cs249 lecture notes, Fall 2001
Week 5, Monday

Quiz 3

Homework 4 due Wednesday 10 October


Homework 4
----------

Here are some debugging tips that might make life easier:

1) Start with a working program.  Make small changes at a time,
and then run the program again.  If there is an error, you have
a pretty good idea where it is!

2) If the program runs into an error, reduce the level of
recursion to the simplest level that causes the error.  This
will simplify the debugging effort.

3) If you know what variable is causing the error, try
displaying the value of that variable when it gets assigned,
or when it gets passed as an argument.

4) Inside a function, it is often useful to add a line right
at the beginning that displays the values of the arguments.



Vectors
-------

MATLAB syntax

>> v = [3, 4]
>> v(1)
ans = 3
>> v(2)
ans = 4
>> norm (v)
ans=5

Vector arithmetic

division by a scalar

function vn = normalize (v)
    vn = v / norm (v);
end


addition, substraction

function vp = perpendicular (v)
    vp = [-v(2), v(1)];
end

Drawing Koch curves with two-dimensional vectors

    Fundmental theorem in linear algebra: given any
    two (non-parallel) vectors in 2-space, you can describe
    any other vector as a linear combination of the two.


Drawing lines
-------------

Foreshadowing of matrics

function drawline (v1, v2)
    z = [v1;v2];
    line (z(:,1), z(:,2))
end


function triangle (v1, v2, v3, color)
    z = [v1;v2;v3];
    fill (z(:,1), z(:,2), color)
end


Recursion
---------

function countdown (n)
    if n == 0
      disp ('Blastoff!')
    else
      disp (n)
      countdown (n-1)
    end
end

Draw a workspace diagram for this
sequence of function invocations.


Have a look at snow.m

function draw_snow (v1, v2, n)
    if (n == 0)
        drawline (v1, v2);
        return
    end
    
    v = v2 - v1;
    p1  = v1 + v / 3;
    p2  = v1 + 2 * v / 3;    
    p3  = v1 + v / 2;

    length = norm (v);
    height = length/3 * sqrt(3)/2;
    p4 = p3 + height * normalize (perp (v));
    
    draw_snow (v1, p1, n-1);
    draw_snow (p2, v2, n-1);
    draw_snow (p1, p4, n-1);
    draw_snow (p4, p2, n-1);
end

Notice that unless n==0, we don't draw any lines at all!

We just compute some intermediate values and make
recursive calls.