fsurf

Plot 3-D surface

Syntax

fsurf(f)

fsurf(f,xyinterval)

fsurf(funx,funy,funz)

fsurf(funx,funy,funz,uvinterval)

fsurf(___,LineSpec)

fsurf(___,Name,Value)

fsurf(ax,___)

fs = fsurf(___)

Description

fsurf(f) creates a surface plot of the function z = f(x,y) over the default interval [-5 5] for x and y.

fsurf(f,xyinterval) plots over the specified interval. To use the same interval for both x and y, specify xyinterval as a two-element vector of the form [min max]. To use different intervals, specify a four-element vector of the form [xmin xmax ymin ymax].

fsurf(funx,funy,funz) plots the parametric surface defined by x = funx(u,v), y = funy(u,v), z = funz(u,v) over the default interval [-5 5] for u and v.

fsurf(funx,funy,funz,uvinterval) plots over the specified interval. To use the same interval for both u and v, specify uvinterval as a two-element vector of the form [min max]. To use different intervals, specify a four-element vector of the form [umin umax vmin vmax].

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

fsurf(___,Name,Value) specifies surface properties using one or more name-value pair arguments. Use this option after any of the input argument combinations in the previous syntaxes.

fsurf(ax,___) plots into the axes specified by ax instead of the current axes (gca).

fs = fsurf(___) returns a FunctionSurface object or ParameterizedFunctionSurface object, depending on the inputs. Use fs to query and modify properties of a specific surface. For a list of properties, see FunctionSurface Properties or ParameterizedFunctionSurface Properties.

Examples

3-D Surface Plot of Expression

Plot the expression $$\sin (x)+\cos (y)$$ over the default interval $$-5<x<5$$ and $$-5<y<5$$.

fsurf(@(x,y) sin(x)+cos(y))

Specify Interval of Surface Plot and Plot Piecewise Expression

Plot the piecewise expression

$$\begin{array}{cc}erf(x)+\cos (y)& -5<x<0\\ \sin (x)+\cos (y)& 0<x<5\end{array}$$

over $$-5<y<5.$$

Specify the plotting interval as the second input argument of fsurf. When you plot multiple surfaces over different intervals in the same axes, the axis limits adjust to include all the data.

f1 = @(x,y) erf(x)+cos(y);
fsurf(f1,[-5 0 -5 5])
hold on
f2 = @(x,y) sin(x)+cos(y);
fsurf(f2,[0 5 -5 5])
hold off

Parameterized Surface Plot

Plot the parameterized surface

$$\begin{array}{c}x=r\cos (u)\sin (v)\\ y=r\sin (u)\sin (v)\\ z=r\cos (v)\\ wherer=2+\sin (7u+5v)\end{array}$$

for $$0<u<2\pi$$ and $$0<v<\pi$$. Add light to the surface using camlight.

r = @(u,v) 2 + sin(7.*u + 5.*v);
funx = @(u,v) r(u,v).*cos(u).*sin(v);
funy = @(u,v) r(u,v).*sin(u).*sin(v);
funz = @(u,v) r(u,v).*cos(v);
fsurf(funx,funy,funz,[0 2*pi 0 pi]) 
camlight

Add Title and Axis Labels and Format Ticks

For $$x$$ and $$y$$ from $$-2\pi$$ to $$2\pi$$, plot the 3-D surface $$y\sin (x)-x\cos (y)$$. Add a title and axis labels and display the axes outline.

fsurf(@(x,y) y.*sin(x)-x.*cos(y),[-2*pi 2*pi])
title('ysin(x) - xcos(y) for x and y in [-2\pi,2\pi]')
xlabel('x');
ylabel('y');
zlabel('z');
box on

Set the x-axis tick values and associated labels using the XTickLabel and XTick properties of axes object. Access the axes object using gca. Similarly, set 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 = -2*pi:pi/2:2*pi;
ax.YTickLabel = {'-2\pi','-3\pi/2','-\pi','-\pi/2','0','\pi/2','\pi','3\pi/2','2\pi'};

Specify Surface Properties

Plot the parametric surface $$x=u\sin (v)$$, $$y=-u\cos (v)$$, $$z=v$$ with different line styles for different values of $$v$$. For $$-5<v<-2$$, use a dashed green line for the surface edges. For $$-2<v<2$$, turn off the edges by setting the EdgeColor property to 'none'.

funx = @(u,v) u.*sin(v);
funy = @(u,v) -u.*cos(v);
funz = @(u,v) v;

fsurf(funx,funy,funz,[-5 5 -5 -2],'--','EdgeColor','g')
hold on
fsurf(funx,funy,funz,[-5 5 -2 2],'EdgeColor','none')
hold off

Modify Surface After Creation

Plot the parametric surface

$$\begin{array}{c}x=e^{-\left|u\right|/10}\sin (5|v|)\\ y=e^{-\left|u\right|/10}\cos (5|v|)\\ z=u.\end{array}$$

Assign the parameterized function surface object to a variable.

x = @(u,v) exp(-abs(u)/10).*sin(5*abs(v));
y = @(u,v) exp(-abs(u)/10).*cos(5*abs(v));
z = @(u,v) u;
fs = fsurf(x,y,z)

fs = 
  ParameterizedFunctionSurface with properties:

