SIGGRAPH Asia 2014-course "an introduction to Ricci flow and volumetric approximation with applications to shape modeling"
Extending a shape-driven map to the interior of the input shape and to the surrounding volume is a difficult problem since it typically relies on the integration of shape-based and volumetric information, together with smoothness conditions, interpolating constraints, preservation of feature values at both a local and global level. This survey discusses the main volumetric approximation schemes for both 3D shapes and d-dimensional data, and provides a unified discussion on the integration of surface-based and volume-based shape information. Then, it describes the application of shape-based and volumetric techniques to shape modeling through volumetric parameterization and polycube splines; feature-driven approximation through kernels and radial basis functions. We also discuss the Hamilton's Ricci flow, which is a powerful tool to compute the conformal shape structure and to design Riemannian metrics of manifolds by prescribed curvatures. We conclude the presentation by discussing applications to shape analysis and medicine.
Publication Source (Journal or Book title)
SIGGRAPH Asia 2014 Courses, SA 2014
Patanè, G., Li, X., & Gu, D. (2014). SIGGRAPH Asia 2014-course "an introduction to Ricci flow and volumetric approximation with applications to shape modeling". SIGGRAPH Asia 2014 Courses, SA 2014 https://doi.org/10.1145/2659467.2659469