Dear SPM experts,
I'm trying to calculate the displacement between two successive volumes based on the rp files, basically the same what e.g. Artrepair is doing, so assuming a voxel with a certain distance to the origin.
However, the Artrepair formula seems to be an estimate only, with displacement d defined as the square root of ( (delta x)^2 + (delta y)^s + (delta z)^2 + C^2 * ( (delta pitch)^2 + (delta roll)^2 + (delta yaw)^2 ) ), with pitch, roll yaw converted from original rad to degree and then backconverted into rad with C = 65 pi/180°.
Power et al. (2012) use the formula delta x + delta y + delta z + delta alpha + delta beta + delta gamma (the magnitude each), and they additionally state "Rotational displacements were converted from degrees to millimeters by calculating displacement on the surface of a sphere of radius 50 mm".
Now I wonder, given some coordinates for a point on the sphere (x1, y1, z1), e.g. (0 0 50), the coordinates for the origin (0 0 0) and the rp parameters, what would the exact formula for the displacement be? I made a few sketches, and it seemed after definition of lots of triangles and calculations I would be able to calculate the exact displacement, but I guess the formula is accessible somewhere anyway ;)
Thank you!
Gabor
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