Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Visualization of Volume Data with Quadratic Super Splines
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Interactive volume isosurface rendering using BT volumes
Proceedings of the 2008 symposium on Interactive 3D graphics and games
IEEE Transactions on Visualization and Computer Graphics
Quasi-interpolation by quadratic C1-splines on truncated octahedral partitions
Computer Aided Geometric Design
High-Quality Rendering of Varying Isosurfaces with Cubic Trivariate C1-Continuous Splines
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
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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 tetrahedrat 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-Brzier 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 sptines and show that they are welt suited for graphics processing unit {GPU}- based, interactive, high-quality visualization of isosurfaces from discrete data.