VQS Transformation with an Incremental Approach

This paper presents an incremental method to 3D transformation by VQS structures. For interpolated scaling, rotation and translation between two animation key frames, with constant intervals in size, angle and distance, the proposed approach reduces the VQS transformation cost by more than an half. Moreover, all interpolations for VQS key frames are performed implicitly at no cost. In other words, the expensive trigonometric functions in quaternion Slerp and exponential functions in scalar interpolation are completely eliminated from the process. The method is fast, accurate, numerically stable and also preserves all geometric characteristics of the original transformation and interpolation algorithms.