In these notes, we introduce a powerful technique for solving geometric problems. This technique, called the plane sweep technique, appears in Shamos’ Ph.D. thesis from 1978—which is considered the birthplace of computational geometry—although the concept was known already to geometers. The plane sweep technique gives efficient and reasonably simple algorithms for a large variety of geometric p...

Constructs, maintains, modifies, traverses, queries, and presents arrangements on two-dimensional parametric surfaces. Complete and Robust All inputs are handled correctly (including degenerate input). Exact number types are used to achieve robustness. Generic – easy to interface, extend, and adapt Modular – geometric and topological aspects are separated Supports among the others: various poin...

In this paper, we propose an improved plumb-line algorithm, the Partial-Scan Plumb-Line (PSPL) algorithm, to solve the point-in-region problem. In the PSPL algorithm, every edge of the region (or polygon) is represented as two half segments, and all half segments of the region are sorted according to their dominating points. This is a standard representation for regions in spatial databases, pr...

Liquid chromatography coupled to mass spectrometry (LC-MS) has become a major tool for the study of biological processes. High-throughput LC-MS experiments are frequently conducted in modern laboratories, generating an enormous amount of data per day. A manual inspection is therefore no longer a feasible task. Consequently, there is a need for computational tools that can rapidly provide inform...

One of the most representative and studied Distance-Based Queries in Spatial Databases is the K-Closest-Pairs Query (KCPQ). This query involves two spatial data sets and a distance function to measure the degree of closeness, along with a given number K of elements of the result. The output is a set of pairs of objects (with one object element from each set), with the K lowest distances. In thi...

In our earlier work, we have shown that visual constraint surfaces can be used t o effect visual guarded and visual compliant motions (which are analogous t o guarded and compliant motion using force control). Here we show how the backpro 'ection a proach to fine-motion plannin can be edended to e z p i i t visual constraints. Specij! cally, by deriving a con guration space rePTsentation of vis...

Algebraic speciications allied to rewriting are used more and more often in design and logical prototyping of programs. We show how these techniques can be applied to a basic problem in computational geometry, namely the construction of planar subdivisions. We build up a simple, complete and convergent system of rules to cope with this problem and show how it is transformed to describe concrete...

We introduce a general framework for processing a set of curves defined on a continuous two-dimensional parametric surface, while sweeping the parameter space. A major goal of our work is to maximize code reuse in implementing algorithms that employ the prevalent sweep-line paradigm, and consequently to minimize the effort needed to extend the implementation of the paradigm to various surfaces ...

We present a new line sweep algorithm, HeapSweep, for reporting bichromatic (`purple') intersections between a red and a blue family of line segments. If the union of the segments in each family is connected as a point set, HeapSweep reports all k purple intersections in time O((n + k)(n) log 3 n), where n is the total number of input segments and (n) is the familiar inverse Ackermann function....

We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation...