For a self{similar or self{aane tile in R n we study the following questions: 1) What is the boundary? 2) What is the convex hull? We show that the boundary is a graph directed self{aane fractal, and in the self{similar case we give an algorithm to compute its dimension. We give necessary and suucient conditions for the convex hull to be a polytope, and we give a description of the Gauss map of...

We develop efficient algorithms for problems in computational geometry—convex hull, smallest enclosing box, ECDF, two-set dominance, maximal points, all-nearest neighbor, and closest-pair—on the OTIS-Mesh optoelectronic computer. We also demonstrate the algorithms for computing convex hull and prefix sum with condition on a multi-dimensional mesh, which are used to compute convex hull and ECDF ...

A new name for the Oriental genus Nyssomyia Hull, 1962 (Diptera: Asilidae) is proposed. Homonymy exists between this Oriental robber fly genus and the more senior Neotropical phlebotomine sand fly genus Nyssomyia Barretto, 1962 (sensu Galati 2003) (Diptera: Psychodidae), and the following replacement name is proposed: Ekkentronomyia nom. nov. for Nyssomyia Hull (nec Barretto 1962). Accordingly,...

The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words, reducing topic quality and interpretability. Rather than finding an approximate convex hull in a high-dimensional space, we propose to find an exact convex hull i...

For a self similar or self a ne tile in R we study the following questions What is the boundary What is the convex hull We show that the boundary is a graph directed self a ne fractal and in the self similar case we give an algorithm to compute its dimension We give necessary and su cient conditions for the convex hull to be a polytope and we give a description of the Gauss map of the convex hull

The visual hull relates the shape of an object to its silhouettes. This paper develops the theory of the visual hull of piecewise smooth objects, as those used in CAD applications. We show that the surface of the visual hull can be constructed using patches of nine visual event surfaces of the aspect graph of the object. A detailed analysis allows to prune away many surfaces and patches that ar...

We prove a tight asymptotic bound of Θ(δ log(n/δ)) on the worst case computational complexity of the convex hull of the union of two convex objects of sizes summing to n requiring δ orientation tests to certify the answer. Our algorithm is deterministic, it uses portions of the convex hull of input objects to describe the final convex hull, and it takes advantage of easy instances, such as thos...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...