Coordinates of a point in 3D provided connecting points are known

[joinforfun89]

Hi ,


Given 3 points A[x1,y1,z1], B[x2,y2,z2] and C, and given the distance between B and C is known and the angle ABC is supplied. How do we ascertain the coordinates of the point C ?

I can calculate the dot product using the angle, by defining vectors BC and AC and then use the distance formula to get another equation for the coordinates of C. But I have a hunch that there is a simpler way to do this. I need to program this, and therefore the requirement for a simpler solution.

If there is a derivation that you know please point me towards it.

Thanks a lot in advance.


MORE Information Added:

I didn't include all the information earlier and yes Mathman is right that as stated this problem doesn't have a unique solution. This is actually a smaller part of the bigger problem I have. Here it goes.

A-B-C-D are 4 points. We define rx = length(B-C), angle, eta = (A-B-C) and angle theta = (B-C-D) and the torsion angle omega= (A-B-C-D). What I really need to do is to find the coordinates of C and D provided that I have the new values of rx, eta, theta and omega. Any pointers would be welcome.

Thanks again.

[mathman]

The problem as stated does not have enough information to get a unique solution for C. Since the problem is 3d, there will be a circle of points satisfying the requirements.

[joinforfun89]

The problem as stated does not have enough information to get a unique solution for C. Since the problem is 3d, there will be a circle of points satisfying the requirements.

I have added more information; please take a look if you get a chance ! Thank a lot.

[willem2]

You want to find 2 unknown points knowing 1 length and 3 angles. That can't be done either.