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Robotics
Volume 14
Issue 11
10.3390/robotics14110160
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation

by
Mahrukh Mahrukh
1,*,
Gianluca Palli
1,
Mattia Gambazza
2 and
Claudio Melchiorri
1
1
Department of Electrical, Electronic and Information Engineering (DEI), University of Bologna, 40136 Bologna, Italy
2
R&D Division, SACMI Imola S.C., 40026 Imola, Italy
*
Author to whom correspondence should be addressed.
Robotics 2025, 14(11), 160; https://doi.org/10.3390/robotics14110160 (registering DOI)
Submission received: 8 September 2025 / Revised: 13 October 2025 / Accepted: 26 October 2025 / Published: 31 October 2025
(This article belongs to the Section Sensors and Control in Robotics)
Versions Notes

Abstract

This paper presents a comparative study on the suitability of free-boundary surface parameterization techniques for generating trajectories on 3D surfaces. The approach maps a 3D surface to a 2D parametric domain through four parameterization methods: Least-Squares Conformal Mapping, Boundary First Flattening, As-Rigid-As-Possible, and Conformal Equivalence of Triangular Meshes. Structured trajectory patterns are generated in the 2D domain and projected back to 3D. We introduce center-to-boundary geodesic deviation measure, which yields a deviation profile over the boundary loop and reflects how well central alignment is preserved under each parameterization method. The results highlight differences in distortion and geodesic preservation, reflecting the suitability of methods for path generation.
Keywords: parameterization; robotic path; path mapping; geodesic deviation parameterization; robotic path; path mapping; geodesic deviation

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MDPI and ACS Style

Mahrukh, M.; Palli, G.; Gambazza, M.; Melchiorri, C. Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation. Robotics 2025, 14, 160. https://doi.org/10.3390/robotics14110160

AMA Style

Mahrukh M, Palli G, Gambazza M, Melchiorri C. Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation. Robotics. 2025; 14(11):160. https://doi.org/10.3390/robotics14110160

Chicago/Turabian Style

Mahrukh, Mahrukh, Gianluca Palli, Mattia Gambazza, and Claudio Melchiorri. 2025. "Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation" Robotics 14, no. 11: 160. https://doi.org/10.3390/robotics14110160

APA Style

Mahrukh, M., Palli, G., Gambazza, M., & Melchiorri, C. (2025). Comparative Study on the Suitability of Free-Boundary Parameterization Techniques for 3D Geometry-Aware Path Generation. Robotics, 14(11), 160. https://doi.org/10.3390/robotics14110160

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