Cage-based deformation techniques are widely used to con-trol the deformation of an enclosed fine-detail mesh. Achieving deforma-tion based on vertex constraints has been extensively studied for the case of pure meshes, but few works specifically examine how such vertex con-straints can be used to efficiently deform the template and estimate the corresponding cage pose. In this paper, we show that this can be achieved very efficiently with two contributions: (1) we provide a linear estima-tion framework for cage vertex coordinates; (2) the regularization of the deformation is expressed on the cage vertices rather than the enclosed mesh, yielding a computationally efficient solution which fully benefits from cage-based parameterizations. We demonstrate the practical use of this scheme for two applications: animation edition from sparse screen-space user-specified constraints, and automatic cage extraction from a sequence of meshes, for animation re-edition.