Page 151 - Computational Statistics Handbook with MATLAB

138 Computational Statistics Handbook with MATLAB

Sur
aacePlotPlot
ce
Su rf faacePlotcePlots s ss
SSuurr ff
If we have data that represents a function defined over a bivariate domain,
(
,
such as z = f x y) , then we can view our values for z as a surface. MATLAB
provides two functions that display a matrix of z values as a surface: mesh
and surf.
The mesh function displays the values as points above a rectangular grid
in the x-y plane and connects adjacent points with straight lines. The mesh
lines can be colored using various options, but the default method maps the
height of the surface to a color.
The surf function is similar to mesh, except that the open spaces between
the lines are filled in with color, with lines shown in black. Other options
available with the shading command remove the lines or interpolate the
color across the patches. An example of where the ability to display a surface
can be used is in visualizing a probability density function (see Chapter 8).

Example 5.12
In this example, we begin by generating a grid over which we evaluate a
bivariate normal density function. We then calculate the z values that corre-
spond to the function evaluated at each x and y. We can display this as a sur-
face using surf, which is shown in Figure 5.18.
% Create a bivariate standard normal.
% First create a grid for the domain.
[x,y] = meshgrid(-3:.1:3,-3:.1:3);
% Evaluate using the bivariate standard normal.
z = (1/(2*pi))*exp(-0.5*(x.^2+y.^2));
% Do the plot as a surface.
surf(x,y,z)

Special effects can be achieved by changing color maps and using lighting.
For example, lighting and color can help highlight structure or features on
functions that have many bumps or a jagged surface. We will see some exam-
ples of how to use these techniques in the next section and in the exercises at
the end of the chapter.

Contour ContourContour Contour Plot Plots PlotPlot s ss
We can also use contour plots to view our surface. Contour plots show lines
of constant surface values, similar to topographical maps. Two functions are
available in MATLAB for creating 2-D and 3-D contour plots. These are called
contour and contour3.
The pcolor function shows the same information that is in a contour plot
by mapping the surface height to a set of colors. It is sometimes useful to com-
bine the two on the same plot. MATLAB provides the contourf function

© 2002 by Chapman & Hall/CRC