Education-driven research in CAD

We argue for a new research category, named education-driven research (EDR), which fills the gap between traditional field-specific research that is not concerned with educational objectives and research in education that focuses on fundamental teaching and learning principles and possibly on their customization to broad areas (such as mathematics or physics), but not to specific disciplines (such as CAD). The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions in a specialized domain, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and can rarely be carried out by generalists with primary expertise in broad education principles. We illustrate the concept of EDR with three examples in CAD: (1) the Split and Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, in these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic B-spline curve; (2) develop a new subdivision curve that is better approximated by its control polygon than either a cubic B-spline or an interpolating 4-point subdivision curve; (3) discover how a circuit inclusion tree may be used for identifying the faces in an arrangement; and (4) rectify a common misconception about the computation of the Hausdorff error between triangle meshes. We invite the scientific community to encourage the development of EDR by publishing its results as genuine research contributions in peer-reviewed professional journals.     

A fast algorithm for an envelope construction of a huge set of topologically consistent polygons

This paper describes an efficient algorithm for the determination of an envelope of a set of polygons. The polygons have to be aligned along their borders – the case which, for example, appears in geographic information systems. The edges, which belong to two neighbouring polygons, are called twin edges, and are eliminated first. To accelerate the geometric search, a two-level uniform plane subdivision structure is proposed. The remaining non-twin edges belong to the envelope, and they have to be joined to form the simple polygons at the end. For this task, a new algorithm has been developed. At the end, spatial relationships between resulting polygons are established. The whole algorithm for envelope determination works in expected time O(n log n) using O(n) memory space, where n is the total number of edges belonging to the input polygons. In the last part of the paper, practical results using data from a geographical database are considered.     

基于单调链的简单多边形距离算法

简单多边形的距离问题是计算机图形学中的一个研究难点,为了能快速地获得距离信息,提出一种基于单调链的简单多边形距离算法.算法先对多边形边界进行关于坐标轴的单调链分割,然后根据可见性原则确定候选链对,再结合层次树理论和分支限界策略计算链对距离以求解多边形的最近距离.试验结果表明,该算法性能优于其他同类算法.     

Waste minimization in irregular stock cutting

This paper addresses a category of two dimensional NP-hard knapsack problem in which a given convex/non-convex planner items (polygons) have to be cut out of a single convex/non-convex master surface (stock). This cutting process is found in many industrial applications such as sheet metal processes, home-textile, garment, wood, leather and paper industries. An approach is proposed to solve this problem, which depends on the concept of the difference between the area of a collection of polygons and the area of their convex hull. The polygon assignment inside the stock is subjected to feasibility tests to avoid overlapping, namely, angle test, bound test, point inclusion and polygon intersection test. An iterative scheme is used to generate different polygon placements while optimizing the objective function. Computer software is developed to solve and optimize the problem under consideration. Few examples are conducted for different combinations of convex, non-convex items and stocks. Well-known benchmark problems from the literature are tested and compared with our approach. The results of our algorithm have an interesting computational time and can compete with the results of previous work in some particular problems. The computational performance of the developed software indicates the efficiency of the algorithm for solving 2-D irregular cutting of non-convex polygons out of non-convex stock.     

Parallel methods for visibility and shortest-path problems in simple polygons

In this paper we give efficient parallel algorithms for solving a number of visibility and shortest-path problems for simple polygons. Our algorithms all run inO(logn) time and are based on the use of a new data structure for implicitly representing all shortest paths in a simple polygonP, which we call thestratified decomposition tree. We use this approach to derive efficient parallel methods for computing the visibility ofP from an edge, constructing the visibility graph of the vertices ofP (using an output-sensitive number of processors), constructing the shortest-path tree from a vertex ofP, and determining all-farthest neighbors for the vertices inP. The computational model we use is the CREW PRAM.This research was announced in preliminary form in theProceedings of the 6th ACM Symposium on Computational Geometry, 1990, pp. 73–82. The research of Michael T. Goodrich was supported by the National Science Foundation under Grants CCR-8810568 and CCR-9003299, and by the NSF and DARPA under Grant CCR-8908092.     

Drug treatment completion and post-discharge employment in the TOPPS-II Interstate Cooperative Study

The objective of this study was to use administrative data to examine the effect of drug treatment completion on patients' subsequent employment and wages earned in the year following discharge, and to compare the consistency of these results across three states. Drug treatment and wage data from 20,495 drug treatment patients were used in this study. Treatment data were provided by the state substance abuse management information systems for Baltimore City, Washington State, and Oklahoma. Wage data were provided by the agency in each state responsible for collecting and reporting wage information. A quasi-experimental design was used to compare treatment completers and non-completers in the year after an index treatment episode. In addition, employment history in the year prior to the index episode was used to statistically adjust for group differences. The index episode of care may have included services under more than one treatment modality. The full social security number was used to link the drug treatment and wage administrative datasets. Treatment completers were 22% to 49% more likely than non-completers to be employed and to earn higher wages in the year following treatment, holding other variables constant. Patients staying in treatment longer than 90 days were 22% to 43% more likely to be employed in the year following treatment than those who stayed a shorter time. These findings were consistent across the three project states with different client populations, treatment delivery systems, and labor markets.     

多边形的隐函数表示法

文章提出了一种方法,用一个隐函数表示一个多边形。先把被表示的多边形分解成树形结构,然后使用R函数对满足多边形边的连续函数F(x,y)=0进行交、并等布尔操作,以获得表示整个多边形的隐函数。     

最佳逼近圆周的正多边形算法(Ⅲ)

利用渐近平均距离定义了圆周的最佳逼近正多边形 ,在上述意义下 ,解决了圆周的最佳逼近正多边形半径R的计算问题