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Abstract. Sleep disorders are a wide-spread phenomenon that can gravely affect personal health and well-being. An individual sleep analysis is a first step in identifying unusual sleeping patterns and providing suitable means for further therapy and preventing escalation of symptoms. Typically such an analysis is an intrusive method and requires the user to stay in a sleep laboratory. In this work we present a method for detecting sleep patterns based on invisibly installed capacitive proximity sensors integrated into the bed frame. These sensors work with weak electric fields and do not disturb sleep. Using the movements of the sleeping person we are able to provide a continuous analysis of different sleep phases. The method was tested in a prototypical setup over multiple nights.

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The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C 1 splines on uniform tetrahedral partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octahedron is further split into a fixed number of disjunct tetrahedra. The Bernstein-Bézier coefficients of the piecewise polynomials are directly determined by appropriate combinations of the data values in a local neighbourhood. As previously shown, the splines provide an approximation order two for smooth functions as well as their derivatives. We present the first visualizations using these splines and show that they are well suited for graphics processing unit (GPU)based, interactive, high-quality visualization of isosurfaces from discrete data.