~~NOTOC~~
===== Matlab Help for Typical Situations in Homeworks ======

=== Some recommendations for the fastest progress ===
  - Do not trust any results unless you verified them.
  - <fc #FF0000>Always verify your results</fc>.
  - Try to visualize your results.
  - Each Matlab command has help. E.g. for ''plot''<code>help plot % text version
doc plot % html version</code>

== Debugging ==

Matlab has a powerful debugger. Either put breakpoints everywhere you want, or use the command ''keyboard'' in your code to stop processing at the place. Exit the debugging mode:

  dbquit
  
You can also start debugging automatically in case of error by turning on
  
  dbstop error


== Saving intermediate data ==

Especially when some user input is needed, it is wise to store intermediate data for later reuse. Following example could be helpful

  if( ~exist( 'my_points.mat', 'file' ) )
    [x y] = ginput( 7 );
    save( 'my_points.mat', 'x', 'y' );
  else
    load( 'my_points.mat' );
  end

=== Vectors and its transformations ===

<fc #FF0000>Vectors are stored as column matrices.</fc>
  u = [1;2];
  X = [1;2;3];
  Xmore = [1 2 3; 4 5 6]';  % transpose at the end

Vectors are multiplied by a matrices on the left:
  P = [1 0 0 -5; 0 1 0 -6; 0 0 1 1];  % a camera
  ux_homog = P * [X;1]; % projection

=== Special matrices: Identity, Zeros, Ones ===
  I = eye(3); % 3x3 identity
  I2 = diag( [1 1 1] ); % same result
  Z = zeros(3); % 3x3 matrix of zeroes
  O = ones(3); % 3x3 matrix of ones

=== Euclidean distance of two 3D points ===
  X1 = [1;2;3];
  X2 = [4;5;6];
  d2 = norm(X1-X2); % cannot be used for more vectors
  d2 = sqrt(sum((X1-X2).^2)); % for matrices with points stored in columns

=== Dot (scalar) product ===
  u1 = [4;5;1];
  u2 = [7;8;1];
  dot12 = u1' * u2; % apostrophe is the transpose
  
=== Element-by-element matrix operations ===
In addition to standard matrix addition and subtraction, there are some operators working element-by-element.
  M1 = [1 2; 3 4; 5 6];
  M2 = [7 8; 9 10; 11 12]; % note the sizes
  A = M1 .* M2; % Hadamard product (multiplication element-by-element; note the dot)
  B = M1 ./ M2; % Hadamard division (division element-by-element)
  C = M1 .^ 2;  % power element-by-element

=== Selection of the real part of complex numbers ===
  numbers = [1 2 sqrt(-3) acos(2) 4 6+3i 7 ];
  is_real = imag( numbers ) == 0; % logical array
  real_only = numbers( is_real );
  
=== Cross product ===
  u1 = [4;5;1];
  u2 = [7;8;1];
  u12x = cross(u1,u2);
  % verification of orthogonality by dot product 
  % (remember the recommendations 1 and 2)
  u12x' * u1 % should be zero
  u12x' * u2 % should be zero

=== Angle given x and y coordinate. ===

Let x = r cos(a) and y = r sin(a). Then the angle can be recovered as 

  a = atan2( y, x );
  
This function is safe when either of its arguments is zero (but not both), and works for four quadrants.

=== Capturing a bitmap snapshot of a figure/axis ===

Let ''hnd'' be some axes handle (e.g. ''gca'') or some figure handle (e.g. ''gcf''). The snapshot identical to the (pixel-wise) appearance of the screen is captured as

  f = getframe( hnd );
  img = f.cdata;

Notes: when capturing a sequence, do not forget to call ''drawnow'' before capturing. Also be careful not to obscure the captured window by other GUI content, mouse pointer, etc.

=== Creating a video sequence ===

  mov = avifile( 'my_file.avi' );
  mov.compression = 'none';
  mov.fps = 25; % or whatever you want
    
  % now iterate creation of frames
  % all frames must have the same size
  mov = addframe( mov, img ); 
  
  % end of frame creation 
  
  mov = close( mov );

Note that video compression (compression different from 'none') usually does not work well, so preferred way is to store raw sequence and compress later.

=== To be continued ... ===