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This fundamental disconnect between two\u2010dimensional (2D) techniques and three\u2010dimensional (3D) realities significantly restricts our ability to fully perceive and to understand the complexity of real\u2010world objects. Over the past several decades, driven by application demands across various industries, advancements in high\u2010speed, high\u2010accuracy, and high\u2010resolution sensors, as well as ever\u2010increasing AI algorithms and computational power, curvy surface reconstruction that can reconstruct continuous, smooth geometrical and physical fields from discrete data by algorithms and mathematics have experienced tremendous developments. However, previous reviews in this field have primarily focused on geometric shapes, optical measurement techniques, or reconstruction algorithms, leaving a comprehensive overview that integrates both geometric and physical dimensions still lacking. Here, for the first time, we bridge this gap by expanding the scope from special curvy imaging to general curvy reconstruction incorporating physical fields, with a particular emphasis on measurement techniques, especially the emerging opportunities from advanced techniques. Initially, a brief overview starts with introducing the theoretical underpinnings and primary issues of curvy surface reconstruction. Next, an in\u2010depth discussion of the main non\u2010contact and contact measurement methods is presented, detailing their operational principles, progress, merits and demerits, and future efforts. Following that, several reconstruction algorithms and their applications are discussed. Finally, our insights on the ongoing challenges and opportunities in this field are summarized.<\/jats:p>","DOI":"10.1002\/advs.202516891","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T04:43:38Z","timestamp":1767588218000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Curvy Surface Reconstruction"],"prefix":"10.1002","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9546-4806","authenticated-orcid":false,"given":"Chen","family":"Shang","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering Shaanxi University of Science and Technology  Xi'an China"},{"name":"Hangzhou Institute of Technology Xidian University  Hangzhou China"},{"name":"State Key Laboratory of Electromechanical Integrated Manufacturing of High\u2010Performance Electronic Equipments Xidian University  Xi'an 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