{"paper":{"title":"Generalized balanced power diagrams for 3D representations of polycrystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Allan Lyckegaard, Andreas Alpers, Andreas Brieden, Henning Friis Poulsen, Peter Gritzmann","submitted_at":"2014-11-17T16:27:40Z","abstract_excerpt":"Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its center-of-mass position, its volume and, if available, by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D x-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear program it can be computed quite efficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4535","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}