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- ArticleJanuary 1988
On continuous Homotopic one layer routing
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 392–402https://doi.org/10.1145/73393.73433We give an Ο(n3·log n) time and Ο(n3) space algorithm for the continuous homotopic one layer routing problem. The main contribution is an extension of the sweep paradigm to a universal cover space of the plane.
- ArticleJanuary 1988
Triangles in space or building (and analyzing) castles in the Air
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 381–391https://doi.org/10.1145/73393.73432We show that the combinatorial complexity of all non-convex cells in an arrangement of n (possibly intersecting) triangles in 3-space is Ο(n7/3+δ), for any δ>0, and that this bound is almost tight in the worst case. Our bound significantly improves a ...
- ArticleJanuary 1988
Arrangements of lines in 3-space: a data structure with applications
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 371–380https://doi.org/10.1145/73393.73431Let an arrangement of blue lines in 3-space be fixed, and imagine a movable red line entangled in the arrangement. We show an Ο(n4α(n)) algorithm for building a data structure that permits enumeration of mutually inaccessible classes of such red lines, ...
- ArticleJanuary 1988
Path planning in 0/1/ weighted regions with applications
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 266–278https://doi.org/10.1145/73393.73421We consider the terrain navigation problem in a two-dimensional polygonal subdivision consisting of obstacles, “free” regions (in which one can travel at no cost), and regions in which cost is proportional to distance traveled. This problem is a special ...
- ArticleJanuary 1988
Searching for empty convex polygons
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 224–228https://doi.org/10.1145/73393.73416A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of ...
- ArticleJanuary 1988
Covering orthogonal polygons with star polygons: the perfect graph approach
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 211–223https://doi.org/10.1145/73393.73415We consider the problem of covering simple orthogonal polygons with star polygons. A star polygon contains a point p, such that for every point q in the star polygon, there is an orthogonally convex polygon containing p and q.
In general, orthogonal ...
- ArticleJanuary 1988
An efficient output-sensitive hidden surface removal algorithm and its parallelization
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 193–200https://doi.org/10.1145/73393.73413In this paper we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly like the terrain maps. A distinguishing feature of this algorithm is that its running ...
- ArticleJanuary 1988
Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 172–182https://doi.org/10.1145/73393.73411The problem of determining the Euclidean shortest path between two points in the presence of m simple polygonal obstacles is studied. An O( m2 logn + nlogn ) algorithm is developed, where n is the total number of points in the obstacles. A simple O(E+T) ...
- ArticleJanuary 1988
New methods for computing visibility graphs
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 164–171https://doi.org/10.1145/73393.73410Let S be a set of n non-intersecting line segments in the plane. The visibility graph GS of S is the graph that has the endpoints of the segments in S as nodes and in which two nodes are adjacent whenever they can “see” each other (i.e., the open line ...
- ArticleJanuary 1988
Red-Blue intersection detection algorithms, with applications to motion planning and collision detection
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 70–80https://doi.org/10.1145/73393.73401Let Γ be a collection of n (possibly intersecting) “red” Jordan arcs of some simple shape in the plane and let Γ' be a similar collection of m “blue” arcs. We present several efficient algorithms for detecting an intersection between an arc of Γ and an ...
- ArticleJanuary 1988
Implicitly representing arrangements of lines or segments
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 56–69https://doi.org/10.1145/73393.73400An arrangement of n lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists of Ο(n2) regions, called faces. In this paper we study the problem of calculating and storing arrangements ...
- ArticleJanuary 1988
A fast Las Vegas algorithm for triangulating a simple polygon
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 18–22https://doi.org/10.1145/73393.73396We present an algorithm that triangulates a simple polygon on n vertices in Ο(n log* n) expected time. The algorithm uses random sampling on the input, and its running time does not depend on any assumptions about a probability distribution from which ...
- ArticleJanuary 1988
Applications of random sampling in computational geometry, II
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 1–11https://doi.org/10.1145/73393.73394Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments ...