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# 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

example

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].

example

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.

example

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).

example

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

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Plot the expression over the default interval and .

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

Plot the piecewise expression

over

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

Plot the parameterized surface

for and . 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

For and from to , plot the 3-D surface . 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'};

Plot the parametric surface , , with different line styles for different values of . For , use a dashed green line for the surface edges. For , 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

Plot the parametric surface

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 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 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 , , . 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

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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);

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.

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);

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);

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;

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.

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

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 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.

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

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

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

Line style, specified as one of the options 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 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.

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

Example: '+'

Example: 'diamond'

Marker size, specified as a positive value in points.

Example: 10

## Output Arguments

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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.