从世界空间骨矩阵计算绑定姿势/皮肤矩阵

Currently i store all bones in world space and load them directly from binary file.

目前我将所有骨骼存储在世界空间中并直接从二进制文件加载它们。

I check this skeleton by placing an "arrow object" with the matrix bone_mat as "modelmatrix". Works as expected.

我通过放置一个矩形bone_mat为“modelmatrix”的“箭头对象”来检查这个骨架。按预期工作。

Variable explanations:

 1. bone_mat        = world_space bone matrix (loaded from file)
 2. bind_pose_mat   = relative transformation from parent bone to current bone
 3. skinning_mat    = final joint transformation matrix

The next step is to calculate the bind pose matrix. The relative bone matrix to its parent.

下一步是计算绑定姿势矩阵。相对骨骼矩阵到其父级。

I do it this way:

我是这样做的：

    /* bone mat * inverse(parent bone mat) */
    mesh->anim_data.skeleton[i].bind_pose_mat = 
urdMat4MulMat4( mesh->anim_data.skeleton[i].bone_mat, urdMat4Inverse(parent_bone->bone_mat) );

I check this matrix by getting it into world space again like this:

我通过再次进入世界空间来检查这个矩阵，如下所示：

    world_space_mat = 
urdMat4MulMat4( mesh->anim_data.skeleton[i].bind_pose_mat, parent_bone->bone_mat);

Which results in the same matrix as bone_mat.

这导致与bone_mat相同的矩阵。

Root bones are stored in world space, as they are not relative to any parent

根骨骼存储在世界空间中，因为它们与任何父级不相关

root_bone.bind_pose_mat = bone_mat

so now that im in local space, i though all i needed to do was

所以现在我在当地的空间，我虽然我需要做的就是

/* interpolated vertex = base_vertex * bones[bone_index].bind_pose_mat */ 
mesh->interpolated[i].vertex = urdMat4MulVec3(skeleton[bone_index].bind_pose_mat , mesh->base[i].vertex);

which results in a distorted mesh.

这会导致网格扭曲。

Edit: After some thoughts, it looks like im not in local space, but in relative space (bind_pose is currently the relative matrix to its parent).

编辑：经过一些思考，看起来我不是在局部空间，而是在相对空间（bind_pose目前是其父级的相对矩阵）。

But im stuck with theory there.

但我坚持理论。

1 个解决方案

#1

Ok, looks like i got it working.

好吧，看起来我搞定了。

Math Equation is (simplified):

数学方程式（简化）：

v' = SUM { w * m * v }

where

哪里

1. w is the weight (all bones have 1.0 weight currently)
2. w是重量（目前所有骨头都有1.0重量）
3. m is the world space bone matrix (animation bone)
4. m是世界空间骨骼矩阵（动画骨骼）
5. v is the relative vertex position of the bind pose
6. v是绑定姿势的相对顶点位置

inv_bone_mat = the inverted world space bone matrix
bone_mat = world space bone matrix

to calculate v:

计算v：

vec3 v_relative = bind_bones[bone_index].inv_bone_mat * vertex_object_space

now all that was needed is:

现在所需要的只是：

vec3 skinned_vertex = frame[current_frame].anim_bones[bone_index].bone_mat * v_relative

ofc this can be extended by multiple bones/weight influences

这可以通过多个骨骼/重量影响来扩展

i hope this helps future readers.

我希望这有助于未来的读者。