fplot3

R2026b

Plot 3-D parametric curve

Syntax

fplot3(xt,yt,zt)

fplot3(xt,yt,zt,[tmin tmax])

fplot3(___,LineSpec)

fplot3(___,Name=Value)

fplot3(ax,___)

fp = fplot3(___)

Description

fplot3(xt,yt,zt) plots the parametric curve xt = x(t), yt = y(t), and zt = z(t) over the default interval –5 < t < 5.

fplot3(xt,yt,zt,[tmin tmax]) plots xt = x(t), yt = y(t), and zt = z(t) over the interval tmin < t < tmax.

fplot3(___,LineSpec) uses LineSpec to set the line style, marker symbol, and line color.

fplot3(___,Name=Value) specifies line properties using one or more name-value arguments. Use this option with any of the input argument combinations in the previous syntaxes. Name=Value settings apply to all the lines plotted. To set options for individual lines, use the objects returned by fplot3.

fplot3(ax,___) plots into the axes object ax instead of the current axes gca.

fp = fplot3(___) returns a parameterized function line object. Use the object to query and modify properties of a specific parameterized line. For details, see ParameterizedFunctionLine Properties.

Examples

Plot 3-D Parametric Line

Plot the 3-D parametric line

$$\begin{array}{c}x=\sin (t)\\ y=\cos (t)\\ z=t\end{array}$$

over the default parameter range [-5 5].

syms t
xt = sin(t);
yt = cos(t);
zt = t;
fplot3(xt,yt,zt)

Specify Parameter Range

Plot the parametric line

$$\begin{array}{c}x=e^{-t/10}\sin (5t)\\ y=e^{-t/10}\cos (5t)\\ z=t\end{array}$$

over the parameter range [-10 10] by specifying the fourth argument of fplot3.

syms t
xt = exp(-t/10).*sin(5*t);
yt = exp(-t/10).*cos(5*t);
zt = t;
fplot3(xt,yt,zt,[-10 10])

Change Line Properties and Display Markers

Plot the same 3-D parametric curve three times over different intervals of the parameter. For the first curve, use a linewidth of 2. For the second, specify a dashed red line style with circle markers. For the third, specify a cyan, dash-dot line style with asterisk markers.

syms t
fplot3(sin(t), cos(t), t, [0 2*pi], LineWidth=2)
hold on
fplot3(sin(t), cos(t), t, [2*pi 4*pi], '--or')
fplot3(sin(t), cos(t), t, [4*pi 6*pi], '-.*c')

Plot 3-D Parametric Line Using Symbolic Functions

Plot the 3-D parametric line

$$\begin{array}{c}x(t)=\sin (t)\\ y(t)=\cos (t)\\ z(t)=\cos (2t).\end{array}$$

syms x(t) y(t) z(t)
x(t) = sin(t);
y(t) = cos(t);
z(t) = cos(2*t);
fplot3(x,y,z)

Plot Multiple Lines on Same Figure

Plot multiple lines either by passing the inputs as a vector or by using hold on to successively plot on the same figure. If you specify LineSpec and Name-Value arguments, they apply to all lines. To set options for individual lines, use the function handles returned by fplot3.

Divide a figure into two subplots using subplot. On the first subplot, plot two parameterized lines using vector input. On the second subplot, plot the same lines using hold on.

syms t
subplot(2,1,1)
fplot3([t -t], t, [t -t])
title('Multiple Lines Using Vector Inputs')

subplot(2,1,2)
fplot3(t, t, t)
hold on
fplot3(-t, t, -t)
title('Multiple Lines Using Hold On Command')

hold off

Modify 3-D Parametric Line After Creation

Plot the parametric line

$$\begin{array}{l}x=e^{-|t|/10}\sin (5|t|)\\ y=e^{-|t|/10}\cos (5|t|)\\ z=t.\end{array}$$

Provide an output to make fplot return the plot object.

syms t
xt = exp(-abs(t)/10).*sin(5*abs(t));
yt = exp(-abs(t)/10).*cos(5*abs(t));
zt = t;
fp = fplot3(xt,yt,zt)

fp = 
  ParameterizedFunctionLine with properties:

    XFunction: exp(-abs(t)/10)*sin(5*abs(t))
    YFunction: exp(-abs(t)/10)*cos(5*abs(t))
    ZFunction: t
        Color: [0.0660 0.4430 0.7450]
    LineStyle: '-'
    LineWidth: 0.5000

  Show all properties

Change the range of parameter values to [-10 10] and the line color to red by using the TRange and Color properties of fp respectively.

fp.TRange = [-10 10];
fp.Color = 'r';

Add Title and Axis Labels and Format Ticks

For $$t$$ values in the range $$-2\pi$$ to $$2\pi$$, plot the parametric line

$$\begin{array}{c}x=t\\ y=t/2\\ z=\sin (6t).\end{array}$$

Add a title and axis labels. Create the x-axis ticks by spanning the x-axis limits at intervals of pi/2. Display these ticks by using the XTick property. Create x-axis labels by using arrayfun to apply texlabel to S. Display these labels by using the XTickLabel property. Repeat these steps for the y-axis.

