Computational Geometry

My involvement with computational geometry is quite restricted to the problem of mesh generation. In particular, I am mainly interested in meshing algorithms that generate provably good quality meshes of triangles/tetrahedra from imaging data. My first research work on mesh generation resulted in an algorithm for converting triangle meshes of polygonal regions into quadrilateral meshes of bounded size. This algorithm was developed in collaboration with Suneeta Ramaswami, who has been working with several instances of the tri-to-quad conversion problem for a long time. More recently, my collaboration with Dr. Ramaswami on an extension of the tri-to-quad conversion problem to surface meshes produced an algorithm for computing irreducible triangulations of compact, connected, and orientable surfaces with an empty boundary in Euclidean spaces. Currently, I am working on a new algorithm for computing Delaunay triangulations from planar regions delimited by smooth curves. This research has been conducted in collaboration with Älper Üngor and Serdar Ayaz (a current Ph.D. candidate under Dr. Üngor's advisory) at the University of Florida as part of the activities of my sabbatical year. Our meshing algorithm improves upon a previous algorithm given by Steve Pav and Noel Walkington in 2005 (see paper).

Ramaswami, S.; Siqueira, M.
“A fast algorithm for computing irreducible triangulations of closed surfaces in Ed”, Computational Geometry: Theory and Applications, 2017 (In Press)
(PDF) (BiBTeX) (DOI)
A longer version of this paper can be found in arXiv
(Code)

Lizier, M.; Siqueira, M.; Daniels II, J.; Silva, C.T.; Nonato, L.G.
“Template-Based Quadrilateral Mesh Generation from Imaging Data”, The Visual Computer, 27(10), 2011, p.887-903.
(PDF) (BiBTeX) (DOI)

Daniels II, J.; Lizier, M.; Siqueira, M.; Silva, C.T.; Nonato, L.G.
“Template-Based Quadrilateral Meshing”, Computer & Graphics, 35(3), 2011, p.471-482. (Special Issue of the IEEE International Conference on Shape Modeling and Applications - SMI 2011, Herzliya, Israel)
(PDF) (BiBTeX) (DOI)

Ramaswami, S.; Siqueira, M.; Sundaram, T.; Gallier, J.; Gee, J.
“Constrained quadrilateral meshes of bounded size”, International Journal of Computational Geometry and Applications , 15(1), 2005, p.55-98.
(PDF) (BiBTeX) (DOI) (Code)

Last update: August 19, 2017