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CMSC828Z: Description of Project 3 - Temporally-varying Multi-resolution Subdivision Surfaces

This project is closely related to project 4 and it might be a good idea that the two students who work on projects 3 and 4 closely collaborate. The goal of this project is to compare implicit and parametric descriptions of temporally varying shapes with regard to their use in the spatio-temporal reconstruction project. As an example for a parametric descriptions of a time-varying shape we suggest to use a time-varying subdivision surface where the locations of the control mesh vertices follow a b-spline path. At each time instance, the subdivision surface consists of a hierarchy of triangular meshes that encode the shape at different resolutions (see the following example:)

The advantage of the subdivison surface is that we can evaluate the position of any point on the object surface very easily. The shape and motion of such a point only depends on a small number of nearby vertices (for a regular neighbourhood in the Loop subdivision scheme this number is 12, see the image below on the left).

This local control makes subdivison surfaces very suitable as a parametric shape representation in our optimization framework. Since we have a fixed parameterization of the shape surface any point on the surface has a unique "identity" (that is parameter value) and its trajectory over time is given as a weighted combination of the trajectories of surrounding control vectors (see image above to the right). One project would be now to combine ideas from the (static) multi-resolution subdivision surfaces as described in the paper Interactive multiresolution mesh editing by Denis Zorin, Peter Schrüder, and Wim Sweldens with a b-spline representation for the control mesh vertex trajectories. It might also be interesting to include ideas about dynamic mesh connectivity from the paper Multiresolution shape deformations for meshes with dynamic vertex connectivity by L. Kobbelt, T. Bareuther, and H-P. Seidel. For an introduction the area of subdivision curves and surfaces take a look at the SIGGRAPH 2000 Course about Subdivision for Modeling and Animation.