First place for Zi Ye
The Eurographics Symposium on Geometry Processing 2018
The paper, written by Zi Ye and his advisor Prof. Tim Hoffmann together with Olga Diamanti, Chengcheng Tang and Leonidas Guibas at Stanford, has appeared in the Journal "Computer Graphics Forum". The main result of the paper is a new discretization of the Dirac operator with applications in geometry processing and shape analysis.
Dirac operator – from Particle Physik to Geometry
Inventing the Dirac operator, the physicist Paul Dirac originally described elementary particles with a specific intrinsic angular momentum, spin ½ - for example, electrons. Surprisingly, this Dirac operator can be used to create and transform surfaces in our 3D space with prescribed curvature. This means, it measures how surfaces bend at every point.
Practically, mathematicians can customize a function, which indicates how much or in which direction the surface should curve at each point, throw this information into the Dirac equation and then the solution produces a surface such that it bends exactly in an expected way.
The discrete Dirac Operator
In the paper "A unified discrete framework for intrinsic and extrinsic Dirac operators for geometry processing", Zi Ye and his coauthors introduce a unified discretization scheme. Discretize means, they decompose continuous, spatial data into a discrete subset. By implementing the scheme on the computer, they can visualize the created surfaces, like the bunny and the cow in the example.
Dirac Animals. The authors compute the eigenfunctions of their intrinsic Dirac operator corresponding to its smallest eigenvalues, and apply them as a spin transformation to deform an input mesh.
The researchers showcase various applications of their operators, such as conformal parameterization, shape filtering and shape matching. The results are numerically more accurate or preciser than in prior publications.
Best Paper Award of the SGP 2018
Zi Ye researches in the field of Discrete Spin Geometry and is pursuing his PhD studies under Tim Hoffmann, Professor for Geometry and Visualization. His research was supported by the DFG Collaborative Research Center SFB TRR109, Discretization in Geometry and Dynamics.
He received the Best Paper Award at the finale of the symposium on geometry processing from 9 to 11 July 2018 in Paris. The SGP is considered as premier venue for disseminating new research ideas and cutting-edge results in geometry processing.