By binding vertexes to certain joints we are able to move clusters of vertexes around a particular joint. After this stage artists are able to take more control over how areas deform by manual Weight Painting.
Initial transformations and interpolation between vertex clusters usually depend on algorithms that were used to skin or weight vertexes to joint: Quaternion interpolation, Heat Distribution functions, etc...
Each 3D Software has its own process of making a skeleton and each of its components may have different names, but the concept is all the same.Joints and Bones may also be named differently depending on the software or users input. Inside 3D Software like Maya, 3D Studio Max, Unreal Engine or Unity3D the naming convention of your bones may all be different.
When the artist has both, a geometrical model of a digital double and its skeletal structure with the proper naming convention and all joint positions and rotations in place, the weight painting process may begin.
The weight painting process is a method of assignment of vertexes to bones, so when a joint gets repositioned or rotated, the whole cluster of vertexes will also get repositioned or rotated accordingly to the joints point of translation and rotation, which is sometimes called the Pivot Point.
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Professional 3D Modeler with 17 years of combined VFX and Games experience, managing Vancouver-based 3D Scanning Studio,
Servicing Visual Effects for Film, Television, Games and Virtual Reality production studios.