This paper presents a new algorithm for correcting incorrect projections of a polyhedral scene. Such projections arise in applications where an image of a polyhedral world is taken and its edges and vertices are extracted. Along the way, the true positions of the vertices in the 2D projection are perturbed due to digitization errors and the preprocessing. As most available algorithms for recons...

The linear theory of discrete Riemann surfaces is applied to polyhedral surfaces embedded in R. As an application we compute the period matrices of some classical examples from the surface theory, in particular the Wente torus and the Lawson surface.

The paper studies combinatorial prototiles of locally finite face-to-face tilings of euclidean d-space Ed by convex d-polytopes. A finite set P of prototiles is called combinatorially aperiodic if P admits a locally finite face-to-face tiling by combinatorially equivalent copies of the prototiles in P, but no such tiling with a combinatorial automorphism of infinite order. The paper describes s...

In this paper we present a method for detecting rounds and fillets in engineering sketches and drawings, and automatically generating a 3D model of the corresponding object, with rounds and fillets applied. This method is useful both as a component of computer-aided sketching tools and in determining design intent—although rounds and fillets are common in engineering parts, they often conceal d...

We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...

The purpose of the paper is to construct a polyhedral Markov field in R in analogy with the planar construction of the original Arak (1982) polygonal Markov field. We provide a dynamic construction of the process in terms of evolution of two-dimensional multi-edge systems tracing polyhedral boundaries of the field in three-dimensional timespace. We also give a general algorithm for simulating G...

We study delta-points in Banach spaces hA,p generated by adequate families A, where 1≤p<∞. When p>1, we prove that neither nor its dual contain delta-points. Under the extra assumption A is regular, same true when p=1. In particular, Schreier and their duals fail to have If consists only of finite sets, are able rule out existence hA,1 Daugavet-points dual. also show if polyhedral, then it eith...