skip to main content
research-article

The area perspective transform: A homogeneous transform for efficient in-volume queries

Published: 22 April 2011 Publication History

Abstract

A key problem in applications such as soft shadows and defocus blur is to identify points or primitives which are inside a volume of space. For example, the soft shadow computation involves finding surfaces which pass in front of an area light as viewed from a point p in the scene. The desired surfaces are those which are inside a frustum defined by the light and p, and can be found by intersecting the frustum with an acceleration structure over geometry. However, accurately computing this intersection is computationally intensive.
In this article, we introduce a homogeneous transform which reduces the computation required to determine the set of points or primitives which are inside a tetrahedral volume. The transform converts tetrahedra into axis-aligned boxes, substantially reducing the cost of intersection with an axis-aligned acceleration structure over points or primitives. We describe the application of this transform to soft shadows and defocus blur, and briefly consider potential uses of the underlying mathematical approach in higher-dimensional problems.

Supplementary Material

MP4 File (tp033_11.mp4)

References

[1]
Aila, T. and Laine, S. 2004. Alias-free shadow maps. In Proceedings of the Eurographics Symposium on Rendering. Eurographics, 161--166.
[2]
Assarsson, U., Dougherty, M., Mounier, M., and Akenine-Möller, T. 2003. An optimized soft shadow volume algorithm with real-time performance. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Conference on Graphics Hardware (HWWS'03). Eurographics, 33--40.
[3]
Benthin, C. and Wald, I. 2009. Efficient ray traced soft shadows using multi-frusta tracing. In Proceedings of the Conference on High Performance Graphics (HPG'09). ACM Press, New York, 135--144.
[4]
Boulos, S., Wald, I., and Shirley, P. 2006. Geometric and arithmetic culling methods for entire ray packets. School of Computing Tech. rep. UUCS-06-10, University of Utah.
[5]
Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed ray tracing. SIGGRAPH Comput. Graph. 18, 3, 137--145.
[6]
Greene, N. 1994. Detecting Intersection of a Rectangular Solid and a Convex Polyhedron, P. S. Heckbert, Ed. Academic Press, Chapter I.7, 74--82.
[7]
Hunt, W. A. and Mark, W. R. 2008. Ray-Specialized acceleration structures for ray tracing. In Proceedings of the IEEE/EG Symposium on Interactive Ray Tracing. 3--10.
[8]
Johnson, G. S., Hux, A., Burns, C. A., Hunt, W. A., Mark, W. R., and Junkins, S. 2009. Soft irregular shadow mapping: Fast, high-quality, and robust soft shadows. In Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D'09). ACM Press, New York, 57--66.
[9]
Johnson, G. S., Mark, W. R., and Burns, C. A. 2004. The irregular z-buffer and its application to shadow mapping. Tech. rep. TR-04-09, Department of Computer Sciences, The University of Texas at Austin.
[10]
Laine, S., Aila, T., Assarsson, U., Lehtinen, J., and Akenine-Möller, T. 2005. Soft shadow volumes for ray tracing. ACM Trans. Graph. 24, 3, 1156--1165.
[11]
Olano, M. and Greer, T. 1997. Triangle scan conversion using 2D homogeneous coordinates. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware. ACM Press, New York, 89--95.
[12]
Sintorn, E., Eisemann, E., and Assarsson, U. 2008. Sample based visibility for soft shadows using alias-free shadow maps. In Proceedings of the Eurographics Symposium on Rendering. Eurographics, 1285--1292. Comput. Graph. Forum. 27, 4.
[13]
Wald, I., Mark, W. R., Günther, J., Boulos, S., Ize, T., Hunt, W., Parker, S. G., and Shirley, P. 2007. State of the art in ray tracing animated scenes. In STAR Proceedings of Eurographics, D. Schmalstieg and J. Bittner, Eds., The Eurographics Association, 89--116.

Cited By

View all

Index Terms

  1. The area perspective transform: A homogeneous transform for efficient in-volume queries

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Transactions on Graphics
      ACM Transactions on Graphics  Volume 30, Issue 2
      April 2011
      104 pages
      ISSN:0730-0301
      EISSN:1557-7368
      DOI:10.1145/1944846
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 22 April 2011
      Accepted: 01 December 2010
      Received: 01 September 2010
      Published in TOG Volume 30, Issue 2

      Permissions

      Request permissions for this article.

      Check for updates

      Author Tags

      1. homogeneous transform
      2. perspective

      Qualifiers

      • Research-article
      • Research
      • Refereed

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)3
      • Downloads (Last 6 weeks)0
      Reflects downloads up to 16 Jan 2025

      Other Metrics

      Citations

      Cited By

      View all

      View Options

      Login options

      Full Access

      View options

      PDF

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media