWidth: 0.5000
         Fill: off
    LevelList: [0.2000 0.4000 0.6000 0.8000 1 1.2000 1.4000]

  Show all properties

Change the line width to 1 and the line style to a dashed line by using dot notation to set properties of the function contour object. Show contours close to 0 and 1 by setting the LevelList property. Add a colorbar.

fc.LineWidth = 1;
fc.LineStyle = '--';
fc.LevelList = [1 0.9 0.8 0.2 0.1];
colorbar

Fill Area Between Contours

Create a plot that looks like a sunset by filling the area between the contours of

$$erf((y+2{)}^3)-e^{(-0.65((x-2{)}^2+(y-2{)}^2))}.$$

f = @(x,y) erf((y+2).^3) - exp(-0.65*((x-2).^2+(y-2).^2));
fcontour(f,'Fill','on');

If you want interpolated shading instead, use the fsurf function and set its 'EdgeColor' option to 'none' followed by the command view(0,90).

Specify Levels for Contour Lines

Set the values at which fcontour draws contours by using the 'LevelList' option.

f = @(x,y) sin(x) + cos(y);
fcontour(f,'LevelList',[-1 0 1])

Control Resolution of Contour Lines

Control the resolution of contour lines by using the 'MeshDensity' option. Increasing 'MeshDensity' can make smoother, more accurate plots, while decreasing it can increase plotting speed.

Create two plots in a 2-by-1 tiled chart layout. In the first plot, display the contours of $$\sin (x)\sin (y)$$. The corners of the squares do not meet. To fix this issue, increase 'MeshDensity' to 200 in the second plot. The corners now meet, showing that by increasing 'MeshDensity' you increase the resolution.

f = @(x,y) sin(x).*sin(y);
tiledlayout(2,1)
nexttile
fcontour(f)
title('Default Mesh Density (71)')

nexttile
fcontour(f,'MeshDensity',200)
title('Custom Mesh Density (200)')

Add Title and Axis Labels and Format Ticks

Plot $$x\sin (y)-y\cos (x)$$. Display the grid lines, add a title, and add axis labels.

fcontour(@(x,y) x.*sin(y) - y.*cos(x), [-2*pi 2*pi], 'LineWidth', 2);
grid on
title({'xsin(y) - ycos(x)','-2\pi < x < 2\pi and -2\pi < y < 2\pi'})
xlabel('x')
ylabel('y')

Set the x-axis tick values and associated labels by setting the XTickLabel and XTick properties of the axes object. Access the axes object using gca. Similarly, set the y-axis tick values and associated labels.

ax = gca;
ax.XTick = ax.XLim(1):pi/2:ax.XLim(2);
ax.XTickLabel = {'-2\pi','-3\pi/2','-\pi','-\pi/2','0','\pi/2','\pi','3\pi/2','2\pi'};
ax.YTick = ax.YLim(1):pi/2:ax.YLim(2);
ax.YTickLabel = {'-2\pi','-3\pi/2','-\pi','-\pi/2','0','\pi/2','\pi','3\pi/2','2\pi'};

Input Arguments

f — Function to plot

function handle

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.

ax — Axes object

axes object

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

LineSpec — Line style and color

character vector | string

Line style and color, specified as a character vector or string containing a line style specifier, a color specifier, or both.

Example: '--r' specifies red dashed lines

These two tables list the line style and color options.

Line Style Specifier	Description
-	Solid line (default)
--	Dashed line
:	Dotted line
-.	Dash-dot line

Color Specifier	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: 'MeshDensity',30

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

'MeshDensity' — Number of evaluation points per direction

71 (default) | number

Number of evaluation points per direction, specified as a number. The default is 71. Because fcontour uses adaptive evaluation, the actual number of evaluation points is greater.

Example: 30

'Fill' — Fill between contour lines

'off' (default) | on/off logical value

Fill between contour lines, 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.

• A value of 'on' fill the spaces between contour lines with color.

• A value of 'off' leaves the spaces between the contour lines unfilled.

'LevelList' — Contour levels

vector of z values

Contour levels, specified as a vector of z values. By default, the fcontour function chooses values that span the range of values in the ZData property.

Setting this property sets the associated mode property to manual.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

'LevelStep' — Spacing between contour lines

0 (default) | scalar numeric value

Spacing between contour lines, specified as a scalar numeric value. For example, specify a value of 2 to draw contour lines at increments of 2. By default, LevelStep is determined by using the ZData values.

Setting this property sets the associated mode property to 'manual'.

Example: 3.4

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

'LineColor' — Color of contour lines

'flat' (default) | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

Color of contour lines, specified as 'flat', an RGB triplet, a hexadecimal color code, a color name, or a short name. To use a different color for each contour line, specify 'flat'. The color is determined by the contour value of the line, the colormap, and the scaling of data values into the colormap. For more information on color scaling, see caxis.

To use the same color for all the contour lines, specify an RGB triplet, a hexadecimal color code, a color name, or a short name.

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'

'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.

Output Arguments

fc — One or more FunctionContour objects

scalar | vector

One or more FunctionContour objects, returned as a scalar or a vector. You can use these objects to query and modify the properties of a specific contour plot. For a list of properties, see FunctionContour Properties.