fimplicit

Plot implicit function

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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.

example

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

example

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.

example

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.

example

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.

example

Examples

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Plot Implicit Function

Open Live Script

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)

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

Specify Plotting Interval

Open Live Script

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])

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

Modify Appearance of Implicit Plot

Open Live Script

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

Figure contains an axes object. The axes object contains 2 objects of type implicitfunctionline.

Modify Implicit Plot After Creation

Open Live Script

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)

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

fp = 
  ImplicitFunctionLine with properties:

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

  Use GET to 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;

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

Input Arguments

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`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
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]`

`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 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: 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 0.4470 0.7410]` (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 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 hexadecimal color codes.

Color Name	Short Name	RGB Triplet	Hexadecimal Color Code
`"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"`

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
`"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

`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 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 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 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 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.

Version History

Introduced in R2016b

fimplicit

Syntax

Description

Examples

Plot Implicit Function

Specify Plotting Interval

Modify Appearance of Implicit Plot

Modify Implicit Plot After Creation

Input Arguments

`f` — Implicit function to plot
function handle

`interval` — Plotting interval for `x` and `y`
`[-5 5]` (default) | two-element vector | four-element vector

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

`ax` — Axes object
axes object

Name-Value Arguments

`MeshDensity` — Number of evaluation points per direction
`151` (default) | scalar

`Color` — Line color
`[0 0.4470 0.7410]` (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"` | `"+"` | `"*"` | `"."` | ...

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

`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"` | ...

Tips

Version History

See Also

Functions

Properties

fimplicit

Syntax

Description

Examples

Plot Implicit Function

Specify Plotting Interval

Modify Appearance of Implicit Plot

Modify Implicit Plot After Creation

Input Arguments

f — Implicit function to plot function handle

interval — Plotting interval for x and y [-5 5] (default) | two-element vector | four-element vector

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

ax — Axes object axes object

Name-Value Arguments

MeshDensity — Number of evaluation points per direction 151 (default) | scalar

Color — Line color [0 0.4470 0.7410] (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" | "+" | "*" | "." | ...

MarkerSize — Marker size 6 (default) | positive value

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" | ...

Tips

Version History

See Also

Functions

Properties

`f` — Implicit function to plot
function handle

`interval` — Plotting interval for `x` and `y`
`[-5 5]` (default) | two-element vector | four-element vector

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

`ax` — Axes object
axes object

`MeshDensity` — Number of evaluation points per direction
`151` (default) | scalar

`Color` — Line color
`[0 0.4470 0.7410]` (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"` | `"+"` | `"*"` | `"."` | ...

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

`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"` | ...