Octave coding - How many vectors rotated by an angle is within the distance of another vector

Question

I don't know if this is the right forum but

I am trying to code a rotating vector v by an angle theta anticlockwise n times around a circle. Afterwards, set a variable r to be the number of these n+1 vectors that are within (strictly less than) distance d of vector w.

So far what I've done is times (n+1) by the rotational vector [cos(theta),-sin(theta);sin(theta),cos(theta)] with vector v.

So

a=(n+1)*[cos(theta),-sin(theta);sin(theta),cos(theta)]*v;

I know I have to somehow incorporate norm(a-w) <= w or something as that gives the distance between the two vectors but I'm kind of stuck on how to do so.

Alternatively, I am also thinking that instead of times'ing by (n+1), I'm thinking that maybe it's wrong and that I have to make a loop like for n=1,2,...,k, if this vector is within norm(a - w) < d then sum, else disregard or something.

This would be easy if it was manual as it would only require multiplying the rotational vector by v and find the distance between the new rotated vector and vector w, and repeat it again for however many n's but I am having trouble coding this.

Any help would be appreciated

Answer 1

You want to do a for loop, as you suggest. Something similar to the following:

A = [cos(theta), -sin(theta); sin(theta), cos(theta)];

r = 0;
for k=1:n
    v = A*v;
    if norm(v-w) < d
        r = r + 1;
    end
end