fimplicit

Plot implicit function

Syntax

fimplicit(f)

fimplicit(f,interval)

fimplicit(ax,___)

fimplicit(___,LineSpec)

fimplicit(___,Name,Value)

fp = fimplicit(___)

Description

fimplicit(f) plots the implicit function defined by f(x,y) = 0 over the default interval [-5 5] for x and y.

fimplicit(f,interval) specifies the plotting interval for x and y.

fimplicit(ax,___) plots into the axes specified by ax instead of into the current axes. Specify the axes as the first input argument, prior to any of the previous input arguments.

fimplicit(___,LineSpec) specifies the line style, marker symbol, and line color. For example, '-r' plots a red line.

fimplicit(___,Name,Value) specifies line properties using one or more name-value pair arguments. For example, 'LineWidth',2 specifies a line width of 2 points.

fp = fimplicit(___) returns the ImplicitFunctionLine object. Use fp to access and modify properties of the line after it is created. For a list of properties, see ImplicitFunctionLine Properties.

Examples

Plot Implicit Function

Plot the hyperbola described by the function $$x^2-y^2-1=0$$ over the default interval of [-5 5] for x and y.

fimplicit(@(x,y) x.^2 - y.^2 - 1)

Specify Plotting Interval

Plot the function $$x^2+y^2-3=0$$ over the intervals [-3 0] for x and [-2 2] for y.

f = @(x,y) x.^2 + y.^2 - 3;
fimplicit(f,[-3 0 -2 2])

Modify Appearance of Implicit Plot

Plot two circles centered at (0,0) with different radius values. For the first circle, use a dotted, red line. For the second circle, use a dashed, green line with a line width of 2 points.

f1 = @(x,y) x.^2 + y.^2 - 1;
fimplicit(f1,':r')

hold on
f2 = @(x,y) x.^2 + y.^2 - 2;
fimplicit(f2,'--g','LineWidth',2)
hold off

Modify Implicit Plot After Creation

Plot the implicit function $$y\sin (x)+x\cos (y)-1=0$$ and assign the implicit function line object to the variable fp.

fp = fimplicit(@(x,y) y.*sin(x) + x.*cos(y) - 1)

fp = 
  ImplicitFunctionLine with properties:

     Function: @(x,y)y.*sin(x)+x.*cos(y)-1
        Color: [0 0.4470 0.7410]
    LineStyle: '-'
    LineWidth: 0.5000

  Show all properties

Use fp to access and modify properties of the implicit function line object after it is created. For example, change the color, line style, and line width.

fp.Color = 'r';
fp.LineStyle = '--';
fp.LineWidth = 2;

Input Arguments

f — Implicit function to plot

function handle

Implicit 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: fimplicit(@(x,y) x.^2 - y.^2 + 1)

interval — Plotting interval for x and y

[-5 5] (default) | two-element vector | four-element vector

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

• Two-element vector of the form [min max] — Use the same plotting interval of [min max] for both x and y.

• Four-element vector of the form [xmin xmax ymin ymax] — Use different plotting intervals for x and y. Plot over the interval [xmin xmax] for x and [ymin ymax] for y.

Example: fimplicit(f,[-2 3 -5 0])

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	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
's'	Square
'd'	Diamond
'^'	Upward-pointing triangle
'v'	Downward-pointing triangle
'>'	Right-pointing triangle
'<'	Left-pointing triangle
'p'	Pentagram
'h'	Hexagram

Color Name	Short Name	RGB Triplet	Appearance
'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]

ax — Axes object

axes object

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

Name-Value 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: fimplicit(f,'MeshDensity',50,'LineWidth',2) specifies the number of evaluation points and the line width.

The ImplicitFunctionLine properties listed here are only a subset. For a complete list, see ImplicitFunctionLine Properties.

MeshDensity — Number of evaluation points per direction

151 (default) | scalar

Number of evaluation points per direction, specified as a scalar.

Color — Line color

[0 0 1] (default) | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

Line color, specified as 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'

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
's'	Square
'd'	Diamond
'^'	Upward-pointing triangle
'v'	Downward-pointing triangle
'>'	Right-pointing triangle
'<'	Left-pointing triangle
'p'	Pentagram
'h'	Hexagram
'none'	No markers	Not applicable

MarkerSize — Marker size

6 (default) | positive value

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

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 Color 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'

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'

Tips

• Use element-wise operators for the best performance and to avoid a warning message. For example, use x.*y instead of x*y. For more information, see Array vs. Matrix Operations.

• When you zoom in on the chart, fimplicit recalculates the data, which can reveal hidden details.