# fimplicit

Plot implicit function

## Syntax

``fimplicit(f)``
``fimplicit(f,interval)``
``fimplicit(ax,___)``
``fimplicit(___,LineSpec)``
``fimplicit(___,Name,Value)``
``fp = fimplicit(___)``

## Description

example

````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`.```
````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.```

example

````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.```

## Examples

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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)`

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])```

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```

Plot the implicit function $y\mathrm{sin}\left(x\right)+x\mathrm{cos}\left(y\right)-1=0$ 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

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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)`

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])`

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 StyleDescriptionResulting Line
`"-"`Solid line

`"--"`Dashed line

`":"`Dotted line

`"-."`Dash-dotted line

MarkerDescriptionResulting 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 NameShort NameRGB TripletAppearance
`"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]`

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.

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

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 NameShort NameRGB TripletHexadecimal Color CodeAppearance
`"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 applicableNot applicableNot applicableNo color

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

RGB TripletHexadecimal Color CodeAppearance
`[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'`

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

Line StyleDescriptionResulting Line
`"-"`Solid line

`"--"`Dashed line

`":"`Dotted line

`"-."`Dash-dotted line

`"none"`No lineNo line

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 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.

MarkerDescriptionResulting 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 markersNot applicable

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

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 NameShort NameRGB TripletHexadecimal Color CodeAppearance
`"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 applicableNot applicableNot applicableNo color

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

RGB TripletHexadecimal Color CodeAppearance
`[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"`

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 NameShort NameRGB TripletHexadecimal Color CodeAppearance
`"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 applicableNot applicableNot applicableNo color

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

RGB TripletHexadecimal Color CodeAppearance
`[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