Good parametrisations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single perfect method and each one has both advantages and disadvantages. In this paper, we propose a novel parametrisation of affine transformations, which is a generalisation to or an improvement of existing methods. Our method adds yet another choice to the existing toolbox and shows better performance in some applications. A C++ implementation is available to make our framework ready to use in various applications.
The group of rigid transformations @math can be parametrised with the dual quaternions, which is a generalisation of the parametrisation of @math by the quaternions. In @cite_12 , they used the dual quaternions to blend rigid transformations and their method works particularly well in skinning. However, for other applications we may be troubled by the complicated structure of the parameter space; the space of the unit dual quaternions is the semi-direct product of the group of the unit quaternions and @math .
@cite_12
2090782210
Skinning of skelet ally deformable models is extensively used for real-time animation of characters, creatures and similar objects. The standard solution, linear blend skinning, has some serious drawbacks that require artist intervention. Therefore, a number of alternatives have been proposed in recent years. All of them successfully combat some of the artifacts, but none challenge the simplicity and efficiency of linear blend skinning. As a result, linear blend skinning is still the number one choice for the majority of developers. In this article, we present a novel skinning algorithm based on linear combination of dual quaternions. Even though our proposed method is approximate, it does not exhibit any of the artifacts inherent in previous methods and still permits an efficient GPU implementation. Upgrading an existing animation system from linear to dual quaternion skinning is very easy and has a relatively minor impact on runtime performance.