How to convert 3D pose sequences to the bvh file format?

Question

I am very new to animation and rendering softwares, so please let me know if I need to provide more information about this. I have a sequence of 3D positions of human joints (basically mocap data), representing different kinds of walking. I have managed to visualize the sequence using python, as I have shown in this video. Each data I have is a numpy array of size TxJx3, where T is the number of frames, J is the number of joints (21 in my case), and 3 represents the 3 co-ordinate values. So my question is, how can I convert these 3D positions into a BVH file, that I can load into blender? Or convert them to any other format so that I can load these data in blender?

Answer 1

OK, found the solution myself. Posting here in case anyone else finds this useful. Please excuse the absence of LaTeX rendering, apparently, stack overflow does not support it (yet), and I'm too new here to be able to attach images.

So, in the BVH format, the following relationship holds between the joints:

$$pos_j = R_{P(j)}offset_j + pos_{P(j)}$$

where $pos_j$ indicates the 3D position of joint $j$, $P(j)$ returns the parent of joint $j$ in whatever DAG the positions are modeled in (generally the DAG starts at the root and points towards the end-effectors) $offset_j$ indicates the offset of joint $j$ relative to its parent $P(j)$ (aka the connecting limb), and $R_{P(j)}$ is the 3D rotation that determines how much should $offset_j$ be rotated from an initial pose (generally a T-pose). In the BVH format, for each parent $P(j)$, we need to store $R_{P(j)}^{-1}R_j$.

The main trouble I had then was working with joints that had multiple children, for example, the root joint, which has connections to both legs as well as the spine. I eventually came across this repo and digging through their function forward_kinematics inside skeleton.py, realized what to do. Basically, for joints with multiple children, I had to make copies with $offset=0$, and assign those as parents of the corresponding chains. Thus I made 3 copies of the root: one became the parent for the left leg chain, one for the right leg chain, and one for the spine. And similarly for the other parents with multiple children. And yes, the visualization works great!