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This paper addresses the issue of trap design for sensor-less automated assembly. First, we present a simple algorithm that determines in O(nmm(nm) log(nm)) time whether an n-sided polygonal part will fall through an m-sided polygonal trap. We then introduce the notion of a minimal trap for a polygonal part, and develop an O(n 4+") algorithm that designs a family of minimal feeders built from t...

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cros...

In this paper, we propose a new shape feature for shapesimilarity search of 3D polygonal-mesh models in digital museum. The shape feature is an extension of the D2 shape functions proposed by Osada. Our proposed shape feature is a combination of geometry and texture which is also invariant to similarity transformation. Experiments showed that, our method achieved better performance improvement ...

In this paper we study the separability in the plane by two criteria: double-wedge separability and Θ-separability. We give an O(N logN)-time optimal algorithm for computing all the vertices of separating double wedges of two disjoint sets of objects (points, segments, polygons and circles) and an O((N/Θ0) logN)-time algorithm for computing a nearly-straight minimal Θ-polygonal chain separating...