To use LaTeX in plots, see latex.

syms t
xt = t;
yt = t/2;
zt = sin(6*t);
fplot3(xt,yt,zt,[-2*pi 2*pi],MeshDensity=30)
view(52.5,30)
xlabel('x')
ylabel('y')
title('x=t, y=t/2, z=sin(6t) for -2\pi < t < 2\pi')
ax = gca;

S = sym(ax.XLim(1):pi/2:ax.XLim(2));
ax.XTick = double(S);
ax.XTickLabel = arrayfun(@texlabel, S, UniformOutput=false);

S = sym(ax.YLim(1):pi/2:ax.YLim(2));
ax.YTick = double(S);
ax.YTickLabel = arrayfun(@texlabel, S, UniformOutput=false);

Create Animation of Parametric Curve

Create an animation by changing the displayed expression using the XFunction, YFunction, and ZFunction properties, and then use drawnow to update the plot. To export to GIF, see imwrite.

By varying the variable from to , animate the parametric curve

syms t
fp = fplot3(t+sin(40*t),-t+cos(40*t), sin(t));
for i=0:pi/10:4*pi
    fp.ZFunction = sin(t+i);
    drawnow
end

Input Arguments

xt — Parametric input for x-axis

symbolic expression | symbolic function

Parametric input for x-axis, specified as a symbolic expression or function. fplot3 uses symvar to find the parameter.

yt — Parametric input for y-axis

symbolic expression | symbolic function

Parametric input for y-axis, specified as a symbolic expression or function. fplot3 uses symvar to find the parameter.

zt — Parametric input for z-axis

symbolic expression | symbolic function

Parametric input for z-axis, specified as a symbolic expression or function. fplot3 uses symvar to find the parameter.

[tmin tmax] — Range of values of parameter

[–5 5] (default) | vector of two numbers

Range of values of parameter, specified as a vector of two numbers. The default range is [-5 5].

ax — Axes object

axes object

Axes object. If you do not specify an axes object, then fplot3 uses the current axes.

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	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]

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.

Example: Marker='o',MarkerFaceColor='red'

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

MeshDensity — Number of evaluation points

23 (default) | number

Number of evaluation points, specified as a number. The default is 23. Because fplot3 uses adaptive evaluation, the actual number of evaluation points is greater.

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 the 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"

This table lists the default color palettes for plots in the light and dark themes.

Palette	Palette Colors
"gem" — Light theme default Before R2025a: Most plots use these colors by default.
"glow" — Dark theme default

You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

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 is displayed 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

MarkerEdgeColor — Marker outline color

"auto" (default) | colorname or short name | RGB triplet | hexadecimal color code

Marker outline color, specified as one of these values:

• "auto" — Use the value of the Color property.

• Color name (or short name) — Specify any of these values: "red" (or "r"), "green" (or "g"), "blue" (or "b"), "cyan" (or "c"), "magenta" (or "m"), "yellow" (or "y"), "black" (or "k"), or "white" (or "w").

• RGB triplet — Specify the red, green, and blue components of a color as decimal values. 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].

• Hexadecimal color code — Specify the red, green, and blue components of a color as hexadecimal values. 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. The color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

This table shows the default color palettes for plots in the light and dark themes. You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

Palette	Palette Colors
"gem" — Light theme default Before R2025a: Most plots use these colors by default.
"glow" — Dark theme default

MarkerFaceColor — Marker fill color

"none" (default) | "auto" | color name or short name | RGB triplet | hexadecimal color code

Marker fill color, specified as one of these values:

• "none" — Do not fill the markers with any color.

• "auto" — Use the same color as the MarkerEdgeColor property.

• Color name (or short name) — Use a named color. Specify "red" (or "r"), "green" (or "g"), "blue" (or "b"), "cyan" (or "c"), "magenta" (or "m"), "yellow" (or "y"), "black" (or "k"), or "white" (or "w").

• RGB triplet — Use a custom color. 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].

• Hexadecimal color code — Use a custom color. 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.

This table lists the default color palettes for plots in the light and dark themes.

Palette	Palette Colors
"gem" — Light theme default Before R2025a: Most plots use these colors by default.
"glow" — Dark theme default

You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

MarkerSize — Marker size

6 (default) | positive value

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

Output Arguments

fp — One or more parameterized function line objects

scalar | vector

One or more parameterized line objects, returned as a scalar or a vector. You can use these objects to query and modify properties of a specific parameterized line. For details, see ParameterizedFunctionLine Properties.

Version History

Introduced in R2016a