Plot 3-D parametric curve - MATLAB fplot3 (2025)

Table of Contents

Syntax Description Examples Plot 3-D Parametric Line Specify Parameter Range Change Line Properties and Display Markers Plot 3-D Parametric Line Using Symbolic Functions Plot Multiple Lines on Same Figure Modify 3-D Parametric Line After Creation Add Title and Axis Labels and Format Ticks Create Animation of Parametric Curve Input Arguments xt — Parametric input for x-axis symbolic expression | symbolic function yt — Parametric input for y-axis symbolic expression | symbolic function zt — Parametric input for z-axis symbolic expression | symbolic function [tmin tmax] — Range of values of parameter [–5 5] (default) | vector of two numbers ax — Axes object axes object LineSpec — Line style, marker, and color string scalar | character vector Name-Value Arguments Output Arguments fp — One or more parameterized function line objects scalar | vector Version History See Also Functions Properties Topics MATLAB Command Americas Europe Asia Pacific FAQs References

Plot 3-D parametric curve

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Syntax

fplot3(xt,yt,zt)

fplot3(xt,yt,zt,[tmintmax])

fplot3(___,LineSpec)

fplot3(___,Name,Value)

fplot3(ax,___)

fp = fplot3(___)

Description

example

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

example

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

example

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

example

fplot3(___,Name,Value) specifiesline properties using one or more Name,Value pairarguments. Use this option with any of the input argument combinationsin the previous syntaxes. Name,Value pair settingsapply to all the lines plotted. To set options for individual lines,use the objects returned by fplot3.

fplot3(ax,___) plotsinto the axes object ax instead of the currentaxes gca.

example

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

Examples

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Plot 3-D Parametric Line

Open Live Script

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

Specify Parameter Range

Open Live Script

Plot the parametric line

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

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

syms txt = 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

Open Live Script

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 tfplot3(sin(t), cos(t), t, [0 2*pi], 'LineWidth', 2)hold onfplot3(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

Open Live Script

Plot the 3-D parametric line

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

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

Open Live Script

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 tsubplot(2,1,1)fplot3([t -t], t, [t -t])title('Multiple Lines Using Vector Inputs')subplot(2,1,2)fplot3(t, t, t)hold onfplot3(-t, t, -t)title('Multiple Lines Using Hold On Command')hold off

Modify 3-D Parametric Line After Creation

Open Live Script

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 txt = 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 0.4470 0.7410] LineStyle: '-' LineWidth: 0.5000 Use GET to 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

Open Live Script

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

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

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 txt = 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

Open Script

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

Input Arguments

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`xt` — Parametric input for x-axis
symbolic expression | symbolic function

Parametric input for x-axis, specified as a symbolic expressionor function. fplot3 uses symvar tofind the parameter.

`yt` — Parametric input for y-axis
symbolic expression | symbolic function

Parametric input for y-axis, specified as a symbolic expressionor function. fplot3 uses symvar tofind the parameter.

`zt` — Parametric input for z-axis
symbolic expression | symbolic function

Parametric input for z-axis, specified as a symbolic expressionor function. fplot3 uses symvar tofind 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 usesthe 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
`"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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

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

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

Output Arguments

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`fp` — One or more parameterized function line objects
scalar | vector

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

Version History

Introduced in R2016a

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Plot 3-D parametric curve - MATLAB fplot3 (2025)

FAQs

How to plot 3-D parametric equations in Matlab? ›

To plot vector functions or parametric equations, you follow the same idea as in plotting 2D functions, setting up your domain for t. Then you establish x, y (and z if applicable) according to the equations, then plot using the plot(x,y) for 2D or the plot3(x,y,z) for 3D command.

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How to plot parametric plot in Matlab? ›

Plot Multiple Lines on Same Figure

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 .

Read The Full Story ›

How do you find the parametric equation of a curve in 3-D? ›

A 3-D curve can be given parametrically by x = f(t), y = g(t) and z = h(t) where t is on some interval I and f, g, and h are all continuous on I. We could specify the curve by the position vector .

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How do you plot parametric equations? ›

To plot a parametric curve, simply create an ordered pair where one or both coordinates are defined in terms of the parameter t. By default, parametric curves are plotted for values of t in the interval [0, 1], but it is possible to adjust the domain manually using the inputs beneath the expression.

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What is the parametric equation of a 3-D line? ›

Parametric Equation of a Line in 3D

These equations x=x0+at, y=y0+bt and z=z0+ct are called the parametric equations of the line that contains the point (x0,y0,z0) and has the direction vector →V=aˆi+bˆj+cˆk.

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What is the function of fplot3? ›

fplot3(___, Name,Value ) specifies line properties using one or more name-value pair arguments. For example, 'LineWidth',2 specifies a line width of 2 points. fplot3( ax ,___) plots into the axes specified by ax instead of the current axes. Specify the axes as the first input argument.

How to plot a 3-D graph in MATLAB using Excel data? ›

Please follow the following steps:

Prepare Your Excel File: Ensure your Excel file is organized such that it represents a grid of Z values. ...
Read Data from Excel File: Use the readmatrix function to read the data from the Excel file into MATLAB.
Extract X, Y, and Z Data: ...
Plot the Surface:

Jun 26, 2024

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What is the formula for a parametric curve? ›

The derivative of the parametrically defined curve x=x(t) and y=y(t) can be calculated using the formula dydx=y′(t)x′(t). Using the derivative, we can find the equation of a tangent line to a parametric curve. The area between a parametric curve and the x-axis can be determined by using the formula A=∫t2t1y(t)x′(t)dt.

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How do you convert to parametric curve? ›

Converting from rectangular to parametric can be very simple: given y=f(x), the parametric equations x=t, y=f(t) produce the same graph. As an example, given y=x2, the parametric equations x=t, y=t2 produce the familiar parabola. However, other parametrizations can be used.

How to plot 3-D cylinder in MATLAB? ›

To draw the cylinder, pass X , Y , and Z to the surf or mesh function. [X,Y,Z] = cylinder( r ) returns the x-, y-, and z- coordinates of a cylinder with the specified profile curve, r , and 20 equally spaced points around its circumference.

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What are the parametric equations for 3-D surfaces? ›

The equations , x = x ( s , t ) , , y = y ( s , t ) , and z = z ( s , t ) are the parametric equations for the surface, or a parametrization of the surface.

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