Some Motivating Matlab Examples

The isosurface and patch functions are used to create an isosurface of the Matlab wind.mat data illustrating where the wind speed over North America is equal to a particular value. Cones are used to show the direction and magnitude of the wind, and streamlines trace the paths of massless particles moving through the volume.

[xx yy zz] = sphere;
s = surf(xx,yy,zz);
set(s, 'EdgeColor','r','FaceColor','none'); 
axis off; 
set(gca,'DataAspectRatio',[1 1 1]);
light; 
set(s,'LineWidth',6) 
hold on;
[xx yy zz] = sphere;
s2=surf(xx/2,yy/2,zz/2);
set(s2,'CData',rand(21),'FaceColor','interp')
colormap(cool(100))
lighting phong;      
set(gca,'CameraViewAngle',7);
set(gcf,'color',[1 1 1]);

3-D model of the familiar Mobius strip shown here with four half-twists instead of the usual one, created with MATLAB 5.0 visualization features.

This surface illustrates the effect of a shock wave on contained fluid. Pressure is represented as height, while the color indicates the Mach number of the local fluid flow.

The new material command allows users to control object reflectance properties.

>> help surf
>> help surfl
>> help matrial
>> help light
>> help peaks

This image shows data from a 256 x 256 x 110 CT scan of an engine block constructed from two types of material. The engine data is displayed as an isosurface using the volume visualization functions in MATLAB 5.3 with lighting and perspective camera projection.

Magnetic Resonance Imaging (MRI) data typically contains a number of slice planes taken through a volume, such as the human body. This figure shows an isosurface with isocaps revealing a cross section of the head interior.

An image of a three dimensional Mandelbrot. While the algorithm is not that complex, the amount of computation is enormous. Depending on programming language and style, the inner loop has at least four multiplications and a square root. For a point in the Mandelbrot set, this loop is executed 1000 times and there are over a million points to check! It is not surprising that the Mandelbrot set was not discovered until the age of computers.

hold on;
[x,y,z] = sphere;
[i,j,k] = cylinder(3);
s2=surf(2.424*x, 2.424*y, (2.424*z)+2.424);
s3=surf(i./(11*k+1),j./(11*k+1),(11*k)+1);
s4=surf(6*x,6*y,(6*z)+6);
set(s2,'EdgeColor','k','FaceColor','k')
set(s2,'LineWidth',1)
set(s3,'EdgeColor','g','FaceColor','none'); 
set(s3,'LineWidth',2)
set(s4,'EdgeColor','r','FaceColor','none')
set(s4,'LineWidth',2)
axis([-6 6 -6 6 0 12]), axis off, grid off;
set(gca,'DataAspectRatio',[1 1 1]);
light;
view(-37.5,30);
shading interp;
material shiny;
lighting phong;
set(gcf,'color',[0.5 0.5 0.5]);