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This paper proposes a methodology that allows users to control character's motion interactively but continuously. Inspired by the work of Gleicher et al. [GSKJ03], we propose a semi-automatic method to build fat graphs where a node corresponds to a pose and its incoming and outgoing edges represent the motion segments starting from and ending at similar poses. A group of edges is built into a fat edge that parameterizes similar motion segments into a blendable form. Employing the existing motion transition and blending methods, our run-time system allows users to control a character interactively in continuous parameter spaces with conventional input devices such as joysticks and the mice. The capability of the proposed methodology is demonstrated through several applications. Although our method has some limitations on motion repertories and qualities, it can be adapted to a number of real-world applications including video games and virtual reality applications.