A nonlinear exaggerated kernel framework for expressive hair motion in tracking solution-based simulation

This paper proposes a nonlinear exaggerated kernel framework for controlling the motion of ghost strands in a more expressive and stable manner in tracking solution-based hair simulation. Conventional kernel-based interpolation methods restrict interpolation coefficients between 0 and 1, which makes it difficult to sufficiently represent nonlinear hair motions such as swaying, overlapping, and splitting of ghost strands, even when large momentum is applied to guide strands. In particular, for ghost strands located between two target strands, a problem arises where motion is excessively reduced due to momentum cancellation. To address this issue, this study introduces the concept of high-frequency component enhancement from signal processing and designs an exaggerated kernel that combines a sigmoid-based low-frequency response with a nonlinear high-frequency response. The proposed kernel allows interpolation coefficients to exceed 1, thereby nonlinearly amplifying the motion of ghost strands in regions where the relative motion direction difference between strands is large. In addition, to alleviate the strand length increase problem that may occur due to exaggerated interpolation, an absolute-value-based exaggerated kernel and a positive-component-constrained kernel are introduced to ensure physical stability. Furthermore, considering that the root and tip of hair have different dynamic characteristics, a root-tip weighted kernel framework with different frequency characteristics depending on position is proposed. Through this, stable motion is maintained near the root, while natural hair motion with emphasized swaying and splitting can be effectively expressed near the tip. Through various experimental results, it is confirmed that the proposed method is superior in terms of visual expressiveness and dynamic diversity compared to conventional kernel-based tracking solutions, and it is shown that the expressiveness of hair motion can be effectively improved without modifying the physical simulation model.