{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:52:20Z","timestamp":1760151140960,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,17]],"date-time":"2022-02-17T00:00:00Z","timestamp":1645056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Progressive iterative approximation (PIA) technique is an efficient and intuitive method for data fitting. In CAGD modeling, if the given data points are taken as initial control points, PIA process generates a series of shaping curves by adjusting the control points iteratively, while the limit curve interpolates the data points. Such format was used successfully for Shepard-type curves. The aim of the paper is to construct simple variants of the PIA method for Shepard-type curves producing novel curves modeling data points, so the designer can choose among several pencils of shapes outlining original control polygon. Matrix formulations, convergence results, error estimates, algorithmic formulations, critical comparisons, and numerical tests are shown. An application to a progressive modeling format by truncated wavelet transform is also presented, improving in some sense analogous process by truncated Fourier transform. By playing on two shapes handles\u2014the number of base wavelet transform functions and the iteration level of PIA algorithm\u2014several new contours modeling the given control points are constructed.<\/jats:p>","DOI":"10.3390\/sym14020398","type":"journal-article","created":{"date-parts":[[2022,2,17]],"date-time":"2022-02-17T20:26:41Z","timestamp":1645129601000},"page":"398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["New Progressive Iterative Approximation Techniques for Shepard-Type Curves"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1482-4898","authenticated-orcid":false,"given":"Umberto","family":"Amato","sequence":"first","affiliation":[{"name":"Istituto per le Scienze Applicate ed i Sistemi Automatici ed Intelligenti, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 80131 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-2320","authenticated-orcid":false,"given":"Biancamaria","family":"Della Vecchia","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma \u2018La Sapienza\u2019, Piazzale Aldo Moro 5, 00185 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,17]]},"reference":[{"key":"ref_1","first-page":"611","article-title":"Modelling by Shepard-type curves and surfaces","volume":"20","author":"Amato","year":"2016","journal-title":"J. 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