B. Chazelle and M. Sharir. An algorithm for generalized point location and its application. J. Symbolic Comput., 10:281-309, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....inequalities de ning the arcs (again these are equations describing a cylinder, a sphere, or a plane) In order to verify the intersection property we need a method to detect intersections between the triangles in P and the surface patches of bd . We will apply a standard approach suggested in [9] and [8] and transform this problem to a semialgebraic point location problem. Lemma 4.6. Let be a set of k semialgebraic sets of constant description complexity in R . For any 0 we can build a data structure of size O(k ) randomized expected time, such that for any query triangle ....

B. Chazelle and M. Sharir. An algorithm for generalized point location and its application. J. Symbolic Comput., 10:281-309, 1990.

....data structure, or prove that the problem is hard in some respect. Computational geometry problems can be motivated by either fundamental issues, such as vhether or not there is a linear time algorithm to triangulate a poly gon [15] or by practical issues, such as point location data structures [8, 16, 32, 55], pattern layout algorithms [62] and industrial part casting algorithms [13, 77] The vork in this dissertation is motivated by a hydrology problem from geographic information systems. A geographic information system (GIS) is a system for apturing, storing, checking, integrating, manipulating, ....

B. Chazelle and M. Sharir. An algorithm for generalized point location and its application. J. Symbolic Cornput., 10:281-309, 1990.

....for each simplex s, s Pi has a constant number of components. In constant time we compute the components of Pi s using the general approach for computing topological properties of real algebraic manifolds of Schwartz and Sharir [SS83] Additional computational details are given in [CS88] and [Cha85] Furthermore, we can perform point location in the resulting data structure [SS83] Since the Zone Z Pi (R) has complexity O(r 4 log r) we have at most O(r 4 log r) components of Pi Z Pi (R) to deal with. Assuming that the triangles in T are pairwise disjoint, each ....

B. Chazelle and M. Sharir. An algorithm for generalized point location and its applications. Technical Report 153, Courant Institute of Mathematical Sciences, Robotics Lab., May 1988.

....been known. For the special case of the shortest vertical distance between two sets of edges of non intersecting polyhedral terrains Chazelle et al. CEGS89a] give an O(n 4=3 ffl ) randomized expected time algorithm. 3 The problem of the minimum vertical separation for segments was solved in [CS90] in time O(n 1:99987 ) The method in [CS90] maps a segment into a point in 6 dimensional space. Using the representation in [CS90] and the more recent decomposition technique of [CEGS89b] it is possible to obtain a time bound of roughly O(n 2 Gamma1=9 ) O(n 1:8889 ) Independently, ....

....vertical distance between two sets of edges of non intersecting polyhedral terrains Chazelle et al. CEGS89a] give an O(n 4=3 ffl ) randomized expected time algorithm. 3 The problem of the minimum vertical separation for segments was solved in [CS90] in time O(n 1:99987 ) The method in [CS90] maps a segment into a point in 6 dimensional space. Using the representation in [CS90] and the more recent decomposition technique of [CEGS89b] it is possible to obtain a time bound of roughly O(n 2 Gamma1=9 ) O(n 1:8889 ) Independently, Guibas, Sharir and others [Gui91] have considered ....

[Article contains additional citation context not shown here]

B. Chazelle and M. Sharir. An algorithm for generalized point location and its applications. J. of Symbolic Computation, (10):281--309, 1990.

No context found.

B. Chazelle and M. Sharir, An algorithm for generalized point location and its application, J. Symbolic Computation 10 (1990), 281-309.

....for additional discussion of the results and comparison with previous work) Computing the biggest line segment that can be placed inside a simple n gon. We present a randomized algorithm with expected running time O(n 8 5 # ) for any # 0, considerably improving the previous algorithm of [15] whose running time is O(n 1.999878 ) 1 . Computing the smallest width annulus that contains a given set of n points in the plane. We give a randomized algorithm with expected running time O(n 8 5 # ) for any # 0, considerably improving the quadratic time algorithm of [19] Finding ....

