# fimplicit3

Plot 3-D implicit function

## Description

example

fimplicit3(f) plots the 3-D implicit function defined by f(x,y,z) = 0 over the default interval [-5 5] for x, y, and z.

example

fimplicit3(f,interval) specifies the plotting interval for x, y, and z.

fimplicit3(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.

fimplicit3(___,LineSpec) specifies the line style, marker symbol, and line color. For example, '-r' specifies red lines.

example

fimplicit3(___,Name,Value) specifies surface properties using one or more name-value pair arguments. For example, 'FaceAlpha',0.6 specifies a transparency value of 0.6 for a semi-transparent surface.

example

fs = fimplicit3(___) returns the ImplicitFunctionSurface object. Use fs to access and modify properties of the surface after it is created. For a list of properties, see ImplicitFunctionSurface Properties.

## Examples

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Plot the hyperboloid ${x}^{2}+{y}^{2}-{z}^{2}=0$ over the default interval of $\left[-5,5\right]$ for x, y, and z.

f = @(x,y,z) x.^2 + y.^2 - z.^2;
fimplicit3(f)

Plot the upper half of the hyperboloid ${x}^{2}+{y}^{2}-{z}^{2}=0$ by specifying the plotting interval as [0 5] for z. For x and y, use the default interval [-5 5].

f = @(x,y,z) x.^2 + y.^2 - z.^2;
interval = [-5 5 -5 5 0 5];
fimplicit3(f,interval)

Plot the implicit surface ${x}^{2}+{y}^{2}-{z}^{2}=0$. Remove the lines by setting the EdgeColor property to 'none'. Add transparency by setting the FaceAlpha property to a value between 0 and 1.

f = @(x,y,z) x.^2 + y.^2 - z.^2;
fimplicit3(f,'EdgeColor','none','FaceAlpha',.5)

Plot an implicit surface and assign the implicit surface object to the variable fs.

f = @(x,y,z) 1./x.^2 - 1./y.^2 + 1./z.^2;
fs = fimplicit3(f)

fs =
ImplicitFunctionSurface with properties:

Function: @(x,y,z)1./x.^2-1./y.^2+1./z.^2
EdgeColor: [0 0 0]
LineStyle: '-'
FaceColor: 'interp'

Show all properties

Use fs to access and modify properties of the implicit surface after it is created. For example, show only the positive x values by setting the XRange property to [0 5]. Remove the lines by setting the EdgeColor property to 'none'. Add transparency by setting the FaceAlpha property to 0.8.

fs.XRange = [0 5];
fs.EdgeColor = 'none';
fs.FaceAlpha = 0.8;

## Input Arguments

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3-D implicit function to plot, specified as a function handle to a named or anonymous function.

Specify a function of the form w = f(x,y,z). The function must accept three 3-D array input arguments and return a 3-D array 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: fimplicit3(@(x,y,z) x.^2 + y.^2 - z.^2)

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

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

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

Example: fimplicit3(f,[-2 3 -4 5 -3 3])

Line style, marker, and color, specified as a string 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 fimplicit3 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: fimplicit3(f,'MeshDensity',50,'FaceAlpha',0.5) specifies the number of evaluation points and a transparency value.

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

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

Face transparency, specified as a scalar in the range [0,1]. Use uniform transparency across all of the faces. A value of 1 is fully opaque and 0 is completely transparent. Values between 0 and 1 are semitransparent.

Face color, specified as 'interp', an RGB triplet, a hexadecimal color code, a color name, or a short name. The default value of 'interp' interpolates the colors based on the ZData 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. 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.

[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"

Line color, specified as 'interp', an RGB triplet, a hexadecimal color code, a color name, or a short name. The default RGB triplet value of [0 0 0] corresponds to black. The 'interp' value colors the edges based on the ZData 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. 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.

[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"

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.

## 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, fimplicit3 recalculates the data, which can reveal hidden details.

## Version History

Introduced in R2016b