Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
Quasi-interpolation by quadratic piecewise polynomials in three variables
Computer Aided Geometric Design
Faster Isosurface Ray Tracing Using Implicit KD-Trees
IEEE Transactions on Visualization and Computer Graphics
Ray-Tracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering
IEEE Transactions on Visualization and Computer Graphics
Spline approximation of general volumetric data
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Interactive Isosurface Ray Tracing of Time-Varying Tetrahedral Volumes
IEEE Transactions on Visualization and Computer Graphics
An explicit quasi-interpolation scheme based on C 1 quartic splines on type-1 triangulations
Computer Aided Geometric Design
Quasi-interpolation by quadratic C1-splines on truncated octahedral partitions
Computer Aided Geometric Design
Quasi-interpolation by quadratic piecewise polynomials in three variables
Computer Aided Geometric Design
Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
Computer Aided Geometric Design
Mathematics and Computers in Simulation
SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology
Computers and Graphics
Galilean invariant extraction and iconic representation of vortex core lines
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
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We propose a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition. We discuss the smoothness and approximation properties of our model and compare to alternative piecewise polynomial constructions. We observe, as a nonstandard phenomenon, that the derivatives of our splines yield optimal approximation order for smooth data, while the theoretical error of the values is nearly optimal due to the averaging rules. Our approach enables efficient reconstruction and visualization of the data. As the piecewise polynomials are of the lowest possible total degree two, we can efficiently determine exact ray intersections with an isosurface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow us to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasiinterpolating method and demonstrate high visual quality for rendered isosurfaces.