% MCS 320 Wednesday 11 April 2007
% Lecture 2 : Plotting
% stage 1 : sampling of the function
% stage 2 : rendering of the samples
%
% 1. Basic Plotting
%
x = -pi:pi/20:pi; % defines plotting range
s = sin(x); % sample the sine function
plot(x,s);  % render the samples
% The increment pi/20 determines the resolution
% of the samples
plot(x,s,'+');
% MATLAB overwrote the first figure with the new plot
hold on
plot(x,s,'r');
% with the hold on we have asked MATLAB to
% keep the previous plot
figure % create a new figure window
plot(x,s,'g');
axis([-pi,pi,-2,+2]);
%
% 2. Polar plots
%
% suppose we want to plot a spiral
t = 0:0.1:10*pi;
r = 0.01*t.^2 - 0.02; % COMPONENTWISE squaring
polar(t,r);
%
% 3. Three Dimensional Plots
%
% Note the distinction between a space curve,
% which is one dimensional, and a surface, 
% which is two dimensional.
% First we plot the surface cos(x*y):
% Stage 1: we define a grid to sample the cos()
xa = -2:0.2:+2;  % range for x
ya = xa;         % same range for y
[x,y] = meshgrid(xa,ya); % creates a 2D grid
size(x)

ans =

    21    21

% Stage 2: we compute the samples COMPONENTWISE
z = cos(x.*y);
figure
mesh(x,y,z);
% the rendering is Stage 3
% The other 3D object we can plot is a space curve
% Let us plot a helix:
t = 0:0.1:10*pi; % sampling range
plot3(cos(3*t),sin(3*t),t); % sample and plot
rotate3d
% plot3 is to plot space curves
% mesh will render surfaces
% For a surface, instead of "mesh" we can make 
% a contourplot
figure
contour(z)
figure
mesh(x,y,z);
%
% 4. Subplots
%
% Often we like to have different plots
% in the same figure window, like a contourplot
% next to a the full 3D visualization of
% a surface
figure
subplot(2,1,1) % declare 2 rows 1 column 
mesh(x,y,z)
subplot(2,1,2) % activate the second plot
contour(z)
subplot(2,1,1) % activate the first plot
view([10,-10]);
view([10,10]);
diary off