Partition of Unity Parametrics (PUPs) is a generalization of NURBS that allows one to use arbitrary basis functions to model parametric curves and surfaces. One interesting problem is the finding of subdivision, reverse subdivision, and multiresolution (MR) schemes for this recently developed and flexible class of parametric curves and surfaces.
Subdivision is used to increase resolution and can be applied to upsampling and evaluating parametric curves and surfaces. Reverse subdivision, on the other hand, is used to decrease resolution and along with subdivision, can be combined into a MR framework which has numerous applications, including: macroscopic/microscopic modification, compression, feature transfer, and level of detail visualization. Deriving PUPs MR schemes makes it possible to introduce such applications to the PUPs framework.
In this thesis, we introduce a systematic approach for determining uniform subdivision schemes for PUPs curves and tensor-product surfaces using least squares. Additionally, we derive PUPs MR masks based on their subdivision filters. We model the problem such that the resulting MR schemes are banded and optimal in terms of minimizing MR reconstruction error.