Date of Submission
Winter 2024
Academic Program
Mathematics
Project Advisor 1
Charles Doran
Abstract/Artist's Statement
The study of Ricci flow in differential geometry provides a foundational approach to understandng the intrinsic geometry of surfaces through the evolution of curvature. By deforming the Riemannian metric over time, Hamilton’s Ricci flow enables surfaces to reach a state of uniform curvature, simplifying complex geometric structures and facilitating computational analysis. My thesis builds on this framework by visualizing the intrinsic unfolding of Ricci flow as it acts on discrete 3D meshes, illustrating how these structures conform to a 2D plane while preserving their geometric integrity. This visualization provides a unique perspective on the behavior of Ricci flow in transitioning complex surfaces from three to two dimensions. Through this approach we acquire insights into the nature of curvature while also showing its implications for practical applications, such as surface registration and shape analysis in fields such as computer graphics.
Open Access Agreement
On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Hossain, Nasif, "From Geometry to Visualization: Exploring Euclidean Discrete Surface Ricci Flow" (2024). Senior Projects Fall 2024. 9.
https://digitalcommons.bard.edu/senproj_f2024/9
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