Optimization of cross-derivatives for ribbon-based multi-sided surfaces

Günpınar E., TAŞMEKTEPLİGİL A. A., Vaitkus M., Salvi P.

Graphical Models, vol.140, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 140
  • Publication Date: 2025
  • Doi Number: 10.1016/j.gmod.2025.101275
  • Journal Name: Graphical Models
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, Geobase, INSPEC, zbMATH
  • Keywords: Computer-aided design, Optimization, Transfinite surfaces
  • Yıldız Technical University Affiliated: Yes

Abstract

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.