Calculating bind pose/skinning matrix from world space bone matrices

Question

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

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

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.

I do it this way:

    /* 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:

    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.

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

root_bone.bind_pose_mat = bone_mat

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

/* 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.

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).

But im stuck with theory there.

Answer 1

Ok, looks like i got it working.

Math Equation is (simplified):

v' = SUM { w * m * v }

where

1. w is the weight (all bones have 1.0 weight currently)
2. m is the world space bone matrix (animation bone)
3. v is the relative vertex position of the bind pose

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

to calculate v:

vec3 v_relative = bind_bones[bone_index].inv_bone_mat * vertex_object_space

now all that was needed is:

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

ofc this can be extended by multiple bones/weight influences

i hope this helps future readers.