Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

Approximation Schemes for Partitioning: Convex Decomposition and Surface Approximation

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved approximation guarantees.Comment: 21 pages, 6 figure

Weighted skeletons and fixed-share decomposition

AbstractWe introduce the concept of weighted skeleton of a polygon and present various decomposition and optimality results for this skeletal structure when the underlying polygon is convex

A Novel Approach for Extraction of Polygon Regions

This paper presents a new algorithm to find out whether a polygon exists around a reference point given within the graphical domain. The algorithm is based on creating discrete line segments and then searching them using the orientations formed at segments intersections. The computational complexity of the searching algorithm has been determined as O( n2

A Haptic Modeling System

Haptics has been studied as a means of providing users with natural and immersive haptic sensations in various real, augmented, and virtual environments, but it is still relatively unfamiliar to the general public. One reason is the lack of abundant haptic content in areas familiar to the general public. Even though some modeling tools do exist for creating haptic content, the addition of haptic data to graphic models is still relatively primitive, time consuming, and unintuitive. In order to establish a comprehensive and efficient haptic modeling system, this chapter first defines the haptic modeling processes and its scopes. It then proposes a haptic modeling system that can, based on depth images and image data structure, create and edit haptic content easily and intuitively for virtual object. This system can also efficiently handle non-uniform haptic property per pixel, and can effectively represent diverse haptic properties (stiffness, friction, etc)

Unifying AoI Minimization and Remote Estimation — Optimal Sensor/Controller Coordination with Random Two-way Delay

The ubiquitous usage of communication networks in modern sensing and control applications has kindled new interests on the timing coordination between sensors and controllers, i.e., how to use the waiting time\u27\u27 judicially to improve the system performance. Contrary to the common belief that a zero-wait policy is optimal, Sun et al. showed that a controller can strictly improve the data freshness, the so-called Age-of-Information (AoI), by postponing transmission in order to lengthen the duration of staying in a good state. The optimal waiting policy for the sensor side was later characterized in the context of remote estimation. Instead of focusing on the sensor and controller sides separately, this work develops the jointly optimal sensor/controller waiting policy in a Wiener-process system. This work generalizes the above two important results in the sense that not only do we consider joint sensor/controller designs (as opposed to sensor-only or controller-only schemes), but we also assume random delay in both the forward and feedback directions (as opposed to random delay in only one direction). In addition to provable optimality, extensive simulation is used to verify the performance of the proposed scheme

A concurrent approach to automated manufacturing process planning

textWith the increasing demand of fast-paced and hybrid manufacturing processes in modern industry, it is desirable to expedite the iterations between design and manufacturing through intelligent computational techniques. In this research, we propose a concurrent approach of this kind to streamline the design and manufacturing processes. With this approach, a CAD design is automatically analyzed in terms of its manufacturability in the early design stage. If the part is manufacturable, a set of process plans optimized in time, cost, fixture quality and tolerance satisfaction are reported in real time. If the part is not manufacturable, the potential design changes are provided for better manufacturing. In the approach, the geometric information of 3D models and the empirical knowledge in manufacturing processes, fixtures, and tolerances are combined and encapsulated into a graph-grammar based reasoning. The reasoning systematically extracts meaningful manufacturing details that later constitute complete process plans for any given solid model. The plans are then evaluated and optimized using a specially designed multi-objective best first search technique. The complete approach enables a concurrent and efficient manufacturability analysis tool that closely resembles real manufacturing planning practice. Numerous case studies with real engineering parts are presented to characterize the novelty and contributions of this approach. The optimality of the suggested plans is verified through computational comparisons, and the practicality of the plans is validated with hands-on implementations on the shop floor.Mechanical Engineerin