fsurf

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

syms x y
fsurf(sin(x)+cos(y))

Plot the real part of $${tan}^{-1}(x+iy)$$ over the default range $$-5<x<5$$ and $$-5<y<5$$.

syms f(x,y)
f(x,y) = real(atan(x + i*y));
fsurf(f)

Plot $$\sin (x)+\cos (y)$$ over $$-\pi <x<\pi$$ and $$-5<y<5$$ by specifying the plotting interval as the second argument of fsurf.

syms x y
f = sin(x) + cos(y);
fsurf(f, [-pi pi -5 5])

Plot the parameterized surface

for $$0<s<2\pi$$ and $$0<t<\pi$$.

Improve the plot's appearance by using camlight.

syms s t
r = 2 + sin(7*s + 5*t);
x = r*cos(s)*sin(t);
y = r*sin(s)*sin(t);
z = r*cos(t);
fsurf(x, y, z, [0 2*pi 0 pi])
camlight
view(46,52)

Plot the piecewise expression of the Klein bottle

for $0<u<2\pi$ and $0<v<2\pi$.

Show that the Klein bottle has only a one-sided surface.

syms u v;
r = @(u) 4 - 2*cos(u);
x = piecewise(u <= pi, -4*cos(u)*(1+sin(u)) - r(u)*cos(u)*cos(v),...
    u > pi, -4*cos(u)*(1+sin(u)) + r(u)*cos(v));
y = r(u)*sin(v);
z = piecewise(u <= pi, -14*sin(u) - r(u)*sin(u)*cos(v),...
    u > pi, -14*sin(u));
h = fsurf(x,y,z, [0 2*pi 0 2*pi]);

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.

Create the x-axis ticks by spanning the x-axis limits at intervals of pi/2. Convert the axis limits to precise multiples of pi/2 by using round and get the symbolic tick values in S. 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 x y
fsurf(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')

ax = gca;
S = sym(ax.XLim(1):pi/2:ax.XLim(2));
S = sym(round(vpa(S/pi*2))*pi/2);
ax.XTick = double(S);
ax.XTickLabel = arrayfun(@texlabel,S,'UniformOutput',false);

S = sym(ax.YLim(1):pi/2:ax.YLim(2));
S = sym(round(vpa(S/pi*2))*pi/2);
ax.YTick = double(S);
ax.YTickLabel = arrayfun(@texlabel,S,'UniformOutput',false);

Plot the parametric surface $$x=s\sin (t)$$, $$y=-s\cos (t)$$, $$z=t$$ with different line styles for different values of $$t$$. For $$-5<t<-2$$, use a dashed line with green dot markers. For $$-2<t<2$$, use a LineWidth of 1 and a green face color. For $$2<t<5$$, turn off the lines by setting EdgeColor to none.

syms s t
fsurf(s*sin(t),-s*cos(t),t,[-5 5 -5 -2],'--.','MarkerEdgeColor','g')
hold on
fsurf(s*sin(t),-s*cos(t),t,[-5 5 -2 2],'LineWidth',1,'FaceColor','g')
fsurf(s*sin(t),-s*cos(t),t,[-5 5 2 5],'EdgeColor','none')

Plot the parametric surface

Specify an output to make fcontour return the plot object.

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

fs = 
  ParameterizedFunctionSurface with properties:

    XFunction: exp(-abs(u)/10)*sin(5*abs(v))
    YFunction: exp(-abs(u)/10)*cos(5*abs(v))
    ZFunction: u
    EdgeColor: [0.1294 0.1294 0.1294]
    LineStyle: '-'
    FaceColor: 'interp'

  Show all properties

Change the range of u to [-30 30] by using the URange property of fs. Set the line color to blue by using the EdgeColor property and specify white, dot markers by using the Marker and MarkerEdgeColor properties.

fs.URange = [-30 30];
fs.EdgeColor = 'b';
fs.Marker = '.';
fs.MarkerEdgeColor = 'w';

Plot multiple surfaces using vector input to fsurf. Alternatively, use hold on to plot successively on the same figure. When displaying multiple surfaces on the same figure, transparency is useful. Adjust the transparency of surface plots by using the FaceAlpha property. FaceAlpha varies from 0 to 1, where 0 is full transparency and 1 is no transparency.

Plot the planes $$x+y$$ and $$x-y$$ using vector input to fsurf. Show both planes by making them half transparent using FaceAlpha.

syms x y
h = fsurf([x+y x-y]);
h(1).FaceAlpha = 0.5;
h(2).FaceAlpha = 0.5;
title('Planes (x+y) and (x-y) at half transparency')

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 $$x=\sin (s)$$, $$y=\cos (s)$$, and $$z=(t/10)\sin (1/s)$$. 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 plot's resolution.

syms s t

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

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

Show contours for the surface plot of the expression f by setting the 'ShowContours' option to 'on'.

syms x y
f = 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')

Create a symbolic expression f for the function

Plot the expression f as a surface. Improve the appearance of the surface plot by using the properties of the handle returned by fsurf, the lighting properties, and the colormap.

Create a light by using camlight. Increase brightness by using brighten. Remove the lines by setting EdgeColor to 'none'. Increase the ambient light using AmbientStrength. For details, see Lighting, Transparency, and Shading. Turn the axes box on. For the title, convert f to LaTeX using latex. Finally, to improve the appearance of the axes ticks, axes labels, and title, set 'Interpreter' to 'latex'.

syms x y
f = 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);
h = fsurf(f,[-3 3]);

camlight(110,70)
brighten(0.6)
h.EdgeColor = 'none';
h.AmbientStrength = 0.4;

a = gca;
a.TickLabelInterpreter = 'latex';
a.Box = 'on';
a.BoxStyle = 'full';

xlabel('$x$','Interpreter','latex')
ylabel('$y$','Interpreter','latex')
zlabel('$z$','Interpreter','latex')
title_latex = ['$' latex(f) '$'];
title(title_latex,'Interpreter','latex')

Plot a cylindrical shell bounded below by the $$x-y$$ plane and above by the plane $$z=x+2$$.

syms r t u
fsurf(cos(t),sin(t),u*(cos(t)+2),[0 2*pi 0 1])
hold on;

Add a surface plot of the plane $$z=x+2$$.

fsurf(r*cos(t),r*sin(t),r*cos(t)+2,[0 1 0 2*pi])

Apply rotation and translation to the surface plot of a torus.

A torus can be defined parametrically by

where

Define the values for $$a$$ and $$R$$ as 1 and 5, respectively. Plot the torus using fsurf.

syms theta phi
a = 1;
R = 4;
x = (R + a*cos(theta))*cos(phi);
y = (R + a*cos(theta))*sin(phi);
z = a*sin(theta);
fsurf(x,y,z,[0 2*pi 0 2*pi])
hold on

Apply rotation to the torus around the $$x$$-axis. Define the rotation matrix. Rotate the torus by 90 degrees or $$\pi /2$$ radians.

alpha = pi/2;
Rx = [1 0 0;
      0 cos(alpha) -sin(alpha);
      0 sin(alpha) cos(alpha)];
r = [x; y; z];
r_90 = Rx*r;

Shift the center of the torus by 5 along the $$x$$-axis. Add a second plot of the rotated and translated torus to the existing graph.

fsurf(r_90(1)+5,r_90(2),r_90(3))
axis([-5 10 -5 10 -5 5])
hold off