    XFunction: @(u,v)exp(-abs(u)/10).*sin(5*abs(v))
    YFunction: @(u,v)exp(-abs(u)/10).*cos(5*abs(v))
    ZFunction: @(u,v)u
    EdgeColor: [0 0 0]
    LineStyle: '-'
    FaceColor: 'interp'

  Show all properties

Change the plotting interval for u to [-30 30] by setting the URange property of object. Add transparency to the surface by setting the FaceAlpha property to a value between 0 (transparent) and 1 (opaque).

fs.URange = [-30 30];

fs.FaceAlpha = .5;

Show Contours Below Surface Plot

Show contours below a surface plot by setting the 'ShowContours' option to 'on'.

f = @(x,y) 3*(1-x).^2.*exp(-(x.^2)-(y+1).^2)...
    - 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2)...
    - 1/3*exp(-(x+1).^2 - y.^2);
fsurf(f,[-3 3],'ShowContours','on')

Control Resolution of Surface Plot

Control the resolution of a surface plot using the 'MeshDensity' option. Increasing 'MeshDensity' can make smoother, more accurate plots while decreasing it can increase plotting speed.

Divide a figure into two using subplot. In the first subplot, plot the parametric surface $$x=\sin (s)$$, $$y=\cos (s)$$, $$z=(t/10)\sin (1/s)$$. The surface has a large gap. Fix this issue by increasing the 'MeshDensity' to 40 in the second subplot. fsurf fills the gap, showing that by increasing 'MeshDensity' you increased the resolution.

subplot(2,1,1)
fsurf(@(s,t) sin(s), @(s,t) cos(s), @(s,t) t/10.*sin(1./s))
view(-172,25)
title('Default MeshDensity = 35')

subplot(2,1,2)
fsurf(@(s,t) sin(s), @(s,t) cos(s), @(s,t) t/10.*sin(1./s),'MeshDensity',40)
view(-172,25)
title('Increased MeshDensity = 40')

Input Arguments

f — 3-D function to plot

function handle

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

Specify a function of the form z = f(x,y). The function must accept two matrix input arguments and return a matrix 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: f = @(x,y) sin(x) + cos(y);

xyinterval — Plotting interval for x and y

[-5 5 -5 5] (default) | vector of form [min max] | vector of form [xmin xmax ymin ymax]

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

• Vector of form [min max] — Use the interval [min max] for both x and y

• Vector of form [xmin xmax ymin ymax] — Use the interval [xmin xmax] for x and [ymin ymax] for y.

funx — Parametric function for x coordinates

function handle

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

Specify a function of the form x = funx(u,v). The function must accept two matrix input arguments and return a matrix 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 = @(u,v) u.*sin(v);

funy — Parametric function for y coordinates

function handle

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

Specify a function of the form y = funy(u,v). The function must accept two matrix input arguments and return a matrix 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) @(u,v) -u.*cos(v);

funz — Parametric function for z coordinates

function handle

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

Specify a function of the form z = funz(u,v). The function must accept two matrix input arguments and return a matrix 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 = @(u,v) v;

uvinterval — Plotting interval for u and v

[-5 5 -5 5] (default) | vector of form [min max] | vector of form [umin umax vmin vmax]

Plotting interval for u and v, specified in one of these forms:

• Vector of form [min max] — Use the interval [min max] for both u and v

• Vector of form [umin umax vmin vmax] — Use the interval [umin umax] for u and [vmin vmax] for v.

ax — Axes object

axes object

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

LineSpec — Line specification

character vector | string

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 Specifier	Description
-	Solid line (default)
--	Dashed line
:	Dotted line
-.	Dash-dot line

Marker Specifier	Description
o	Circle
+	Plus sign
*	Asterisk
.	Point
x	Cross
s	Square
d	Diamond
^	Upward-pointing triangle
v	Downward-pointing triangle
>	Right-pointing triangle
<	Left-pointing triangle
p	Pentagram
h	Hexagram

Color Specifier	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 list here are only a subset. For a full list, see FunctionSurface Properties orParameterizedFunctionSurface Properties.

'MeshDensity' — Number of evaluation points per direction

35 (default) | number

Number of evaluation points per direction, specified as a number. The default is 35. Because fsurf objects use adaptive evaluation, the actual number of evaluation points is greater.

Example: 100

'ShowContours' — Display contour plot under plot

'off' (default) | 'on'

Display contour plot under plot, specified as 'off' (default) or 'on'.

'EdgeColor' — Line color

[0 0 0] (default) | 'interp' | RGB triplet | hexadecimal color code | 'r' | 'g' | 'b' | ...

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. 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'

'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.

'Marker' — Marker symbol

'none' (default) | 'o' | '+' | '*' | '.' | 'x' | ...

Marker symbol, specified as one of the markers listed in this table. By default, the object does not display markers. Specifying a marker symbol adds markers at the intersection points of mesh lines.

Value	Description
'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

Example: '+'

Example: 'diamond'

'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

fs — One or more FunctionSurface or ParameterizedFunctionSurface objects

scalar | vector

One or more FunctionSurface or ParameterizedFunctionSurface objects, returned as a scalar or a vector.

• If you use the fsurf(f) syntax or a variation of this syntax, then fsurf returns FunctionSurface objects.

• If you use the fsurf(funx,funy,funz) syntax or a variation of this syntax, then fsurf returns ParameterizedFunctionSurface objects.

You can use these objects to query and modify properties of a specific surface. For a list of properties, see FunctionSurface Properties and ParameterizedFunctionSurface Properties.