A new analog for the giant polygons in the Chryse-Acidalia area suggests that those features may have formed in a major body of water – likely a Late Hesperian to Early Amazonian ocean. This analog -terrestrial polygons in subsea, passive margin basinsderives from 3D seismic data that show similar-scale, polygonal fault systems in the subsurface of more than 50 terrestrial offshore basins. The ...

In the Independent Set of Convex Polygons problem we are given a set of weighted convex polygons in the plane and we want to compute a maximum weight subset of non-overlapping polygons. This is a very natural and well-studied problem with applications in many different areas. Unfortunately, there is a very large gap between the known upper and lower bounds for this problem. The best polynomial ...

In this paper we present optimal algorithms to compute monotone stabbers for convex polygons. More precisely, given a set of m convex polygons with n vertices in total we want to stab the polygons with an x-monotone polygonal chain such that each polygon is entered at its leftmost point and departed at its rightmost point. Since such a stabber does not exist in general, we study two related pro...

An increased number of polygons in virtual objects cause a delay in simulation time, making it difficult to handle haptic interactions, which need real-time processing in virtual worlds. Previous studies reduced the number of polygons in objects by representing the roughness of an object’s surface as a texture, thus reducing the processing time. However, it is difficult to simulate the interact...

Let S be a set of 2n points on a circle such that for each point p ∈ S also its antipodal (mirrored with respect to the circle center) point p′ belongs to S. A polygon P of size n is called antipodal if it consists of precisely one point of each antipodal pair (p, p′) of S. We provide a complete characterization of antipodal polygons which maximize (minimize, respectively) the area among all an...

This paper proposes an optimal algorithm for constructing the surface adjacency relation in a list of polygons extracted from 3D medical images. The discrete nature of data allows us to build this adjacency relation in a time proportional to the number of triangles T. We have payed a special attention on the memory requirements, since our method takes as input the surface extracted by the March...

This paper describes an approach to the representation of polygons by real functions and its application to sweeping. We combine an algorithm employing a monotone function of a boolean operation, with R-functions. Application of this method results in a continuous function F(x,y) with zero value at polygon edges. We discuss and illustrate different sweeping techniques with the use of functional...

The boundaries of conic polygons consist of conic segments or second degree curves. The conic polygon has two degenerate or special cases: the linear polygon and the circular-arc polygon. The natural problem — boolean operation on linear polygons, has been well studied. Surprisingly, (almost) no article focuses on the problem of boolean operation on circular-arc polygons, which actually can als...

Abstract: In this paper, we consider addressable procedures with DNA strands for logic and arithmetic operations. Using a theoretical model for DNA computing, we first show a DNA representation of binary numbers of bits, and propose a procedure to assign values for the representation. The procedure is applicable to binary numbers of bits in lab steps in parallel. Next, we propose a procedure fo...