Basics of MATLAB and Beyond

N = 20;dt = 2*pi/N;t = 0:dt:(N-1)*dt;x = [cos(t) cos(t)];y = [sin(t) sin(t)];z = [zeros(size(t)) ones(size(t))];The matrix of vertices isvert = [x’ y’ z’];The matrix of faces must be defined so that each row gives, in order, theindices of the vertices that we want to join. The first face is formed byjoining the vertices 1,N +1,N + 2 and 2; the second face is formed byjoining the vertices 2,N +2,N + 3 and 3; and so on. The faces matrixtherefore must have the form:⎛⎞1 N +1 N +2 2⎜ 2 N +2 N +3 3 ⎟⎜⎝....N − 1 2N − 1 2N NN 2N N +1 1The faces matrix can be defined as follows:.⎟⎠faces = [1:N; N+1:2*N; [N+2:2*N N+1]; [2:N 1]]’;We now have all the data we need to draw the patch:clf1view(3)0.5h = patch(’vertices’,vert,...’faces’,faces,’facecolor’,’y’);1 010xyz0y −1 −1 xTo colour the patch, we need to specify the temperature at each of thevertices. We assume a heat source is located at (x, y, z) =(−.5, 0, 0.25),and that the temperature at any point on the cylinder is inversely proportionalto its distance away from the source. The temperature at thevertices is calculated as follows:dist = sqrt((x + 0.5).^2 + y.^2 + (z - 0.25).^2);T = 1./dist;We can now do the patch colouring:colormap(hot)set(h,’facevertexcdata’,T’,...’facecolor’,’interp’,...’edgecolor’,’none’);zc○ 2000 by CRC Press LLC