Dwell orientation (polar an azimuthal angles)

[adnan Jafar]

Hi,

I’m having difficulty calculating the orientation of the dwell points given the catheter path and the dwell positions on it in some x-y-z coordinate system. My current approach involves fitting a spline to the catheter coordinates, finding the closest catheter coordinate to each dwell point, and then using the derivative of the spline at that point as the potential direction vector. My question is: Would the angles theta and phi be calculated as follows?

• θ=cos−1(z/r), where r is the magnitude of the direction vector (which would be 1 in this case)
• ϕ=arctan2(y,x)

Does this seem correct?  My endpoint is to know the orientation of dwell points along with its position (which i know already).

Regards,

Adnan