Question for math wizards

[Daklu]

I'm working with 3-point vectors (x, y, and t) where x and y define the location of point p and t defines the angular orientation of point p relative to the vector's frame of reference. For example, if vector AB is (2, 3, 30), that means point B (B is actually the origin of another frame of reference) is located at x=2 and y=3 in A's coordinate space and it is oriented +30 degrees with respect to A's coordinate space.

Now the problem:

Given vector AB in unknown coordinate space A, how can I calculate vector BA in coordinate space B? In other words, knowing only vector AB's values (2, 3, 30), I need to find vector BA. I'm pretty sure it's solvable mathematically--I can sketch it out on paper and visualize the solution. What I have so far works for some restricted situations but isn't robust enough to handle an arbitrary input.

Any ideas?

[drjdpowell]

Any ideas?

Only thoughts:

-- I would separate the changing of frames of reference (AB in A-frame --> AB in B-frame) from the inverting of the vector (since the later is then trivial)

-- shouldn't the change of reference frame involve two relative angles? rather that the single angle your code snippet seems to have?

-- James

[Grampa_of_Oliva_n_Eden]

I'm working with 3-point vectors (x, y, and t) where x and y define the location of point p and t defines the angular orientation of point p relative to the vector's frame of reference. For example, if vector AB is (2, 3, 30), that means point B (B is actually the origin of another frame of reference) is located at x=2 and y=3 in A's coordinate space and it is oriented +30 degrees with respect to A's coordinate space.

Now the problem:

Given vector AB in unknown coordinate space A, how can I calculate vector BA in coordinate space B? In other words, knowing only vector AB's values (2, 3, 30), I need to find vector BA. I'm pretty sure it's solvable mathematically--I can sketch it out on paper and visualize the solution. What I have so far works for some restricted situations but isn't robust enough to handle an arbitrary input.

Any ideas?

Without really thinking too much...

If you use complex notation the work is generally simler since you can just add vectors.

Ben

[vugie]

General expressions are as follows:

If you want to bring it to your notation (which I find strange personally) think of point P as negated B