| Title: | On double Pythagorean-hodograph curves of degree seven |
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| Authors: | ID Knez, Marjetka (Author)
ID Praprotnik, Selena (Author) |
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| Files: |  PDF - Presentation file, download (3,59 MB)
MD5: 969A6834C66D421F6FD2DD7837B52B6A
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0167839626000257
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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: | This paper presents a comprehensive and constructive analysis of degree 7 double Pythagorean-hodograph (DPH) curves for the three distinct structural classes. A unified framework is introduced for their construction, particularly useful for interpolation tasks involving prescribed boundary data. The approach explicitly identifies the degrees of freedom available in each class and distinguishes between helical and non-helical curve types. Furthermore, the structure of a specific rational curve in the complex plane that via the normalized Hopf map generates the tangent indicatrix is revealed for all degree 7 DPH curves. This confirms known results for helical curves and extends the interpretation to non-helical cases. The practical applicability of the derived curves is demonstrated through a numerical interpolation example, which also validates the stated number of degrees of freedom. |
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| Keywords: | double Pythagorean-hodograph curves, helical/non-helical curves, quaternions, Hopf map, Frenet frame, interpolation |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 20 str. |
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| Numbering: | Vol. 126, article no. 102532 |
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| PID: | 20.500.12556/DiRROS-28916  |
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| UDC: | 519.6 |
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| ISSN on article: | 0167-8396 |
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| DOI: | 10.1016/j.cagd.2026.102532 |
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| COBISS.SI-ID: | 275061507 |
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| Publication date in DiRROS: | 14.04.2026 |
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| Views: | 144 |
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| Downloads: | 131 |
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