# Towards Robust Direction Invariance in Character Animation

## TL;DR

This paper investigates the challenge of achieving robust direction invariance in character animation, demonstrating the theoretical limitations and proposing a practical remedy that improves learning speed and quality in deep learning methods.

## Contribution

It proves the nonexistence of a singularity-free scheme for direction invariance, connects the problem to the hairy ball theorem, and introduces a motion-based remedy to enhance deep learning approaches.

## Key findings

- Robust direction invariant features improve learning speed.
- The proposed method enhances final animation quality.
- Theoretical proof of the nonexistence of a universal singularity-free scheme.

## Abstract

In character animation, direction invariance is a desirable property. That is, a pose facing north and the same pose facing south are considered the same; a character that can walk to the north is expected to be able to walk to the south in a similar style. To achieve such direction invariance, the current practice is to remove the facing direction's rotation around the vertical axis before further processing. Such a scheme, however, is not robust for rotational behaviors in the sagittal plane. In search of a smooth scheme to achieve direction invariance, we prove that in general a singularity free scheme does not exist. We further connect the problem with the hairy ball theorem, which is better-known to the graphics community. Due to the nonexistence of a singularity free scheme, a general solution does not exist and we propose a remedy by using a properly-chosen motion direction that can avoid singularities for specific motions at hand. We perform comparative studies using two deep-learning based methods, one builds kinematic motion representations and the other learns physics-based controls. The results show that with our robust direction invariant features, both methods can achieve better results in terms of learning speed and/or final quality. We hope this paper can not only boost performance for character animation methods, but also help related communities currently not fully aware of the direction invariance problem to achieve more robust results.