Theses Defense

Ph.D. thesis defense: Optimal Sampling Lattices And Trivariate Box Splines, Alireza Entezari

Abstract: The Body Centered Cubic (BCC) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices signi?cantly outperform the accuracy of the commonly-used Cartesian 3-D lattice.

M.Sc. thesis defense: Visual Fidelity of 3D Regular Sampling and Reconstruction, Tai Meng

Abstract: For generic 3D sampling, the Body Centered Cubic (BCC) lattice and the Face Centered Cubic (FCC) lattice are significantly superior to the traditionally popular Cartesian Cubic (CC) lattice. Motivated by the goal of high visual fidelity in the visualization community, this thesis investigates the relative perceptual merits of high quality reconstruction filters for CC, BCC, and FCC sampled data. We recruited 24 participants and gave them pairs of images to discriminate.

Ph.D. Thesis DEFENSE : Ramsay Dyer

In the Euclidean plane, a Delaunay triangulation can be characterized by the requirement that the circumcircle of each triangle be empty of vertices of all other triangles. For triangulating a surface S in R^3, the Delaunay paradigm has typically been employed in the form of the restricted Delaunay triangulation, where the empty circumcircle property is defined by using the Euclidean metric in R^3 to measure distances on the surface. More recently, the intrinsic (geodesic) metric of S has also been employed to define the Delaunay condition.