We document the limitations of isotropic textures in conveying three-dimensional shape. We measured the perceived shape and pitch of upright and pitched corrugated surfaces overlaid with different classes of isotropic textures: patterns containing isotropic texture elements, isotropically filtered noise patterns, and patterns containing ellipses or lines of all orientations. Frequency modulatio...

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...

Complex surface structures have stimulated a great deal of interests due to many potential applications in surface devices. However, in the fabrication of complex surface micro-/nanostructures, there are always great challenges in precise design, or good controllability, or low cost, or high throughput. Here, we present a route for the accurate design and highly controllable fabrication of surf...

Define a “slice” curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy’s arm lemma to permit nonconvex “openings” of a planar convex chain.

Relative convex hulls have been suggested for multigridconvergent surface area estimation. Besides the existence of a convergence theorem there is no efficient algorithmic solution so far for calculating 3D relative convex hulls. This article discusses an approximative solution based on minimum-length polygon calculations. It is illustrated that this approximative calculation also proves (exper...

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.

We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian’s Fast Marching Method and Polthier’s straightest geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and non-convex surfaces. r 2005 Elsevier Ltd. All rights reserved.

Suppose τ is a train track on a surface S. Let C (τ) be the set of isotopy classes of simple closed curves carried by τ. Masur and Minsky [2004] prove that C (τ) is quasi-convex inside the curve complex C (S). We prove that the complement, C (S)−C (τ), is quasi-convex.

We compare the perimeter measure with the Airault-Malliavin surface measure and we prove that all open convex subsets of abstract Wiener spaces have finite perimeter. By an explicit counter–example, we show that in general this is not true for compact convex domains.