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: Erkan Gunpinar, A. Alper Tasmektepligil, Márton Vaitkus, Péter Salvi
Format: Article
Language:English
Published: Elsevier 2025-08-01
Series:Graphical Models
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S1524070325000220
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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
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issn 1524-0703
language English
publishDate 2025-08-01
publisher Elsevier
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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