Matrix calculations for gpu skinning

Question

I'm trying to do skeletal animation in OpenGL using Assimp as my model import library.

What exactly do I need to the with the bones' offsetMatrix variable? What do I need to multiply it by?

Answer 1

Let's take for instance this code, which I used to animate characters in a game I worked. I used Assimp too, to load bone information and I read myself the OGL tutorial already pointed out by Nico.

glm::mat4 getParentTransform()
{
    if (this->parent)
        return parent->nodeTransform;
    else 
        return glm::mat4(1.0f);
}

void updateSkeleton(Bone* bone = NULL)
{ 
    bone->nodeTransform =  bone->getParentTransform() // This retrieve the transformation one level above in the tree
    * bone->transform //bone->transform is the assimp matrix assimp_node->mTransformation
    * bone->localTransform;  //this is your T * R matrix

    bone->finalTransform = inverseGlobal // which is scene->mRootNode->mTransformation from assimp
        * bone->nodeTransform  //defined above
        * bone->boneOffset;  //which is ai_mesh->mBones[i]->mOffsetMatrix


    for (int i = 0; i < bone->children.size(); i++) {
        updateSkeleton (&bone->children[i]);
    }
}

Essentially the GlobalTransform as it is referred in the tutorial Skeletal Animation with Assimp or properly the transform of the root node scene->mRootNode->mTransformation is the transformation from local space to global space. To give you an example, when in a 3D modeler (let's pick Blender for instance) you create your mesh or you load your character, it is usually positioned (by default) at the origin of the Cartesian plane and its rotation is set to the identity quaternion.

However you can translate/rotate your mesh/character from the origin (0,0,0) to somewhere else and have in a single scene even multiple meshes with different positions. When you load them, especially if you do skeletal animation, it is mandatory to translate them back in local space (i.e. back at the origin 0,0,0 ) and this is the reason why you have to multiply everything by the InverseGlobal (which brings back your mesh to local space).

After that you need to multiply it by the node transform which is the multiplication of the parentTransform (the transformation one level up in the tree, this is the overall transform) the transform (formerly the assimp_node->mTransformation which is just the transformation of the bone relative to the node's parent) and your local transformation (any T * R) you want to apply to do: forward kinematic, inverse kinematic or key-frame interpolation.

Eventually there is the boneOffset (ai_mesh->mBones[i]->mOffsetMatrix) that transforms from mesh space to bone space in bind pose as stated in the documentation.

Here there is a link to GitHub if you want to look at the whole code for my Skeleton class.

Hope it helps.

Answer 2

The offset matrix defines the transform (translation, scale, rotation) that transforms the vertex in mesh space, and converts it to "bone" space. As an example consider the following vertex and a bone with the following properties;

Vertex Position<0, 1, 2>

Bone Position<10, 2, 4>
Bone Rotation<0,0,0,1>  // Note - no rotation
Bone Scale<1, 1, 1>

If we multiply a vertex by the offset Matrix in this case we would get a vertex position of <-10, -1, 2>.

How do we use this? You have two options on how to use this matrix which is down to how we store the vertex data in the vertex buffers. The options are;

1) Store the mesh vertices in mesh space 2) Store the mesh vertices in bone space

In the case of #1, we would take the offsetMatrix and apply it to the vertices that are influenced by the bone as we build the vertex buffer. And then when we animate the mesh, we later apply the animated matrix for that bone.

In the case of #2, we would use the offsetMatrix in combination with the animation matrix for that bone when transforming the vertices stored in the vertex buffer. So it would be something like (Note: you may have to switch the matrix concatenations around here);

anim_vertex = (offset_matrix * anim_matrix) * mesh_vertex

Does this help?

Answer 3

As I already assumed, the mOffsetMatrix is the inverse bind pose matrix. This tutorial states the correct transformations that you need for linear blend skinning:

You first need to evaluate your animation state. This will give you a system transform from animated bone space to world space for every bone (GlobalTransformation in the tutorial). The mOffsetMatrix is the system transform from world space to bind pose bone space. Therefore, what you do for skinning is the following (assuming that a specific vertex is influenced by a single bone): Transform the vertex to bone space with mOffsetMatrix. Now assume an animated bone and transform the intermediate result back from animated bone space to world space. So:

boneMatrix[i] = animationMatrix[i] * mOffsetMatrix[i]

If the vertex is influenced by multiple bones, LBS simply averages the results. That's where the weights come into play. Skinning is usually implemented in a vertex shader:

vec4 result = vec4(0);
for each influencing bone i
    result += weight[i] * boneMatrix[i] * vertexPos;

Usually, the maximum number of influencing bones is fixed and you can unroll the for loop.

The tutorial uses an additional m_GlobalInverseTransform for the boneMatrix. However, I have no clue why they do that. Basically, this undoes the overall transformation of the entire scene. Probably it is used to center the model in the view.