{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:28:01Z","timestamp":1750307281235,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2011,4,1]],"date-time":"2011-04-01T00:00:00Z","timestamp":1301616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2011,4]]},"abstract":"<jats:p>\n            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\n            <jats:italic>p<\/jats:italic>\n            in the scene. The desired surfaces are those which are inside a frustum defined by the light and\n            <jats:italic>p<\/jats:italic>\n            , and can be found by intersecting the frustum with an acceleration structure over geometry. However, accurately computing this intersection is computationally intensive.\n          <\/jats:p>\n          <jats:p>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.<\/jats:p>","DOI":"10.1145\/1944846.1944848","type":"journal-article","created":{"date-parts":[[2011,5,3]],"date-time":"2011-05-03T12:48:53Z","timestamp":1304426933000},"page":"1-6","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["The area perspective transform"],"prefix":"10.1145","volume":"30","author":[{"given":"Warren A.","family":"Hunt","sequence":"first","affiliation":[{"name":"Intel Corporation"}]},{"given":"Gregory S.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Intel Corporation"}]}],"member":"320","published-online":{"date-parts":[[2011,4,22]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383533.2383555"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/844174.844180"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1572769.1572791"},{"key":"e_1_2_2_4_1","unstructured":"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.  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."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/964965.808590"},{"key":"e_1_2_2_6_1","first-page":"74","article-title":"Detecting Intersection of a Rectangular Solid and a Convex Polyhedron, P. S. Heckbert, Ed. Academic Press","author":"Greene N.","year":"1994","unstructured":"Greene , N. 1994 . Detecting Intersection of a Rectangular Solid and a Convex Polyhedron, P. S. Heckbert, Ed. Academic Press , Chapter I .7, 74 -- 82 . Greene, N. 1994. Detecting Intersection of a Rectangular Solid and a Convex Polyhedron, P. S. Heckbert, Ed. Academic Press, Chapter I.7, 74--82.","journal-title":"Chapter"},{"volume-title":"Proceedings of the IEEE\/EG Symposium on Interactive Ray Tracing. 3--10","author":"Hunt W. A.","key":"e_1_2_2_7_1","unstructured":"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 . 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."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1507149.1507159"},{"key":"e_1_2_2_9_1","unstructured":"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.  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."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073327"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/258694.258723"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01267.x"},{"volume-title":"STAR Proceedings of Eurographics, D. Schmalstieg and J. Bittner, Eds., The Eurographics Association, 89--116","author":"Wald I.","key":"e_1_2_2_13_1","unstructured":"Wald , I. , Mark , W. R., G &amp;#252;nther, 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 . Wald, I., Mark, W. R., G&amp;#252;nther, 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."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1944846.1944848","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1944846.1944848","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:59:30Z","timestamp":1750244370000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1944846.1944848"}},"subtitle":["A homogeneous transform for efficient in-volume queries"],"short-title":[],"issued":{"date-parts":[[2011,4]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["10.1145\/1944846.1944848"],"URL":"https:\/\/doi.org\/10.1145\/1944846.1944848","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2011,4]]},"assertion":[{"value":"2010-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-04-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}