Smooth Motion Stitching via Laplacian Optimization in Rodrigues Vector Space

Abstract

This paper presents a motion editing framework for smooth motion stitching based on Laplacian optimization in Rodrigues vector space. By representing joint rotations as continuous Rodrigues vectors, motion stitching is formulated as a temporal Laplacian optimization problem, enabling smooth transitions between motion segments while preserving characteristic temporal variations of reference motions. The proposed approach supports both intra-category replacement and cross-category motion stitching without relying on learning-based models or complex manual tuning, and is computationally efficient for interactive editing. Through a series of stitching experiments and comparisons with linear interpolation, we demonstrate that Laplacian editing produces stable and visually coherent transitions under a wide range of motion differences. Furthermore, an analysis of rotational continuity clarifies that rotation-axis inversions are rare in real motion data and explains why numerical instabilities observed in synthetic axis-flipping scenarios do not arise in practical motion stitching. These results highlight the importance of rotational representation in stabilizing temporal optimization and suggest that the proposed framework is well suited not only for animation authoring but also for motion analysis and future extensions incorporating perceptual or physiological cues.