# Documentation

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# fplot3

3-D parametric curve plotter

## Syntax

fplot3(funx,funy,funz)
fplot3(funx,funy,funz,tinterval)
fplot3(___,LineSpec)
fplot3(___,Name,Value)
fplot3(ax,___)
fp = fplot3(___)

## Description

example

fplot3(funx,funy,funz) plots the parametric curve defined by x = funx(t), y = funy(t), and z = funz(t) over the default interval [-5,5] for t.

example

fplot3(funx,funy,funz,tinterval) plots over the specified interval. Specify the interval as a two-element vector of the form [tmin tmax].

example

fplot3(___,LineSpec) sets the line style, marker symbol, and line color. For example, '-r' specifies a red line. Use this option after any of the previous input argument combinations.
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.

example

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

## Examples

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Plot the 3-D parametric line

over the default parameter range [-5 5].

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

Plot the parametric line

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

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

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

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

Plot multiple lines in the same axes using hold on.

fplot3(@(t)t, @(t)t, @(t)t) hold on fplot3(@(t)-t, @(t)t, @(t)-t) hold off

Plot the parametric line

Assign the parameterized function line object to a variable.

xt = @(t)exp(-abs(t)/10).*sin(5*abs(t)); yt = @(t)exp(-abs(t)/10).*cos(5*abs(t)); zt = @(t)t; fp = fplot3(xt,yt,zt)
fp = ParameterizedFunctionLine with properties: XFunction: @(t)exp(-abs(t)/10).*sin(5*abs(t)) YFunction: @(t)exp(-abs(t)/10).*cos(5*abs(t)) ZFunction: @(t)t Color: [0 0.4470 0.7410] LineStyle: '-' LineWidth: 0.5000 Show all properties 

Change the range of parameter values to [-10 10] and change the line color to red.

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

For values in the range to , plot the parametric line

Add a title, x-axis label, and y-axis label. Additionally, change the view of the axes and display the axes box outline.

xt = @(t)t; yt = @(t)t/2; zt = @(t)sin(6*t); fplot3(xt,yt,zt,[-2*pi 2*pi],'MeshDensity',30,'LineWidth',1); title('x=t, y=t/2, z=sin(6t) for -2\pi<t<2\pi') xlabel('x'); ylabel('y'); view(52.5,30) box on

Access the axes object using gca. Specify the x-axis tick values and associated labels using the XTick and XTickLabel properties of the axes object. Similarly, specify the y-axis tick values and associated labels.

ax = gca; ax.XTick = -2*pi:pi/2:2*pi; ax.XTickLabel = {'-2\pi','-3\pi/2','-\pi','-\pi/2','0','\pi/2','\pi','3\pi/2','2\pi'}; ax.YTick = -pi:pi/2:pi; ax.YTickLabel = {'-\pi','-\pi/2','0','\pi/2','\pi'};

## Input Arguments

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Parametric function for x coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form x = funx(t). The function must accept a vector input argument and return a vector 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: funx = @(t) sin(2*t);

Parametric function for y coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form y = funy(t). The function must accept a vector input argument and return a vector 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: funy = @(t) cos(2*t);

Parametric function for z coordinates, specified as a function handle to a named or anonymous function.

Specify a function of the form z = funz(t). The function must accept a vector input argument and return a vector 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: funz = @(t) t;

Interval for parameter t, specified as a two-element vector of the form [tmin tmax].

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

Line specification, specified as a character vector or string with a line style, marker, and color. The elements can appear in any order, and you can omit one or more options. To show only markers with no connecting lines, specify a marker and omit the line style.

Example: 'r--o' specifies a red color, a dashed line, and circle markers

Line Style SpecifierDescription
-Solid line (default)
--Dashed line
:Dotted line
-.Dash-dot line
Marker SpecifierDescription
oCircle
+Plus sign
*Asterisk
.Point
xCross
sSquare
dDiamond
^Upward-pointing triangle
vDownward-pointing triangle
>Right-pointing triangle
<Left-pointing triangle
pPentagram
hHexagram
Color SpecifierDescription

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 single 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.

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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.

Line color, specified as an RGB triplet or one of the color options listed in the table.

For a custom color, specify an RGB triplet. 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]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
'red' or 'r'Red[1 0 0]
'green' or 'g'Green[0 1 0]
'blue' or 'b'Blue[0 0 1]
'yellow' or 'y'Yellow[1 1 0]
'magenta' or 'm'Magenta[1 0 1]
'cyan' or 'c'Cyan[0 1 1]
'white' or 'w'White[1 1 1]
'black' or 'k'Black[0 0 0]

Example: 'blue'

Example: [0 0 1]

Line style, specified as one of the line styles 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. If the line has markers, then the line width also affects the marker edges.

Example: 0.75

Marker symbol, specified as one of the values in this table. By default, a line does not have markers. Add markers at selected points along the line by specifying a marker.

ValueDescription
'o'Circle
'+'Plus sign
'*'Asterisk
'.'Point
'x'Cross
'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

Marker outline color, specified as 'auto', an RGB triplet, or one of the color options listed in the table. The default value of 'auto' uses the same color as the Color property.

For a custom color, specify an RGB triplet. 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]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
'red' or 'r'Red[1 0 0]
'green' or 'g'Green[0 1 0]
'blue' or 'b'Blue[0 0 1]
'yellow' or 'y'Yellow[1 1 0]
'magenta' or 'm'Magenta[1 0 1]
'cyan' or 'c'Cyan[0 1 1]
'white' or 'w'White[1 1 1]
'black' or 'k'Black[0 0 0]
'none'No colorNot applicable

Example: [0.5 0.5 0.5]

Example: 'blue'

Marker fill color, specified as 'auto', an RGB triplet, or one of the color options listed in the table. The 'auto' value uses the same color as the MarkerEdgeColor property.

For a custom color, specify an RGB triplet. 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]. Alternatively, you can specify some common colors by name. This table lists the long and short color name options and the equivalent RGB triplet values.

OptionDescriptionEquivalent RGB Triplet
'red' or 'r'Red[1 0 0]
'green' or 'g'Green[0 1 0]
'blue' or 'b'Blue[0 0 1]
'yellow' or 'y'Yellow[1 1 0]
'magenta' or 'm'Magenta[1 0 1]
'cyan' or 'c'Cyan[0 1 1]
'white' or 'w'White[1 1 1]
'black' or 'k'Black[0 0 0]
'none'No colorNot applicable

Example: [0.3 0.2 0.1]

Example: 'green'

Marker size, specified as a positive value in points.

Example: 10

## Output Arguments

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