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Our algorithm is based on the recently introduced idea of Shrink-and-Expand, where images of interior vertices are initially clustered at one point (Shrink-), before being sequentially moved to non-degenerate positions yielding a bijective map (-and-Expand). In this context, we introduce the concept of the\n            <jats:italic>cluster mesh<\/jats:italic>\n            , i.e. the unexpanded interior mesh consisting of geometrically degenerate simplices. Using local, per-vertex connectivity information solely from the cluster mesh, we show that a viable expansion sequence guaranteed to produce a bijective map can always be found as long as the mesh is\n            <jats:italic>shellable.<\/jats:italic>\n            In addition to robustness guarantees for this ubiquitous class of inputs, other practically relevant benefits include improved parsimony and reduced algorithmic complexity. While inheriting some of the worst-case high run time requirements of the state of the art, significant acceleration for the average case is experimentally demonstrated.\n          <\/jats:p>","DOI":"10.1145\/3687992","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T15:46:04Z","timestamp":1732031164000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5239-1507","authenticated-orcid":false,"given":"Valentin Z\u00e9non","family":"Nigolian","sequence":"first","affiliation":[{"name":"University of Bern, Bern, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2340-3462","authenticated-orcid":false,"given":"Marcel","family":"Campen","sequence":"additional","affiliation":[{"name":"Osnabr\u00fcck University, Osnabr\u00fcck, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3190-1341","authenticated-orcid":false,"given":"David","family":"Bommes","sequence":"additional","affiliation":[{"name":"University of Bern, Bern, Switzerland"}]}],"member":"320","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3572897"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461931"},{"key":"e_1_2_1_3_1","volume-title":"Tutte embeddings of tetrahedral meshes. 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