{"title":"FastSpline: Automatic Generation of Interpolants for Lattice Samplings","authors":"J. Horacsek, U. Alim","doi":"10.1145/3577194","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50935,"journal":{"name":"ACM Transactions on Mathematical Software","volume":"49 1","pages":"1 - 35"},"PeriodicalIF":2.7000,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Mathematical Software","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1145/3577194","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 2
Abstract
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.
期刊介绍:
As a scientific journal, ACM Transactions on Mathematical Software (TOMS) documents the theoretical underpinnings of numeric, symbolic, algebraic, and geometric computing applications. It focuses on analysis and construction of algorithms and programs, and the interaction of programs and architecture. Algorithms documented in TOMS are available as the Collected Algorithms of the ACM at calgo.acm.org.