Research interests:

I conduct research in Modeling of Curves and Surfaces, Computational Geometry, and Digital Topology.

Modeling of Curves and Surfaces:

Recently, some colleagues of mine and I developed a new representation for smooth surfaces defined from triangle meshes, which is based on the manifold approach pioneered by Cindy Grimm and John Hughes. Our work has several advantages over previous ones and it has been presented in the SMI 2009 and published by the Computer & Graphics journal. Most of my current research efforts are devoted to extensions of this work.

See my publications on the topic “Modeling of Curves and Surfaces”.

Computational Geometry:

During my Ph.D. studies, Dr. Suneeta Ramaswami and I developed an algorithm for converting triangle meshes of planar domains into quadrilateral meshes with some provable guarantees. Our work was presented in the IMR 2003 and an extended version of our paper was then published in the International Journal of Computational Geometry and Applications, in 2005. Since then, Dr. Ramaswami and I have studied the problem of meshing spatial domains (defined by a surface quadrilateral mesh) with hexahedra such that the resulting hexahedral mesh conforms  to the surface quadrilateral mesh. Although we have not come up with any new solution yet,  we have made some progress and I am currently very interested in this problem.

See my publications on the topic “Computational Geometry and Mesh Generation”.

Digital Topology:

My interest in digital topology was triggered by a paper by Dr. Longin Jan Latecki on well-composedness I came across during my Ph.D. studies. Later, I found out  Dr. Longin Jan Latecki and I lived in the same city! So, I contacted him and we developed a randomized  algorithm for converting ill-composed digital binary images into well-composed ones. The latter images have many interesting properties, one of which was crucial for the main result of my thesis. Since then, I have co-authored a few papers related to well-composedness. Although I am not doing research on this topic at the moment, any problem that can benefit from well-composedness or my algorithm will certainly get me interested.

See my publications on the topic “Digital Topology”.