Moving a polygon around the corner in a corridor
SCG '86 Proceedings of the second annual symposium on Computational geometry
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Fast searching in a real algebraic manifold with applications to geometric complexity
Proc. of the international joint conference on theory and practice of software development (TAPSOFT) Berlin, March 25-29, 1985 on Mathematical foundations of software development, Vol. 1: Colloquium on trees in algebra and programming (CAAP'85)
Compliant motion planning with geometric models
SCG '87 Proceedings of the third annual symposium on Computational geometry
Separating two simple polygons by a sequence of translations
Discrete & Computational Geometry
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Implicitly representing arrangements of lines or segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On the general motion planning problem with two degrees of freedom
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
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Let &Ggr; be a collection of n (possibly intersecting) “red” Jordan arcs of some simple shape in the plane and let &Ggr;' be a similar collection of m “blue” arcs. We present several efficient algorithms for detecting an intersection between an arc of &Ggr; and an arc of &Ggr;'. (i) If the arcs of &Ggr;' form the boundary of a simply connected region, then we can detect a “red-blue” intersection in time &Ogr; (&lgr;s(m)log2 m + (&lgr;a(m) + n)log(n + m)) where &lgr;s(m) is the (almost-linear) maximum length of (m, s) Davenport-Schinzel sequences, and where s is a fixed parameter, depending on the shape of the given arcs. Another case where we can detect an intersection in close to linear time is when the union of the arcs of &Ggr; and the union of the arcs of &Ggr;' are both connected. (ii) In the most general case, we can detect an intersection in time &Ogr; ((m√&lgr;s(n) + n√&lgr;s(m))log1.5(m+n)). For several special but useful cases, in which many faces in the arrangements of &Ggr; and &Ggr;' can be computed efficiently, we obtain randomized algorithms which are better than the general algorithm. In particular when all arcs in &Ggr; and &Ggr;' are line segments, we obtain a randomized &Ogr;((m+n)4/3+c) intersection detection algorithm. We apply the algorithm in (i) to obtain an &Ogr;(&lgr;s(n) log2 n) algorithm (for some small s 0) for planning the motion of an n-sided simple polygon around a right-angle corner in a corridor, improving a previous &Ogr;(n2) algorithm of [MY86], and to derive an efficient technique for fast collision detection for a simple polygon moving (translating and rotating) in the plane along a prescribed path.