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A tetrahedron is to be moved along a trajectory such that at the end of the...

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Advance Math

A tetrahedron is to be moved along a trajectory such that at theend of the trajectory (t=1)

it is rotated 45 deg. about the vector [1,1,1] (positiverotation) and the centroid of the
tetrahedron is translated to [x,y,z]=[2.525, 1.675, 1.575].Calculate the transformation
matrix at t=.50 using linear interpolation for the translationaland rotational part of the
transformation matrix. (Hint: for the rotational part interpolatethe quaternion
representation of the rotational part).

A tetrahedron originally has coordinates at t=0:

P1=(1.5,0.20,1.5)

P2=(2,0,0)

P3=(1,0,0)

P4=(1.6,2.5,0.8)

Centroid=(1.525,0.675,0.575)

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