Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Discrete-time signal processing
Discrete-time signal processing
Footprint evaluation for volume rendering
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Lossless compression of volume data
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Opacity-weighted color interpolation, for volume sampling
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Design of accurate and smooth filters for function and derivative reconstruction
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Multidimensional Digital Signal Processing
Multidimensional Digital Signal Processing
Alias-Free Voxelization of Geometric Objects
IEEE Transactions on Visualization and Computer Graphics
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Shear-Warp deluxe: the Shear-Warp algorithm revisited
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Space-time points: 4d splatting on efficient grids
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
A new object-order ray-casting algorithm
Proceedings of the conference on Visualization '02
Linear and Cubic Box Splines for the Body Centered Cubic Lattice
VIS '04 Proceedings of the conference on Visualization '04
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
A Frequency-Sensitive Point Hierarchy for Images and Volumes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Modified marching octahedra for optimal regular meshes
ACM SIGGRAPH 2002 conference abstracts and applications
Lattice-Based Volumetric Global Illumination
IEEE Transactions on Visualization and Computer Graphics
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Symmetric box-splines on the A*n lattice
Journal of Approximation Theory
Proceedings of the 26th Spring Conference on Computer Graphics
Generating distance maps with neighbourhood sequences
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Topology preserving digitization with FCC and BCC grids
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Aliasing properties of voxels in three-dimensional sampling lattices
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
GPU accelerated image aligned splatting
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Applications of optimal sampling lattices for volume acquisition via 3D computed tomography
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
Quasi-interpolation on the body centered cubic lattice
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
High-quality volumetric reconstruction on optimal lattices for computed tomography
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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The classification of volumetric data sets as well as their rendering algorithms are typically based on the representation of the underlying grid. Grid structures based on a Cartesian lattice are the de-facto standard for regular representations of volumetric data. In this paper we introduce a more general concept of regular grids for the representation of volumetric data. We demonstrate that a specific type of regular lattice --- the so-called body-centered cubic --- is able to represent the same data set as a Cartesian grid to the same accuracy but with 29.3% fewer samples. This speeds up traditional volume rendering algorithms by the same ratio, which we demonstrate by adopting a splatting implementation for these new lattices. We investigate different filtering methods required for computing the normals on this lattice. The lattice representation results also in lossless compression ratios that are better than previously reported. Although other regular grid structures achieve the same sample efficiency, the body-centered cubic is particularly easy to use. The only assumption necessary is that the underlying volume is isotropic and band-limited - an assumption that is valid for most practical data sets.