3-D Math Question

[floatingpoint]

Hi
Thanks for looking at this.

I have 4 points in 3-D Cartesian system and I know the coordinates of points 1,2 and 3.
The question is how to determine the (x,y,z) coordinates of point 4 given the
following information:
a] Distance between point 3 and point 4.
b] Angle between the points 2, 3 and 4.
c] The torsion angle between points 1,2, 3 and 4.

It would be very helpful if someone can describe the math that needs to be done with the equations. Please don't use any advanced math like rotation matrices, etc.


Any help would be greatly appreciated.

Thanks.

[WingedPanther]

At the very least, you will need trigonometry. It would be helpful if you had some examples, just to step through the calculations.

[floatingpoint]

I don't have specific examples because I need to program this for any general case. Yes I guess Trigonometry is needed but I don't know how to proceed . Thanks for looking at the question.

[WingedPanther]

I can help step you through the math (and thus the logic), but you need to start with some values to play with.

[floatingpoint]

I can help step you through the math (and thus the logic), but you need to start with some values to play with.

Ok. Let's start with the most general case where we can set up the coordinate system ourselves.
Point 1 is at the origin, [0,0,0]
Point 2 is along the Z axis say [0,0,10]
Point 3 is in the XZ plane [3,5,0]
Now the inputs are distance between 1-2 = 10
angle 1-2-3 can be calculated from the coordinates.
angle 2-3-4 to be imposed as 60 degrees.
Torsion angle 1-2-3-4 to be imposed as 120 degrees.

I hope this helps you to help me

[WingedPanther]

You need the distance from point 4 to one of the points.