This paper considers the problem of inferring the geometry of an object from values of the signed distance sampled on a uniform grid. The problem is motivated by the desire to effectively and efficiently model objects obtained by 3D imaging technology such as magnetic resonance, computed tomography, and positron emission tomography. Techniques recently developed for automated segmentation convert intensity to signed distance, and the voxel structure imposes the uniform sampling grid. The specification of the signed distance function (SDF) throughout the ambient space would provide an implicit and function-based representation (f-rep) model that uniquely specifies the object, and we refer to this particular f-rep as the signed distance function representation (SDF-rep). However, a set of uniformly sampled signed distance values may uniquely determine neither the distance function nor the shape of the object. Here, we employ essential properties of the signed distance to construct the upper and lower bounds on the allowed variation in signed distance, which combine to produce interval-valued extensions of the signed distance function. We employ an interval extension of the signed distance function as an interval SDF-rep that defines the range of object geometries that are consistent with the sampled SDF data. The particular interval extensions considered include a tight global extension and more computationally efficient local extensions that provide useful criteria for root exclusion/isolation. To illustrate a useful application of the interval bounds, we present a reliable approach to top-down octree membership classification for uniform samplings of signed distance functions.
Opportunities for Ice Storage to Provide Ancillary Services to Power Grids Incorporating Wind Turbine Generation Christopher FinleyChair of the Supervisory Committee:Professor Ashley F Emery Mechanical EngineeringPower generation using wind turbines increases the electrical system balancing, regulation and ramp rate requirements due to the minute to minute variability in wind speed and the difficulty in accurately forecasting wind speeds. The addition of thermal energy storage, such as ice storage, to a building's space cooling equipment increases the operational flexibility of the equipment by allowing the owner to choose when the chiller is run. The ability of the building owner to increase the power demand from the chiller (e.g. make ice) or to decrease the power demand (e.g. melt ice) to provide electrical system ancillary services was evaluated.
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