Fast Study Quadric Interpolation in the Conformal Geometric Algebra Framework

Interpolating trajectories of points and geometric entities is an important problem for kinematics. To describe these trajectories, several algorithms have been proposed using matrices, quaternions, dual-quaternions, the Study quadric; last one allows embedding motors as 8D vectors into projective space P7, where interpolation rotations translations becomes a linear problem. Furthermore, conformal algebra (CGA) effective intuitive framework representing manipulating in Euclidean spaces, it use quaternions dual-quaternions formulated Motors. In this paper, new methodology accelerating quadric Interpolation based on Conformal Geometric Algebra presented. This uses General Purpose Graphics Processing Units (GPUs) applied medical robotics, but can also be extended to other areas such aeronautics, graphics processing.