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Inspired by\n            <jats:italic toggle=\"yes\">k<\/jats:italic>\n            -curves by [Yan et al. 2017], each patch provides a single control point that is being interpolated at a local extremum of Gaussian curvature. The challenge is to solve the inverse problem of finding the center control point of a B\u00e9zier patch given the boundary control points and the handle. Unlike the situation in 2D, bi-quadratic B\u00e9zier patches may exhibit none, one, or several extrema, and finding them is non-trivial. We solve the difficult inverse problem, including the possible selection among several extrema, by learning the desired function from samples, generated by computing Gaussian curvature of random patches. This approximation provides a stable solution to the ill-defined inverse problem and is much more efficient than direct numerical optimization, facilitating the interactive modeling framework. The local solution is used in an iterative optimization incorporating continuity constraints across patches. We demonstrate that the surface varies smoothly with the handle location and that the resulting modeling system provides local and generally intuitive control. The idea of learning the inverse mapping from handles to patches may be applicable to other parametric surfaces.\n          <\/jats:p>","DOI":"10.1145\/3618383","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T10:20:48Z","timestamp":1701771648000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["K-Surfaces: B\u00e9zier-Splines Interpolating at Gaussian Curvature Extrema"],"prefix":"10.1145","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7043-9983","authenticated-orcid":false,"given":"Tobias","family":"Djuren","sequence":"first","affiliation":[{"name":"TU Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5469-607X","authenticated-orcid":false,"given":"Maximilian","family":"Kohlbrenner","sequence":"additional","affiliation":[{"name":"TU Berlin, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9854-8466","authenticated-orcid":false,"given":"Marc","family":"Alexa","sequence":"additional","affiliation":[{"name":"TU Berlin, Germany"}]}],"member":"320","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Edwin Norman Nilson, and Joseph Leonard Walsh","author":"Ahlberg J. 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