Work

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

Year: 2025

Type: article

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 solution space is expanded by allowing twist-incompatible cross-derivatives, optimized using cost functions based on curvature metrics. An automated optimization procedure is introduced to determine rotation angles of twist-compatible 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.

Source: Graphical Models

DOI: 10.1016/j.gmod.2025.101275

Authors: Erkan Gunpinar, A. Alper Tasmektepligil, Márton Vaitkus, Péter Salvi

Institutions: Istanbul Technical University, Yıldız Technical University, Budapest University of Technology and Economics

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,180

Funders: Hungarian Scientific Research Fund, Istanbul Teknik Üniversitesi, Bilimsel Araştırma Projeleri Birimi, İstanbul Teknik Üniversitesi