== MS_interpolate

 MS_INTERPOLATE - Symmetry preserving elasticity interpolation 

 // Part of MSAT - The Matlab Seismic Anisotropy Toolkit //

 Symmetry aware linear interpolation between two elasticity matrices. 

 [ required_outputs, ... ] = MS_template( required_inputs, ... )

 Usage: 
     [ Cint ] = MS_interpolate( C1, C2, frac)                    
         Returns an elasticity matrix interpolated frac distance
         between elasticity matricies C1 and C2. 


 Notes:
     A common approach to the interpolation of elasticity matricies
     is to interpolate elements component-wise. This fails for cases 
     where the elasticity matricies are just rotated versions of each 
     other. The approach taken here is to first rotate the two matricies
     into a common orientation (the one generated by MS_axes is chosen)
     before interpolating element-wise (Voigt-Reuss-Hill is used). The 
     two rotations into the common orientation are then interpolated 
     and the interpolated matrix rotated back the the starting 
     orientation. Shoemake's (1985) slerp approach is used to interpolate
     the orientations. Rotation matricies are converted to quaternions
     (and back again) using John Fuller's SpinCalc function.

 References:
     Shoemake, K (1985) "Animating rotation with quaternion curves" ACM 
     SIGGRAPH Computer Graphics vol.19 pp.245-254.

 See also: MS_AXES, MS_VRH
