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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
Algorithms for vertical and orthogonal L1 linear approximation of points
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 352–361https://doi.org/10.1145/73393.73429This paper presents algorithms for approximating a set of n points by a linear function, or a line, that minimizes the L1 norm of vertical and orthogonal distances. The algorithms find exact solutions based upon geometric properties of the problems as ...
- ArticleJanuary 1988
On maximum flows in polyhedral domains
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 341–351https://doi.org/10.1145/73393.73428We introduce a new class of problems concerned with the computation of maximum flows through two-dimensional polyhedral domains. Given a polyhedral space (e.g., a simple polygon with holes), we want to find the maximum “flow” from a source edge to a ...
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- ArticleJanuary 1988
An automatic motion planning system for a convex polygonal mobile robot in 2-dimensional polygonal space
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 329–340https://doi.org/10.1145/73393.73427We present an automatic system for planning the (translational and rotational) collision-free motion of a convex polygonal body B in two-dimensional space bounded by a collection of polygonal obstacles. The system consists of a (combinatorial, non-...
- ArticleJanuary 1988
Coordinated motion planning for two independent robots
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 319–328https://doi.org/10.1145/73393.73426We present an Ο(n2) algorithm for planning a coordinated collision-free motion of two independent robot systems of certain kinds, each having two degrees of freedom, which move in the plane amidst polygonal obstacles having a total of n corners. We ...
- ArticleJanuary 1988
The complexity of planar compliant motion planning under uncertainty
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 309–318https://doi.org/10.1145/73393.73425We consider the computational complexity of planning compliant motions in the plane, given geometric bounds on the uncertainty in sensing and control. We can give efficient algorithms for generating and verifying compliant motion strategies that are ...
- ArticleJanuary 1988
On planning assemblies
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 299–308https://doi.org/10.1145/73393.73424This paper concerns the problem of assembling composite objects. We study the problem on two fronts; Firstly we study the complexity of deciding the existence of an assembly sequence and show that this is PSPACE-hard in general. Secondly we define a new ...
- ArticleJanuary 1988
Motion planning in the presence of movable obstacles
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 279–288https://doi.org/10.1145/73393.73422Motion planning algorithms have generally dealt with motion in a static environment, or more recently, with motion in an environment that changes in a known manner. We consider the problem of finding collision-free motions in a changeable environment. ...
- 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
Clustering algorithms based on minimum and maximum spanning trees
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 252–257https://doi.org/10.1145/73393.73419We consider clustering problems under two different optimization criteria. One is to minimize the maximum intracluster distance (diameter), and the other is to maximize the minimum intercluster distance. In particular, we present an algorithm which ...
- ArticleJanuary 1988
Computing Euclidean maximum spanning trees
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 241–251https://doi.org/10.1145/73393.73418An algorithm is presented for finding a maximum-weight spanning tree of a set of n points in the Euclidean plane, where the weight of an edge (pi, pj) equals the Euclidean distance between the points pi and pj. The algorithm runs in time Ο (n logn) and ...
- 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
Optimal parallel algorithms for polygon and point-set problems
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 201–210https://doi.org/10.1145/73393.73414In this paper we give parallel algorithms for a number of problems defined on polygons and point sets. All of our algorithms have optimal T(n) * P(n) products, where T(n) is the time complexity and P(n) is the number of processors used, and are for the ...
- 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
Hidden surface removal for rectangles
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 183–192https://doi.org/10.1145/73393.73412A simple but important special case of the hidden surface removal problem is one in which the scene consists of n rectangles with sides parallel to the x and y-axes, with viewpoint at z = ∞ (that is, an orthographic projection). This special case has ...
- 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 ...