{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:15:13Z","timestamp":1792671313579,"version":"4.5.0"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["101026017"],"award-info":[{"award-number":["101026017"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["N00014-16-1-2617"],"award-info":[{"award-number":["N00014-16-1-2617"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We provide closed-form expressions for the first moments (i.e., the volume and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is, of a polyhedron intersected with the subset of the three-dimensional real space located on one side of a paraboloid. These closed-form expressions are derived following successive applications of the divergence theorem and the judicious parametrization of the intersection of the polyhedron\u2019s faces with the paraboloid. We provide means for identifying ambiguous discrete intersection topologies, and propose a corrective procedure for preventing their occurence. Finally, we put our proposed closed-form expressions and numerical approach to the test with millions of random and manually engineered polyhedron\/paraboloid intersection configurations. The results of these tests show that we are able to provide robust machine-accurate estimates of the first moments at a computational cost that is within one order of magnitude of that of state-of-the-art half-space clipping algorithms.<\/jats:p>\n                  <jats:p>Reproducibility of computational results. This paper has been awarded the \u201cSIAM Reproducibility Badge: code and data available\u201d, as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at IRL , step-by-step guide , 8e77b35 . 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