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Applied Math Seminar
From Interpolating Subdivisions to Representation of Scattered Data
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In this lecture, I will introduce this topic by extending the cubic B-spline refinement equation to the bivariate setting, thereby arriving at some re-formulation of Loop s scheme to achieve certain degree of freedom. This allows us to extend Loop s approximation subdivision scheme to interpolating surface subdivisions, without increasing the cubic polynomial degree and decreasing the C^2 smoothness property. Subdivision templates for extraordinary vertices of arbitrary valences are derived accordingly. An example of our non-spline results to achieve one-ring templates will be given. I will also discuss how such interpolating subdivision templates can be adopted to construct minimum-supported basis functions for bivariate scattered data interpolation. |