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This paper presents a caging approach which deals with planar boundary clouds collected from a laser scanner. Given the boundary clouds of a target object and two fixed finger positions, our aim is to find potential third finger positions that can prevent target from escaping into infinity. The major challenge in working with boundary clouds lies in their uncertainty in geometric model fitting and the failure of critical orientations. In this paper, we track canonical motions according to the rotational intersection of Configuration space fingers and rasterize Work space with grids to compute the third caging positions. Our approach can generate the capture region with max(O(np),O(h^2))<=O(n^2) cost where n denotes the resolution of grid rasterization, p denotes the resolution of canonical rasterization and h denotes the resolution of boundary rasterization or the number of boundary cloud points. Moreover, we propose a rough approximation which measures a subset of the possible positions by contracting rotations, indicating computational complexity of max(O(n),O(h^2)). In the experimental part, our proposal is compared with state-of-the-art works and applied to many other objects. The approach makes caging fast and effective.

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