| Title: | A family of $C^1$ Clough-Tocher spline spaces on $C^0$ piecewise quadratic domain partitions |
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| Authors: | ID Grošelj, Jan (Author)
ID Knez, Marjetka (Author) |
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| Files: |  PDF - Presentation file, download (5,58 MB)
MD5: 590365C4B01C2ED2DE5D59FB93DDEA42
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0378475425000813
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | The paper addresses the construction of $C^1$ splines on a curved domain that is parametrized by a $C^0$ piecewise geometry mapping composed of quadratic Bézier triangles. The $C^1$ splines are assembled from polynomials of a chosen total degree greater than or equal to four, and their construction is based on the Clough-Tocher splitting technique that ensures locality. In particular, the splines are locally characterized by an interpolation problem described by Hermite data, which resembles the standard macro-element concepts developed for $C^1$ splines on triangulations. |
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| Keywords: | quadratic triangle, quadratic triangulation, isogeometric functions, Clough-Tocher refinement, spline space, dimension, basis functions |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.08.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 368-389 |
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| Numbering: | Vol. 234 |
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| PID: | 20.500.12556/DiRROS-21756  |
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| UDC: | 519.6 |
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| ISSN on article: | 0378-4754 |
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| DOI: | 10.1016/j.matcom.2025.03.006 |
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| COBISS.SI-ID: | 230027267 |
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| Note: |
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| Publication date in DiRROS: | 24.03.2025 |
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| Views: | 528 |
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| Downloads: | 293 |
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| Metadata: |    |
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