Reconstructing Curves from Sparse Samples on Riemannian Manifolds

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, lim...

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Bibliographic Details
Published in:Computer graphics forum 2024-08, Vol.43 (5), p.n/a
Main Authors: Marin, D., Maggioli, F., Melzi, S., Ohrhallinger, S., Wimmer, M.
Format: Article
Language:English
Subjects:
Algorithms
CCS Concepts
Computer graphics
Computing methodologies → Mesh geometry models
Curves
Graph algorithms
Image reconstruction
Mathematics of computing → Paths and connectivity problems
Riemann manifold
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Summary:Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state‐of‐the‐art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state‐of‐the‐art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non‐Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.15136