We study the Minimum-Length Corridor (MLC) problem. Given a rectangular boundary partitioned into rectilinear polygons, the objective is to find a corridor of least total length. A corridor is a set of line segments each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectilinear polygons. The corridor is a tree, and must include at least ...

In this paper, a new construct called connection graph, Gc, is proposed. An efficient geometric algorithm for constructing Gc is given. We present a framework for designing a class of time and space efficient maze-running and line-search rectilinear shortest path and rectilinear minimum spanning tree algorithms based on Gc. We give several example maze-running and line-search algorithms based o...

Arc-shaped forceps are important in pharyngeal cancer surgery, endoscopic sinus surgery, and single port surgery. Rotating the gripper of an arc-shaped forceps with respect to its shaft axis can improve the manipulability of the forceps. Concentric pipe structures consisting of inner and outer pipes are often used for this purpose. The inner pipe transmits rotations from its proximal end to dis...

We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple families of graphs. We also prove some properties of this crossing number. Moreover, we define a variant of this crossing number which is tightly connected to the rectilinear crossing number, and compute it for some sim...

Rectilinear Binary Space Partitioning (BSP) trees are often used for solving various types of range searching problems including ray shooting. We propose a novel method for construction of rectilinear BSP trees for a preferred set of ray shooting queries. Particularly, we study ray sets formed by fixing either the direction or the origin of rays. We analyse and discuss the properties of constru...