A positioning volume ellipsoid method is proposed to represent tumor volume in the workspace of a high-intensity-focused ultrasound (HIFU) surgery platform during the platform's positioning motion. To this simplified tumor model, a nearest neighbor search method is used to determine intermediate configuration and goal configuration, which the treatment head and ultrasound focus must pass in their localization to target volume. Based on the decided configurations, the continuity condition of combined Bezier curve in Euclidean space and De Casteljau algorithm on Lie group SO(3) are integrated to construct a combined Bezier positioning path of C2 continuity at junctional configuration, and an illustration of different positioning path planning is analyzed based on a liver tumor case.
