Interpolatory Hermite Subdivision Scheme of Manifold-Valued Data
Yilin Yang, Drexel University, Class of 2017
Thomas Yu, Professor, Drexel University
Subdivision method is a special kind of multiscale method for interpolation and approximation, which defines a smooth curve or surface as the limit of a sequence of successive refinements. Now subdivision for surface modeling is regularly used in movie production, and is considered to be a core technology in game engines. Our research focuses on the regularity and approximation order properties of subdivision methods for manifold-valued data, which has important applications in many subjects such as motion planning and diffusion tensor imaging. Applying differential geometry ideas, we adapt the Hermite interpolation method to data on manifolds, called “interpolatory Hermite subdivision scheme”; and we observe that the regularity and approximation order of the method in the linear case is preserved in this extension to manifolds without being obstructed by the curvature. Finally using the technique of proximity conditions, we analyze that the interpolatory Hermite subdivision scheme gets full smoothness equivalence and approximation order equivalence for manifold-valued data.
Yilin Yang, Drexel University, Class of 2017
Thomas Yu, Professor, Drexel University
Subdivision method is a special kind of multiscale method for interpolation and approximation, which defines a smooth curve or surface as the limit of a sequence of successive refinements. Now subdivision for surface modeling is regularly used in movie production, and is considered to be a core technology in game engines. Our research focuses on the regularity and approximation order properties of subdivision methods for manifold-valued data, which has important applications in many subjects such as motion planning and diffusion tensor imaging. Applying differential geometry ideas, we adapt the Hermite interpolation method to data on manifolds, called “interpolatory Hermite subdivision scheme”; and we observe that the regularity and approximation order of the method in the linear case is preserved in this extension to manifolds without being obstructed by the curvature. Finally using the technique of proximity conditions, we analyze that the interpolatory Hermite subdivision scheme gets full smoothness equivalence and approximation order equivalence for manifold-valued data.