The (negative) Torricelli triangle T1(ABC) of a nondegenerate (positively oriented) triangle ABC is defined to be the triangle A1B1C1, where ABC1, BCA1, and CAB1 are the equilateral triangles drawn outwardly on the sides of ABC. It is known that not every triangle is the Torricelli triangle of some initial triangle, and triangles that are not Torricelli triangles are characterized in [28]. In t...

We have shown previously that the precision of angle judgments depends strongly on the global stimulus configuration: discrimination thresholds for angles that form part of isosceles triangles are up to 3 times lower than for those that form part of scalene triangles [Kennedy, G. J., Orbach, H. S., & Loffler, G. (2006). Effects of global shape on angle discrimination. VisionResearch, 46(8-9), 1...

A popular question in recreational mathematics is the following: If we drop a spaghetti noodle and it breaks at two random places, what is the probability that we can form a triangle with the three resulting segments? See for example [2, chap.1, sec.6], [3, p.6], [4, p.31], or [7, p.30-36]. This is an elementary problem in geometric probability. Clearly the length of the noodle (or equivalently...

We present an algorithm that quickly finds optimal plans for unforeseen agent preferences within graph-based planning domains where actions have deterministic outcomes and action costs are linearly parameterized by preference parameters. We focus on vehicle route planning for drivers with personal trade-offs for different types of roads, and specifically on settings where these preferences are ...

We often need to refer to adjacent elements (e.g., vertices, edges and faces) in triangle meshes for rendering, mesh simplification and other processes. It is, however, sometimes impossible to prepare the enormous memory needed to represent element connectivity in gigantic triangle meshes. We proposed a memory efficient scheme for referring to adjacent faces around a vertex in non-manifold tria...

By using an example from a robot navigating domain, we argue that to specify declaratively the behavior of an agent, we need to have a formal and explicit notion of \quality plans." To that end, we propose the following three domain independent measures of plan quality: a plan is said to be A-minimalif none of the actions in it can be deleted and have it continue to be a plan; it is said to be ...

In this paper, we describe TCLP, a Temporal Causal Link Planner which takes into account the duration of actions and accepts disjunctive temporal relations, while still using the principles of traditional planners which assume actions are instantaneous. We have defined a model of action with duration, and translate any temporal disjunctive relation between 2 actions with duration into a set of ...

We consider the problem of querying data sources that have limited capabilities and can thus only be accessed by complying with certain binding patterns for their attributes. This is often the case, e.g., in the context of data on the web queryable via web forms as well as in legacy data wrapped in relational tables. In such contexts, computing the answer to a user query cannot be done as in a ...