We prove that rectangle-faced orthostacks, a restricted class of orthostacks, can be grid-edge unfolded without additional refinement. We prove several lemmas applicable to larger classes of orthostacks, and construct an example to illustrate that our algorithm does not directly extend to more general classes of orthostacks.

We consider the NP-complete problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles. We present two different constraintsatisfaction formulations of this problem. The first searches a space of absolute placements of rectangles in the enclosing rectangle, while the other searches a space of relative placements between pairs of rectangles. Both appr...

Definition 2.1. Let f : X × Y → V . A subset R of X × Y is a rectangle1 if it is of the form A × B for some A ⊆ X and B ⊆ Y . The rectangle R is said to be monochromatic (wrt. f) if f is constant on R. A monochromatic rectangle R is a 0-rectangle if f(R) = {0}; it is a 1-rectangle if f(R) = {1}. Observation 2.2. A subset S of X × Y is a rectangle iff for all x, x′ ∈ X and y, y′ ∈ Y (x, x′) ∈ S ...

2 Mathematical Preliminaries 3 2.1 Barycentric Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Inscribed Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Bezier Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Derivatives . . . . . . . . . . ....

We prove that there are superexponentially many combinatorially distinct d-dimensional neighborly Delaunay triangulations on n points. These are the first examples of neighborly Delaunay triangulations that cannot be obtained via a stereographic projection of an inscribed cyclic polytope, and provide the current best lower bound for the number of combinatorial types of Delaunay triangulations. ...

We present numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Method that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladd...