Optimization of cross-derivatives for ribbon-based multi-sided surfaces
This work investigates ribbon-based multi-sided surfaces that satisfy positional and cross-derivative constraints to ensure smooth transitions with adjacent tensor-product and multi-sided surfaces. The influence of cross-derivatives, crucial to surface quality, is studied within Kato’s transfinite s...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2025-08-01
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| Series: | Graphical Models |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1524070325000220 |
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| _version_ | 1850075244278054912 |
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| author | Erkan Gunpinar A. Alper Tasmektepligil Márton Vaitkus Péter Salvi |
| author_facet | Erkan Gunpinar A. Alper Tasmektepligil Márton Vaitkus Péter Salvi |
| author_sort | Erkan Gunpinar |
| collection | DOAJ |
| description | This work investigates ribbon-based multi-sided surfaces that satisfy positional and cross-derivative constraints to ensure smooth transitions with adjacent tensor-product and multi-sided surfaces. The influence of cross-derivatives, crucial to surface quality, is studied within Kato’s transfinite surface interpolation instead of control point-based methods. To enhance surface quality, the surface is optimized using cost functions based on curvature metrics. Specifically, a Gaussian curvature-based cost function is also proposed in this work. An automated optimization procedure is introduced to determine rotation angles of cross-derivatives around normals and their magnitudes along curves in Kato’s interpolation scheme. Experimental results using both primitive (e.g., spherical) and realistic examples highlight the effectiveness of the proposed approach in improving surface quality. |
| format | Article |
| id | doaj-art-a6babe1e19a0413fbf2e05af4633e416 |
| institution | DOAJ |
| issn | 1524-0703 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Graphical Models |
| spelling | doaj-art-a6babe1e19a0413fbf2e05af4633e4162025-08-20T02:46:21ZengElsevierGraphical Models1524-07032025-08-0114010127510.1016/j.gmod.2025.101275Optimization of cross-derivatives for ribbon-based multi-sided surfacesErkan Gunpinar0A. Alper Tasmektepligil1Márton Vaitkus2Péter Salvi3Istanbul Technical University, TurkeyIstanbul Technical University, Turkey; Yildiz Technical University, TurkeyBudapest University of Technology and Economics, HungaryBudapest University of Technology and Economics, Hungary; Correspondence to: 2. Magyar tudósok Blvd., H-1117 Budapest, Hungary.This work investigates ribbon-based multi-sided surfaces that satisfy positional and cross-derivative constraints to ensure smooth transitions with adjacent tensor-product and multi-sided surfaces. The influence of cross-derivatives, crucial to surface quality, is studied within Kato’s transfinite surface interpolation instead of control point-based methods. To enhance surface quality, the surface is optimized using cost functions based on curvature metrics. Specifically, a Gaussian curvature-based cost function is also proposed in this work. An automated optimization procedure is introduced to determine rotation angles of cross-derivatives around normals and their magnitudes along curves in Kato’s interpolation scheme. Experimental results using both primitive (e.g., spherical) and realistic examples highlight the effectiveness of the proposed approach in improving surface quality.http://www.sciencedirect.com/science/article/pii/S1524070325000220Computer-aided designTransfinite surfacesOptimization |
| spellingShingle | Erkan Gunpinar A. Alper Tasmektepligil Márton Vaitkus Péter Salvi Optimization of cross-derivatives for ribbon-based multi-sided surfaces Graphical Models Computer-aided design Transfinite surfaces Optimization |
| title | Optimization of cross-derivatives for ribbon-based multi-sided surfaces |
| title_full | Optimization of cross-derivatives for ribbon-based multi-sided surfaces |
| title_fullStr | Optimization of cross-derivatives for ribbon-based multi-sided surfaces |
| title_full_unstemmed | Optimization of cross-derivatives for ribbon-based multi-sided surfaces |
| title_short | Optimization of cross-derivatives for ribbon-based multi-sided surfaces |
| title_sort | optimization of cross derivatives for ribbon based multi sided surfaces |
| topic | Computer-aided design Transfinite surfaces Optimization |
| url | http://www.sciencedirect.com/science/article/pii/S1524070325000220 |
| work_keys_str_mv | AT erkangunpinar optimizationofcrossderivativesforribbonbasedmultisidedsurfaces AT aalpertasmektepligil optimizationofcrossderivativesforribbonbasedmultisidedsurfaces AT martonvaitkus optimizationofcrossderivativesforribbonbasedmultisidedsurfaces AT petersalvi optimizationofcrossderivativesforribbonbasedmultisidedsurfaces |