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For describing the positioning process of High Intensity Focused Ultrasound (HIFU) Surgery Platform in the application in tumor treatment, a simplified representation of the shape and location of the positioning target tumor in the workspace of the platform by the Positioning Volume Ellipsoid is designed; and the Nearest Neighbor Search method is used to find the closest center point of the simplified ellipsoid tumor model in a selected patient body surface point set determined by the motion parameter of the platform. By the query result the goal positioning path configuration and an intermediate positioning path configuration for the positioning motion are determined for the positioning motion planning. Three new criterions using distance change between Positioning Volume Ellipsoid and the Ultrasound Focus Ellipsoid are proposed to evaluate the result of the whole positioning procedure.