Abstract
This paper describes a novel iterative Inverse Kinematics (IK) solver, FABRIK, that is implemented using Conformal Geometric Algebra (CGA). FABRIK uses a forward and backward iterative approach, finding each joint position via locating a point on a line. We use the IK of a human hand as an example of implementation where a constrained version of FABRIK was employed for pose tracking. The hand is modelled using CGA, taking advantage of CGA’s compact and geometrically intuitive framework and that basic entities in CGA, such as spheres, lines, planes and circles, are simply represented by algebraic objects. This approach can be used in a wide range of computer animation applications and is not limited to the specific problem discussed here. The proposed hand pose tracker is real-time implementable and exploits the advantages of CGA for applications in computer vision, graphics and robotics.
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Notes
- 1.
Editorial note: Note here that in this chapter CGA equations are given in terms of n ∞ and \(\bar{n}\), where \(\bar{n}= -2 n_{o}\).
- 2.
Editorial note: This is essentially (4.2) for n=3.
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Aristidou, A., Lasenby, J. (2011). Inverse Kinematics Solutions Using Conformal Geometric Algebra. In: Dorst, L., Lasenby, J. (eds) Guide to Geometric Algebra in Practice. Springer, London. https://doi.org/10.1007/978-0-85729-811-9_3
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