{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T05:30:32Z","timestamp":1762320632825,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T00:00:00Z","timestamp":1761868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>This paper presents a comparative study on the suitability of free-boundary surface parameterization techniques for generating trajectories on 3D surfaces. The approach maps a 3D surface to a 2D parametric domain through four parameterization methods: Least-Squares Conformal Mapping, Boundary First Flattening, As-Rigid-As-Possible, and Conformal Equivalence of Triangular Meshes. Structured trajectory patterns are generated in the 2D domain and projected back to 3D. We introduce center-to-boundary geodesic deviation measure, which yields a deviation profile over the boundary loop and reflects how well central alignment is preserved under each parameterization method. The results highlight differences in distortion and geodesic preservation, reflecting the suitability of methods for path generation.<\/jats:p>","DOI":"10.3390\/robotics14110160","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:47:58Z","timestamp":1762177678000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7185-0270","authenticated-orcid":false,"given":"Mahrukh","family":"Mahrukh","sequence":"first","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering (DEI), University of Bologna, 40136 Bologna, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9457-4643","authenticated-orcid":false,"given":"Gianluca","family":"Palli","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering (DEI), University of Bologna, 40136 Bologna, Italy"}]},{"given":"Mattia","family":"Gambazza","sequence":"additional","affiliation":[{"name":"R&D Division, SACMI Imola S.C., 40026 Imola, Italy"}]},{"given":"Claudio","family":"Melchiorri","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering (DEI), University of Bologna, 40136 Bologna, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1145\/566654.566590","article-title":"Least Squares Conformal Maps for Automatic Texture Atlas Generation","volume":"21","author":"Petitjean","year":"2002","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_2","first-page":"5","article-title":"Boundary First Flattening","volume":"37","author":"Sawhney","year":"2017","journal-title":"ACM Trans. Graph."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1111\/j.1467-8659.2008.01290.x","article-title":"A Local\/Global Approach to Mesh Parameterization","volume":"27","author":"Liu","year":"2008","journal-title":"Comput. Graph. Forum"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Springborn, B., Schr\u00f6der, P., and Pinkall, U. (2008). Conformal Equivalence of Triangle Meshes. SIGGRAPH \u201908: ACM SIGGRAPH 2008 Papers, Association for Computing Machinery.","DOI":"10.1145\/1508044.1508062"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"McGovern, S., and Xiao, J. (2022, January 20\u201324). UV Grid Generation on 3D Freeform Surfaces for Constrained Robotic Coverage Path Planning. 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Proceedings of the 2022 IEEE Conference on Control Technology and Applications (CCTA), Trieste, Italy.","DOI":"10.1109\/CCTA49430.2022.9966015"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/TCST.2023.3345209","article-title":"Automatic and Flexible Robotic Drawing on Complex Surfaces with an Industrial Robot","volume":"32","author":"Weingartshofer","year":"2024","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Song, D., and Kim, Y.J. (2019, January 20\u201324). Distortion-Free Robotic Surface-Drawing Using Conformal Mapping. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8794034"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/11\/160\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T05:11:16Z","timestamp":1762319476000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/11\/160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,31]]},"references-count":9,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["robotics14110160"],"URL":"https:\/\/doi.org\/10.3390\/robotics14110160","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2025,10,31]]}}}