Traditional methods for evaluating the low-albedo volume rendering integral do not include bounds on the magnitude of approximation error. In this paper, we examine three techniques for solving this integral with error bounds: trapezoid rule, Simpson’s rule, and a power series method. In each case, the expression for the error bound provides a mechanism for computing the integral to any specified precision. The formulations presented are appropriate for polynomial reconstruction from point samples; however, the approach is considerably mom general. The three techniques we present differ in relative efficiency for computing results to a given precision. The trapezoid rule and Simpson’s rule are most efficient for lowto medium-precision solutions. The power series method converges rapidly to a machine precision solution, providing both an efficient means for high-accuracy volume rendering, and a reference standard by which other approximations may be measured. CR
{"title":"Controlled precision volume integration","authors":"K. Novins, J. Arvo","doi":"10.1145/147130.147154","DOIUrl":"https://doi.org/10.1145/147130.147154","url":null,"abstract":"Traditional methods for evaluating the low-albedo volume rendering integral do not include bounds on the magnitude of approximation error. In this paper, we examine three techniques for solving this integral with error bounds: trapezoid rule, Simpson’s rule, and a power series method. In each case, the expression for the error bound provides a mechanism for computing the integral to any specified precision. The formulations presented are appropriate for polynomial reconstruction from point samples; however, the approach is considerably mom general. The three techniques we present differ in relative efficiency for computing results to a given precision. The trapezoid rule and Simpson’s rule are most efficient for lowto medium-precision solutions. The power series method converges rapidly to a machine precision solution, providing both an efficient means for high-accuracy volume rendering, and a reference standard by which other approximations may be measured. CR","PeriodicalId":20479,"journal":{"name":"Proceedings of the 1992 workshop on Volume visualization","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81198582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose this paper introduces the formal notion of the family of r-x-shapes of a finite point set in IR3. Each shape is a polytope, derived from the Delaunay triangulation of the point set, with a parameter cy E R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in worst-case time O(n’). A robust implementation of the algorithm is discussed and seveml applications in the area of scientific computing are mentioned.
通常，科学计算中的数据是抽象形式的空间中的有限点集，有时计算集合的“形状”是有用的或需要的。为此，本文引入了IR3中有限点集的r-x形族的形式化概念。每个形状都是一个多面体，从点集的Delaunay三角剖分中得到，参数cy E R控制所需的细节水平。提出了一种算法，在最坏情况下，在O(n ')时间内，对给定大小为n的集合，构造出整个形状族。讨论了该算法的鲁棒实现，并提到了该算法在科学计算领域的几个应用。
{"title":"Three-dimensional alpha shapes","authors":"H. Edelsbrunner, Ernst P. Mücke","doi":"10.1145/147130.147153","DOIUrl":"https://doi.org/10.1145/147130.147153","url":null,"abstract":"Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the “shape” of the set. For that purpose this paper introduces the formal notion of the family of r-x-shapes of a finite point set in IR3. Each shape is a polytope, derived from the Delaunay triangulation of the point set, with a parameter cy E R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in worst-case time O(n’). A robust implementation of the algorithm is discussed and seveml applications in the area of scientific computing are mentioned.","PeriodicalId":20479,"journal":{"name":"Proceedings of the 1992 workshop on Volume visualization","volume":"PP 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84172088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we describe an algorithm for volume raytracing in a data parallel framework. The algorithm uses the idiom of line drawing to traverse the data set when evaluating the path-integrals corresponding to a raytracing of the volume. Since the rays of a parallel projection correspond to a single line instanced multiple times across the viewing plane the approach lends itself well to implementation on massively parallel computers. We have implemented this algorithm on the Princeton Engine (PE) and the Connection Machine CM2 computers and achieved interactive performance.
{"title":"Data parallel volume rendering as line drawing","authors":"P. Schröder, Gordon Stoll","doi":"10.1145/147130.147142","DOIUrl":"https://doi.org/10.1145/147130.147142","url":null,"abstract":"In this paper we describe an algorithm for volume raytracing in a data parallel framework. The algorithm uses the idiom of line drawing to traverse the data set when evaluating the path-integrals corresponding to a raytracing of the volume. Since the rays of a parallel projection correspond to a single line instanced multiple times across the viewing plane the approach lends itself well to implementation on massively parallel computers. We have implemented this algorithm on the Princeton Engine (PE) and the Connection Machine CM2 computers and achieved interactive performance.","PeriodicalId":20479,"journal":{"name":"Proceedings of the 1992 workshop on Volume visualization","volume":"318 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75697706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A parallel solution to the visualiaation of high resolution uolume data is presented. Baaed on the ray tracing (RT) uiaualization technique, the system works on a distributed memory MIMD architecture. A hybrid strategy to my tracing parallelitation is applied, using ray-dataflow within an image partition approach. This strategy allows the flexible and efiectiue management of huge dataset on architectures with limited local memory. The dataaet is distributed over the nodes using a slice-partitioning technique. The simple data partition chosen implies a atraighforward communications pattern of the visualization processes and this improves both software design and eficiency, while providing deadlock prevention. The partitioning technique used and the network interconnection topology allow for the efjicient implementation of a statical load balancing technique through pre-rendering of a low resolution image. Details related to the practical issues involved in the parallelitation of volumetric RT are discussed, with particular reference to deadlock and termination issues.
{"title":"Parallel volume visualization on a hypercube architecture","authors":"C. Montani, R. Perego, Roberto Scopigno","doi":"10.1145/147130.147139","DOIUrl":"https://doi.org/10.1145/147130.147139","url":null,"abstract":"A parallel solution to the visualiaation of high resolution uolume data is presented. Baaed on the ray tracing (RT) uiaualization technique, the system works on a distributed memory MIMD architecture. A hybrid strategy to my tracing parallelitation is applied, using ray-dataflow within an image partition approach. This strategy allows the flexible and efiectiue management of huge dataset on architectures with limited local memory. The dataaet is distributed over the nodes using a slice-partitioning technique. The simple data partition chosen implies a atraighforward communications pattern of the visualization processes and this improves both software design and eficiency, while providing deadlock prevention. The partitioning technique used and the network interconnection topology allow for the efjicient implementation of a statical load balancing technique through pre-rendering of a low resolution image. Details related to the practical issues involved in the parallelitation of volumetric RT are discussed, with particular reference to deadlock and termination issues.","PeriodicalId":20479,"journal":{"name":"Proceedings of the 1992 workshop on Volume visualization","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1992-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90348965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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