TY  - JOUR
AU  - Horacsek, Joshua
AU  - Alim, Usman
TI  - FastSpline: Automatic Generation of Interpolants for Lattice Samplings
JF  - ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
J2  - ACM T MATH SOFTWARE
VL  - 49
PY  - 2023
IS  - 2
PG  - 35
SN  - 0098-3500
DO  - 10.1145/3577194
UR  - https://m2.mtmt.hu/api/publication/34279199
ID  - 34279199
AB  - Interpolation is a foundational concept in scientific computing and is at the heart of many scientific visualization techniques. There is usually a tradeoff between the approximation capabilities of an interpolation scheme and its evaluation efficiency. For many applications, it is important for a user to navigate their data in real time. In practice, evaluation efficiency outweighs any incremental improvements in reconstruction fidelity. We first analyze, from a general standpoint, the use of compact piece-wise polynomial basis functions to efficiently interpolate data that is sampled on a lattice. We then detail our automatic code-generation framework on both CPU and GPU architectures. Specifically, we propose a general framework that can produce a fast evaluation scheme by analyzing the algebro-geometric structure of the convolution sum for a given lattice and basis function combination. We demonstrate the utility and generality of our framework by providing fast implementations of various box splines on the Body Centered and Face Centered Cubic lattices, as well as some non-separable box splines on the Cartesian lattice. We also provide fast implementations for certain Voronoi-splines that have not yet appeared in the literature. Finally, we demonstrate that this framework may also be used for non-Cartesian lattices in 4D.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Kim, Hyunjun
AU  - Kim, Minho
TI  - Volume reconstruction based on the six-direction cubic box-spline
JF  - GRAPHICAL MODELS
J2  - GRAPH MODELS
VL  - 125
PY  - 2023
PG  - 10
SN  - 1524-0703
DO  - 10.1016/j.gmod.2022.101168
UR  - https://m2.mtmt.hu/api/publication/33908548
ID  - 33908548
AB  - We propose a new volume reconstruction technique based on the six-direction cubic box-spline M6. M6 is C1 continuous and possesses an approximation order of three, the same as that of the tri-quadratic B-spline but with much lower degree. In fact, M6 has the lowest degree among the symmetric box-splines on Z3 with at least C1 continuity. We analyze the polynomial structure induced by the shifts of M6 and propose an efficient analytic evaluation algorithm for splines and their derivatives (gradient and Hessian) based on the high symmetry of M6. To verify the evaluation algorithm, we implement a real-time GPU (graphics processing unit) isosurface raycaster which exhibits interactive performance (54.5 fps (frames per second) with 2413 dataset on 5122 framebuffer) on a modern graphics hardware. Moreover, we analyze M6 as a reconstruction filter and state that it is comparable to the tri-cubic B-spline, which possesses a higher approximation order.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Charaf, Hassan
AU  - Harsányi, Gábor
AU  - Poppe, András
AU  - Imre, Sándor
AU  - Kiss, Bálint
AU  - Dabóczi, Tamás
AU  - Katona, Gyula Y.
AU  - Nagy, Lajos
AU  - Magyar, Gábor
AU  - Kiss, István
TI  - BME VIK annual research report on electrical engineering and computer science 2016
JF  - PERIODICA POLYTECHNICA-ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
J2  - PERIOD POLYTECH ELECTR ENG COMP SCI
VL  - 61
PY  - 2017
IS  - 2
SP  - 83
EP  - 115
PG  - 33
SN  - 2064-5260
DO  - 10.3311/PPee.11067
UR  - https://m2.mtmt.hu/api/publication/30380195
ID  - 30380195
LA  - English
DB  - MTMT
ER  -