Jump to content

Question for math wizards


Recommended Posts

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?

post-7603-0-84059000-1308119754_thumb.pn

Link to comment

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

Link to comment

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?

post-7603-0-84059000-1308119754_thumb.pn

Without really thinking too much...

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

Ben

Link to comment

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Unfortunately, your content contains terms that we do not allow. Please edit your content to remove the highlighted words below.
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...

Important Information

By using this site, you agree to our Terms of Use.