210 複四元数による位置・姿勢補間アルゴリズム

抄録

We are developing an algorithm to interpolate a set of key frames smoothly for keyframe animation. When positions and attitudes are interpolated separately by representing the key frames by 4×4 matrices, the resulting trajectory is not independent of the coordinate frame in which the key frames are defined. On the contrary, we represent a key frame by a double quaternion proposed by McCarthy. A double quaternion is a pair of two quaternions, which corresponds to a rotation in four dimensional space. The key frame trajectory is obtained by simply interpolating the two sets of quaternions separately using Shoemake's formula. Numerical examples of double quaternions corresponding to typical key frames are shown and a motion generated by the algorithm is illustrated.