Skin meshes or skeletal meshes are one of the most important subjects in a 3D world. Skeletal animation is always into focus for the important role they play in organics animation. Skeletal animations are based on the idea that the objects are shaped by multiple bones and can be animated simply by changing the bone's position and orientation. You can find many resources talking about the theory of this subject, but this article talks about the implementation of skeletal meshes with D3D8 and D3DX. But before I start talking about the implementation, I'll give a quick review on the mathematical module behind skin meshes.
Overview of Skin Meshes
Skin meshes are a type of hierarchical scene. Hierarchical scenes are used to connect objects to each other. For example, a finger is attached to the palm, which in turn is attached to the forearm and so on. The coordinates of every object is given relative to its parent's local space, hence, rotating the forearm will cause the palm and the finger to be moved and rotated as well. The following figure shows how a human body can be constructed using a hierarchical scene.
The mathematical formula for this scene is very simple; matrix algebra is the key. For the given scene, if we consider ForearmMat to be the transformation matrix of the forearm, PalmMat to be the transformation matrix of the palm and FingerMat to be the transformation matrix of the finger, then we can simply calculate the transformation matrix of the finger relative to the world by the following formula:
FingerWorldMat = FingerMat * PalmMat * ForearmMat * ... * BodyMat
In the above formula, we considered that the body is the root of the hierarchical mesh, hence, its matrix is relative to the world space. Having our mesh split into parts where each part is transformed by the world matrix of a specific bone will enable us to animate the mesh easily.
However, having the character consisting of separate fixed child objects is not accepted nowadays because it causes cracks at the joints. Hence the rise of skin meshes. Skin meshes got over this problem by having the shape of the smaller parts of the character changing according to the position and orientation of the bones. Skin meshes have the same bone hierarchies, but a single part of a skin mesh can be transformed by more than one bone. Following a linear interpolation formula, vertices can have their position affected by two (or more) bones instead of one bone. Following this method, we can overcome the problem of cracks. This technique is called Vertex Blending. Vertex Blending requires that each vertex have a blending weight(s) so that the vertex shader can determine how the bones affect the vertex. For example, if we have a vertex that's to be affected by two bones, the following formula will give the world's coordinate of the vertex as affected by the two bones:
Vw = Vm * M1 * w + Vm * M2 * (1-w)
Where Vw is the vertex position in world coordinate. Vm is the vertex position relative to the model's local space. M1 and M2 are the transformation matrices of the two bones. w is the blending weight. Note that the number of blending weights required is less than the number of bones by 1.
You can refer to the documentation of DX8 for more details about vertex blending.