Box splines
Accelerated volume rendering and tomographic reconstruction using texture mapping hardware
VVS '94 Proceedings of the 1994 symposium on Volume visualization
A comparison of normal estimation schemes
VIS '97 Proceedings of the 8th conference on Visualization '97
Design of accurate and smooth filters for function and derivative reconstruction
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Optimal regular volume sampling
Proceedings of the conference on Visualization '01
Smart hardware-accelerated volume rendering
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Optimal filter design for volume reconstruction and visualization
VIS '93 Proceedings of the 4th conference on Visualization '93
An evaluation of reconstruction filters for volume rendering
VIS '94 Proceedings of the conference on Visualization '94
Linear and Cubic Box Splines for the Body Centered Cubic Lattice
VIS '04 Proceedings of the conference on Visualization '04
Visualization of Volume Data with Quadratic Super Splines
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Artifacts Caused by Simplicial Subdivision
IEEE Transactions on Visualization and Computer Graphics
Real-time Volume Graphics
IEEE Transactions on Visualization and Computer Graphics
On visual quality of optimal 3D sampling and reconstruction
GI '07 Proceedings of Graphics Interface 2007
An Evaluation of Prefiltered Reconstruction Schemes for Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
Larrabee: a many-core x86 architecture for visual computing
ACM SIGGRAPH 2008 papers
Optimal sampling lattices and trivariate box splines
Optimal sampling lattices and trivariate box splines
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
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
Aliasing properties of voxels in three-dimensional sampling lattices
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
GPU isosurface raycasting of FCC datasets
Graphical Models
Interactive ray casting of geodesic grids
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor's algorithm for splines in box splines basis. Further on, we offer a comparison of quintic box splines with the only other interactive rendering available on BCC lattices that is based on separable kernels for interleaved Cartesian cubic (CC) lattices. While quintic box splines result in superior quality, interleaved CC lattices are still faster, since they can take advantage of the highly optimized circuitry for CC lattices, as it is the case in graphics hardware nowadays. This result is valid with and without prefiltering. Experimental results are shown for both a synthetic phantom and data from optical projection tomography. We provide shader code to ease the adaptation of box splines for the practitioner.