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Interactive Isosurfaces with Quadratic C1 Splines on Truncated Octahedral Partitions

Alexander Marinc, Thomas Kalbe, Markus Rhein, Michael Goesele
Fraunhofer IGD Darmstadt
Visualization and Data Analysis, 2011

@inproceedings{marinc2011interactive,

   title={Interactive Isosurfaces with Quadratic C Splines on Truncated Octahedral Partitions},

   author={Marinc, A. and Kalbe, T. and Rhein, M. and Goesele, M.},

   booktitle={Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series},

   volume={7868},

   pages={6},

   year={2011}

}

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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 C1 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-Bezier coefficients of the piecewise polynomials are directly determined by appropriate combinations of the data values in a local neighborhood. 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 GPU-based, interactive high-quality visualization of isosurfaces from discrete data.
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