....polygon P with n edges, find the biggest stick (i.e. largest line segment) that can be placed inside P (i.e. be disjoint from the exterior of P ) It is easy to design an algorithm for solving this problem in time O(n 2 ) and the goal is to obtain subquadratic solutions. Chazelle and Sharir [15] have given such a subquadratic solution. It runs in time O(n 1.999878 ) and is based on Collins cylindrical algebraic decomposition technique. In this section we give a considerably improved solution, whose running time is O(n 8 5 # ) for any # 0. We note that if the endpoints of the ....

B. Chazelle and M. Sharir, An algorithm for generalized point location and its applications, J. Symbolic Computation 10 (1990), pp. 281--309.

....2 Lemma 3.1 implies that the collection F satisfies the assumptions (F1) F2) of Theorem 2.1. Let CF denote the cell in the arrangement of F that lies above the upper envelope of F . In view of Lemma 3.1, Theorem 2. 1, the above discussion, and standard point location techniques, such as those in [8, 9], we obtain Corollary 3.2 The vertical decomposition C F of CF consists of O(n 3 ) cells, for any 0. Moreover, CF can be preprocessed in time O(n 3 ) into a data structure of size O(n 3 ) for any 0, so that, for any query point p, we can determine in O(log n) time whether ....

B. Chazelle and M. Sharir, An algorithm for generalized point location and its applications, J. Symbolic Computation 10 (1990), 281--309.

....2 Lemma 3.1 implies that the collection F satisfies the assumptions (F1) F2) of Theorem 2.1. Let CF denote the cell in the arrangement of F that lies above the upper envelope of F . In view of Lemma 3.1, Theorem 2. 1, the above discussion, and standard point location techniques (such as those in [8, 9]) we obtain Geometric Optimization October 5, 1995 Width in 3 Space 8 Corollary 3.2 The vertical decomposition C F of CF consists of O(n 3 ) cells, for any 0. Moreover, CF can be preprocessed in time O(n 3 ) into a data structure of size O(n 3 ) for any 0, so that, for ....

B. Chazelle and M. Sharir, An algorithm for generalized point location and its applications, J. Symbolic Computation 10 (1990), 281--309.

....in R 3 can be computed in randomized expected time O(n 17=11 ) for any 0. 5.2 Biggest stick in a simple polygon Let P be a simple polygon in the plane having n edges. We wish to find the longest line segment e that is contained in (the closed set) P . Chazelle and Sharir presented in [13] an Computing lower envelopes April 13, References 19 O(n 1:99 ) time algorithm for this problem, which was later improved by Agarwal et al. 5] to O(n 8=5 ) for any 0. The latter paper reduces this problem, just as in the computation of the width of a point set in 3 space, to that ....

B. Chazelle and M. Sharir, An algorithm for generalized point location and its applications, J. Symbolic Computation 10 (1990), 281--309.

....for additional discussion of the results and comparison with previous work) Biggest stick: Computing the longest line segment that can be placed inside a simple n gon. We present an algorithm with running time O(n 8=5 ffl ) for any ffl 0, 1 considerably improving the previous algorithm of [18] whose running time is O(n 1:9999 ) Minimum width annulus: Computing the smallest width annulus that contains a given set of n points in the plane. We give an algorithm with running time O(n 8=5 ffl ) significantly improving the quadratic time algorithm of [23] Minimum Hausdorff distance ....

....polygon P with n edges, find the biggest stick (i.e. longest line segment) that can be placed inside P (i.e. be disjoint from the exterior of P ) It is easy to design an algorithm for solving this problem in time O(n 2 ) and the goal is to obtain subquadratic solutions. Chazelle and Sharir [18] have given such a subquadratic solution, which runs in time O(n 1:9999 ) and is based on Collins cylindrical algebraic decomposition technique [22] The running time of their algorithm can be improved to O(n 1:9 ) using the results of Chazelle et al. 14] on point location among algebraic ....

B. Chazelle and M. Sharir, An algorithm for generalized point location and its applications, J. Symbolic Computation 10 (1990), pp. 281--309. Applications of Parametric Searching October 21, References 24

No context found.

B. Chazelle and M. Sharir. An algorithm for generalized point location and its application. J. Symbolic Comput., 10:281-309, 1990.

No context found.

B. Chazelle and M. Sharir. An algorithm for generalized point location and its application. J. Symbolic Comput., 10:281--309, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC