1. Introduction to Matlab:
Matlab Graphics
3D Graphics
S. Awad, Ph.D.
M. Corless, M.S.E.E.
E.C.E. Department
University of Michigan-Dearborn

2. 3D Graphics Topics Creating Mesh and Surface Plots
Viewing a Pseudocolor Matrix
Creating Contour Plots
Adding a Color-Bar
Interpolating 3D Data

3. Mesh and Surface Plots
Useful for displaying functions of 2 variables or to visualize large matrices
Given a function f(x,y) of two variables:
Assume that:
» x=[-1:0.2:1]; y=[-1:0.2:1];
We can plot the function z as a mesh or surface plot

4. 4/15/2017
Calculating xx
Height = Length of y
Row = Vector x

5. Generating xx in Matlab
» xx=ones(length(x),1)*x
xx =

6. Calculating yy
Length = Length of y
Column = y Transpose

7. Generating yy in Matlab
» yy=y'*ones(1,length(y))
yy =

8. Find xx & yy Using Meshgrid
» [xx,yy] = meshgrid(x,y)
xx =
yy =

9. Find z Find z using element by element computations
» z=xx.*exp(-xx.^2-yy.^2)
z =

10. Mesh Plot z
» mesh(x,y,z)
Finer increments of x and y will smooth the surface

11. Mesh for a Larger x & y Create a new mesh plot complete with labels
» [xx,yy]=meshgrid(x,y);
» z=xx.*exp(-xx.^2-yy.^2);
» mesh(x,y,z)
» title('Larger Mesh');
» xlabel('X Data');
» ylabel('Y Data');
» zlabel('z=xx.*exp(-xx.^2-yy.^2)');

12. Surface Plot of z » surf(x,y,z)
Plots the colored parametric surface where color is proportional to surface height

13. Pcolor pseudocolor or "checkerboard" plot of matrix
» pcolor(x,y,z)
pseudocolor or "checkerboard" plot of matrix
The values of the elements specify the color in each cell of the plot

14. Contour Plots
contour plot of matrix where z contains heights above a plane
Number of Contour Lines
» contour(x,y,z,16);
» title('Contour');

15. Displaying Contour Heights
To write the values identifying the heights:
» cs=contour(x,y,z,16);
» clabel(cs);
» title('Contour
Heights');

16. Meshc Contour Plots
meshc is same as mesh except that a contour plot is drawn beneath the mesh
» meshc(x,y,z)
Only works for surfaces defined on a rectangular grid

17. Adding a Colorbar
colorbar adds a vertical line (color scale) to show the contour plots

18. 3D Interpolation
Rough or scattered data can be interpolated using mesh
The original data is plotted as a mesh by:
» x=[-3:3]; y=[1:5];
» [xx, yy]=meshgrid(x,y);
» z= xx + yy;
» mesh(x,y,z);
» title('Original Mesh Grid');
» xlabel('X Data'); ylabel('y Data');
» zlabel('z = xx + yy');

19. Mesh of Rough Data Original Course Surface where: x = [-3:3] y = [1:5]
z = xx+yy

20. Interpolation of Data
The original mesh from the data is can be improved by creating interpolated values using griddata:
» xi=[-3:0.5:4]; % Interpolated x axis
» yi=[ 0:0.2:5]; % Interpolated y axis
» [xxi,yyi]=meshgrid(xi,yi);
» % zi = interpolated values
» zi=griddata(xx,yy,z,xxi,yyi);
» mesh(xxi,yyi,zi); % Better surface
» title('Interpolated Mesh Grid');
» xlabel('X Data'); ylabel('y Data');
» zlabel('z = xx + yy');

21. 3D Interpolation Plot Interpolated Smooth Surface where:
xi = [-3:0.5:4]
yi = [ 0:0.2:5]