INTERNATIONAL EDITION. MATLAB for Engineers. Third Edition. Holly Moore

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1 INTERNATIONAL EDITION MATLAB for Engineers Third Edition Holly Moore

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3 5.4 Three-Dimensional Plotting Figure 5.8 Simple mesh created with a single two-dimensional matrix. 5 5 Element,5 5 The code mesh(z) xlabel('') ylabel('') zlabel('') generates the graph in Figure 5.8. The graph is a mesh created by connecting the points deined in z into a rectilinear grid. Notice that the x -axis goes from to and y goes from to. The matrix index numbers were used for the axis values. For example, note that z,5 the value of z in row, column 5 is equal to 5. This element is circled in Figure 5.8. The mesh function can also be used with three arguments: mesh(x,y,z). In this case, x is a list of x -coordinates, y is a list of y -coordinates, and z is a list of z -coordinates. x = linspace(,5,) y = linspace(5,,) z = [,,, 4, 5, 6, 7, 8, 9, ;, 4, 6, 8,,, 4, 6, 8, ;, 4, 5, 6, 7, 8, 9,,, ] The x vector must have the same number of elements as the number of columns in the z vector and the y vector must have the same number of elements as the number of rows in the z vector. The command mesh(x,y,z) creates the plot in Figure 5.9a. Notice that the x -axis varies from to 5, with data plotted from to 5. Compare this scaling with that in Figure 5.8, which used the z matrix index numbers for the x- and y -axes. Surf Plots Surf plots are similar to mesh plots, but surf creates a three-dimensional colored surface instead of a mesh. The colors vary with the value of z. The surf command takes the same input as mesh : either a single input for example, surf(z), in which case it uses the row and column indices as x - and

4 Chapter 5 Plotting Figure 5.9 Mesh and surf plots are created with three input arguments. (a) Mesh Plot (b) Surface Plot (c) Contour Plot (d) Combination Surface and Contour Plot y -coordinates or three matrices. Figure 5.9 b was generated with the same commands as those used to generate Figure 5.9 a, except that surf replaced mesh. The shading scheme for surface plots is controlled with the shading command. The default, shown in Figure 5.9 b, is faceted. Interpolated shading can create interesting effects. The plot shown in Figure 5.9 c was created by adding shading interp to the previous list of commands. Flat shading without the grid is generated when shading flat KEY IDEA The colormap function controls the colors used on surface plots is used, as shown in Figure 5.9d. The color scheme used in surface plots can be controlled with the colormap function. For example, colormap(gray) forces a grayscale representation for surface plots. This may be appropriate if you ll be making black-and-white copies of your plots. Other available colormaps are autumn bone hot spring colorcube hsv summer cool pink winter copper prism jet (default) flag white

5 5.4 Three-Dimensional Plotting Figure 5. Surface and contour plots are different ways of visualizing the same data..5 (a) Mesh Plot.5 (b) Surface Plot.5.5 (c) Contour Plot (d) Combination Surface and Contour Plot.5.5 Use the help command to see a description of the various options: help colormap Another Example A more complicated surface can be created by calculating the values of Z : x= [-:.:]; y= [-:.:]; [X,Y] = meshgrid(x,y); Z = X.*exp(-X.^ - Y.^); In the preceding code, the meshgrid function is used to create the two-dimensional matrices X and Y from the one-dimensional vectors x and y. The values in Z are then calculated. The following code plots the calculated values: subplot(,,) mesh(x,y,z) title('mesh Plot'), xlabel(''), ylabel(''), zlabel('') subplot(,,) surf(x,y,z) title('surface Plot'), xlabel(''), ylabel(''), zlabel('') Either the x, y vectors or the X, Y matrices can be used to deine the x - and y -axes. Figure 5.a is a mesh plot of the given function, and Figure 5. b is a surf plot of the same function.

6 4 Chapter 5 Plotting HINT If a single vector is used in the meshgrid function, the program interprets it as [X,Y] = meshgrid(x,x) You could also use the vector deinition as input to meshgrid : [X,Y] = meshgrid(-:.:) Both of these lines of code would produce the same result as the commands listed in the example. Contour Plots Contour plots are two-dimensional representations of three-dimensional surfaces, much like the familiar contour maps used by many hikers. The contour command was used to create Figure 5. c, and the surfc command was used to create Figure 5.d : subplot(,,) contour(x,y,z) xlabel(''), ylabel(''), title('contour Plot') subplot(,,4) surfc(x,y,z) xlabel(''), ylabel('') title('combination Surface and Contour Plot') Pseudo Color Plots Pseudo color plots are similar to contour plots, except that instead of lines outlining a speciic contour, a two-dimensional shaded map is generated over a grid. MATLAB includes a sample function called peaks that generates the x, y, and z matrices of an interesting surface that looks like a mountain range: [x,y,z] = peaks; With the following code, we can use this surface to demonstrate the use of pseudo color plots, shown in Figure 5. : subplot(,,) pcolor(x,y,z) The grid is deleted when interpolated shading is used: subplot(,,) pcolor(x,y,z) shading interp You can add contours to the image by overlaying a contour plot: subplot(,,) pcolor(x,y,z) shading interp hold on contour(x,y,z,,'k') The number speciies that contour lines are drawn, and the 'k' indicates that the lines should be black. If we hadn t speciied black lines, they would

7 5.5 Editing Plots from the Menu Bar 5 Figure 5. A variety of contour plots is available in MATLAB. (a) Pseudo Color Plot (b) Interpolated Shading (c) Overlaid Pseudo Color and Contour (d) Contour Plot have been the same color as the pseudo color plot and would have disappeared into the image. Finally, a simple contour plot was added to the igure for comparison: subplot(,,4) contour(x,y,z) Additional options for using all the three-dimensional plotting functions are included in the help window. KEY IDEA When you interactively edit a plot, your changes will be lost if you rerun the program 5.5 EDITING PLOTS FROM THE MENU BAR In addition to controlling the way your plots look by using MATLAB commands, you can edit a plot once you ve created it. The plot in Figure 5. was created with the sphere command, which is one of several sample functions, like peaks, used to demonstrate plotting. sphere In the igure, the Insert menu has been selected. Notice that you can insert labels, titles, legends, text boxes, and so on, all by using this menu. The Tools menu allows you to change the way the plot looks, by zooming in or out, changing the aspect ratio, etc. The igure toolbar, underneath the menu toolbar, offers icons that allow you to do the same thing. The plot in Figure 5. doesn t really look like a sphere; it s also missing labels and a title, and the meaning of the colors may not be clear. We edited this plot by irst adjusting the shape: Select Edit:Axes Properties from the menu toolbar. From the Property Editor Axes window, select More Properties : Data Aspect Ratio Mode. Set the mode to manual (see Figure 5. ).