Could someone help me with this maths problem please?
I am working on a little project involving a Tri-Axis accelerometer and I need to be able to calculate the g in a particular direction when the devices installed orientation is initially unknown.
Thus when I power the device on I have three force values let us call these the initial values. ix, iy, iz. (From these initial values we have a sense of orientation also a static total g of 1.0 = sqrt( ix2 iy2 iz2 ))
Now I accelerate the device (keeping the orientation) in a straight line so as to get a g of 1.1 (static 1g plus 0.1 acceleration) this gives me a new set of calibration g values that we can call cx, cy, cz.
What I need please is a formula for calculating the g in any direction from the calibration line/direction.
Say if I move the device forward in the same direction as the calibration direction at 0.1g then the formula/function returns 0.1, if I moved it backward the formula/function returns -0.1. and if I acceleration the device at 90 degrees to the calibration direction the formula/function returns zero.
I have tried a few ideas based on dot products but I have become stuck, any help would be much appreciated.
Added the static/initial values and a set of calibration values:
ix = 0.34
iy = -0.74
iz = -0.68
cx = 0.54
cy = -0.58
cz = -0.84
Many thanks in advance IMK