fplot3

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

example

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.

example

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

example

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

example

fplot3(___,Name,Value) specifies line properties using one or more Name,Value pair arguments. Use this option with any of the input argument combinations in the previous syntaxes. Name,Value pair 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.

example

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

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

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

syms 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

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

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

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: [1x1 sym]
    YFunction: [1x1 sym]
    ZFunction: [1x1 sym]
        Color: [0 0.4470 0.7410]
    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 $- 2 π$ 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 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 Animations

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

By varying the variable i from 0 to 4π, animate the parametric curve

$\begin{array}{l} x = t + \sin (40 t) \\ y = - t + \cos (40 t) \\ z = \sin (t + i) . \end{array}$

To play the animation, click the image.

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

collapse all

`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
character vector | string

Line style, marker, and color, specified as a character vector or string 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
`-`	Solid line
`--`	Dashed line
`:`	Dotted line
`-.`	Dash-dot line

Marker	Description
`'o'`	Circle
`'+'`	Plus sign
`'*'`	Asterisk
`'.'`	Point
`'x'`	Cross
`'_'`	Horizontal line
`'\|'`	Vertical line
`'s'`	Square
`'d'`	Diamond
`'^'`	Upward-pointing triangle
`'v'`	Downward-pointing triangle
`'>'`	Right-pointing triangle
`'<'`	Left-pointing triangle
`'p'`	Pentagram
`'h'`	Hexagram

Color	Description
`y`	yellow
`m`	magenta
`c`	cyan
`r`	red
`g`	green
`b`	blue
`w`	white
`k`	black

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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 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. Thus, 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.

Value	Description
`'o'`	Circle
`'+'`	Plus sign
`'*'`	Asterisk
`'.'`	Point
`'x'`	Cross
`'_'`	Horizontal line
`'\|'`	Vertical line
`'square'` or `'s'`	Square
`'diamond'` or `'d'`	Diamond
`'^'`	Upward-pointing triangle
`'v'`	Downward-pointing triangle
`'>'`	Right-pointing triangle
`'<'`	Left-pointing triangle
`'pentagram'` or `'p'`	Five-pointed star (pentagram)
`'hexagram'` or `'h'`	Six-pointed star (hexagram)
`'none'`	No markers

`'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 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. Thus, 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 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. Thus, 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'

`'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

collapse all

`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.

Documentation

fplot3

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 Animations

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
character vector | string

Name-Value Pair Arguments

`'MeshDensity'` — Number of evaluation points
23 (default) | number

`'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'` | `'+'` | `'*'` | `'.'` | ...

`'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'` | ...

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

Output Arguments

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

See Also

Functions

Properties

Topics

Symbolic Math Toolbox Documentation

Support

Documentation

fplot3

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 Animations

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 character vector | string

Name-Value Pair Arguments

'MeshDensity' — Number of evaluation points 23 (default) | number

'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' | '+' | '*' | '.' | ...

'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' | ...

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

Output Arguments

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

See Also

Functions

Properties

Topics

Symbolic Math Toolbox Documentation

Support

`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
character vector | string

`'MeshDensity'` — Number of evaluation points
23 (default) | number

`'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'` | `'+'` | `'*'` | `'.'` | ...

`'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'` | ...

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

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