Birational Quadratic Planar Maps with Generalized Complex Rational Representations

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dc.citation.articleNumber3609en_US
dc.citation.issueNumber16en_US
dc.citation.journalTitleMathematicsen_US
dc.citation.volumeNumber11en_US
dc.contributor.authorWang, Xuhuien_US
dc.contributor.authorHan, Yuhaoen_US
dc.contributor.authorNi, Qianen_US
dc.contributor.authorLi, Ruien_US
dc.contributor.authorGoldman, Ronen_US
dc.date.accessioned2024-05-03T15:51:12Zen_US
dc.date.available2024-05-03T15:51:12Zen_US
dc.date.issued2023en_US
dc.description.abstractComplex rational maps have been used to construct birational quadratic maps based on two special syzygies of degree one. Similar to complex rational curves, rational curves over generalized complex numbers have also been constructed by substituting the imaginary unit with a new independent quantity. We first establish the relationship between degree one, generalized, complex rational Bézier curves and quadratic rational Bézier curves. Then we provide conditions to determine when a quadratic rational planar map has a generalized complex rational representation. Thus, a rational quadratic planar map can be made birational by suitably choosing the middle Bézier control points and their corresponding weights. In contrast to the edges of complex rational maps of degree one, which are circular arcs, the edges of the planar maps can be generalized to hyperbolic and parabolic arcs by invoking the hyperbolic and parabolic numbers.en_US
dc.identifier.citationWang, X., Han, Y., Ni, Q., Li, R., & Goldman, R. (2023). Birational Quadratic Planar Maps with Generalized Complex Rational Representations. Mathematics, 11(16), Article 16. https://doi.org/10.3390/math11163609en_US
dc.identifier.digitalmathematics-11-03609en_US
dc.identifier.doihttps://doi.org/10.3390/math11163609en_US
dc.identifier.urihttps://hdl.handle.net/1911/115565en_US
dc.language.isoengen_US
dc.publisherMDPIen_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleBirational Quadratic Planar Maps with Generalized Complex Rational Representationsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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