Bvh文件里的旋转顺序（rotation order)用的是intrinsic rotation

bvh文件里的旋转顺序.txt

Bvh文件里的旋转顺序（rotation order)

Bvh内的旋转用的是intrinsic rotation，举例：
Bvh文件里面的旋转顺序如果是“Zrotation Xrotation Yrotation”，说明是先绕Z转，然后绕“一次旋转后“、“新的”X轴转，然后绕“两次旋转后“、“新的”Y轴转。因为intrinsic rotation跟extrinsic rotation有“逆序等价”的关系，并且extrinsic rotation三次旋转的旋转矩阵可以直接连乘，所以整体的旋转：
v_rot = M_whole * v_ori
M_whole = M_z * M_x * M_y * v_ori

从以下两个bvh的介绍文档里面可以推理出上述结论：
1. Biovision BVH
https://research.cs.wisc.edu/graphics/Courses/cs-838-1999/Jeff/BVH.html
“
You can see that the order of the rotation channels appears a bit odd, it goes Z rotation, followed by the X rotation and finally the Y rotation. This is not a mistake, the BVH format uses a somewhat unusual rotation order. Place the data elements into your data structure in this order.
”

“
A straightforward way to create the rotation matrix is to create 3 separate rotation matrices, one for each axis of rotation. Then concatenate the matrices from left to right Y, X and Z.
vR = vYXZ
”

2. Motion Capture File Formats Explained
http://www.dcs.shef.ac.uk/intranet/research/public/resmes/CS0111.pdf


3. blender的import_bvh.py文件里
https://github.com/blender/blender-addons/blob/master/io_anim_bvh/import_bvh.py

这里对旋转顺序做了一个倒序，blender bpy.mathutils.Euler用的都是extrinsic rotation，倒序说明从bvh里面读取的角度是当做intrinsic rotation来处理的。