Library

feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. In this paper, we give an algorithm for output-sensitive construction of an f-face convex hull of a set of n points in general position in E 4 . Our algorithm runs in $O((n+f)\log^2 f)$ time and uses O(n+f) space. This is the first algorithm within a polylogarithmic factor of optimal $O(n \log f + f)$ time over the whole range of f. By a standard lifting map, we obtain output-sensitive algorithms for the Voronoi diagram or Delaunay triangulation in E 3 and for the portion of a Voronoi diagram that is clipped to a convex polytope. Our approach simplifies the ``ultimate convex hull algorithm'' of Kirkpatrick and Seidel in E 2 and also leads to improved output-sensitive results on constructing convex hulls in E d for any even constant d 〉 4.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 21 (1999), S. 405-420 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We give a linear-time algorithm for computing the medial axis of a simple polygon P . This answers a long-standing open question—previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms, then xy monotone histograms. We can compute the medial axes for xy monotone histograms and merge to obtain the medial axis for P .
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 22 (1999), S. 619-631 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We prove that a unique simple polygon is determined, up to similarity, by the interior angles at its vertices and the cross-ratios of diagonals of any given triangulation. (The cross-ratio of a diagonal is the product of the ratio of edge lengths for the two adjacent triangles.) This establishes a conjecture of Driscoll and Vavasis, and shows the correctness of a key step of their algorithm for computing Schwarz—Christoffel transformations mapping a disk to a polygon.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 24 (2000), S. 605-622 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We prove a generalization of the famous Ham Sandwich Theorem for the plane. Given gn red points and gm blue points in the plane in general position, there exists an equitable subdivision of the plane into g disjoint convex polygons, each of which contains n red points and m blue points. For g=2 this problem is equivalent to the Ham Sandwich Theorem in the plane. We also present an efficient algorithm for constructing an equitable subdivision.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 20 (1998), S. 389-402 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Given a set of points S={p 1 ,. . ., p n } in Euclidean d -dimensional space, we address the problem of computing the d -dimensional annulus of smallest width containing the set. We give a complete characterization of the centers of annuli which are locally minimal in arbitrary dimension and we show that, for d=2 , a locally minimal annulus has two points on the inner circle and two points on the outer circle that interlace anglewise as seen from the center of the annulus. Using this characterization, we show that, given a circular order of the points, there is at most one locally minimal annulus consistent with that order and it can be computed in time O(n log n) using a simple algorithm. Furthermore, when points are in convex position, the problem can be solved in optimal Θ(n) time.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 12 (1994), S. 18-29 
    ISSN: 1432-0541
    Keywords: Computational geometry ; Closest pair ; Point location ; Centroid ; Amortization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give an algorithm that computes the closest pair in a set ofn points ink-dimensional space on-line, inO(n logn) time. The algorithm only uses algebraic functions and, therefore, is optimal. The algorithm maintains a hierarchical subdivision ofk-space into hyperrectangles, which is stored in a binary tree. Centroids are used to maintain a balanced decomposition of this tree.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 12 (1994), S. 30-53 
    ISSN: 1432-0541
    Keywords: Computational geometry ; Ray shooting ; Multilevel data structures ; Hidden surface removal ; Output-sensitive
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we study the ray-shooting problem for three special classes of polyhedral objects in space: axis-parallel polyhedra, curtains (unbounded polygons with three edges, two of which are parallel to thez-axis and extend downward to minus infinity), and fat horizontal triangles (triangles parallel to thexy-plane whose angles are greater than some given constant). For all three problems structures are presented usingO(n 2+ɛ) preprocessing, for any fixedɛ 〉 0, withO(logn) query time. We also study the general ray-shooting problem in an arbitrary set of triangles. Here we present a structure that usesOn 4+ɛ) preprocessing and has a query time ofO(logn). We use the ray-shooting structure for curtains to obtain an algorithm for computing the view of a set of nonintersecting prolyhedra. For any ɛ 〉 0, we can obtain an algorithm with running time $$O(n^{1 + \varepsilon } \sqrt k )$$ , wheren is the total number of vertices of the polyhedra andk is the size of the output. This is the first output-sensitive algorithm for this problem that does not need a depth order on the faces of the polyhedra.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 8
    ISSN: 1432-0541
    Keywords: Computational geometry ; Ray-shooting ; Triangulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetP be a simple polygon withn vertices. We present a simple decomposition scheme that partitions the interior ofP intoO(n) so-called geodesic triangles, so that any line segment interior toP crosses at most 2 logn of these triangles. This decomposition can be used to preprocessP in a very simple manner, so that any ray-shooting query can be answered in timeO(logn). The data structure requiresO(n) storage andO(n logn) preprocessing time. By using more sophisticated techniques, we can reduce the preprocessing time toO(n). We also extend our general technique to the case of ray shooting amidstk polygonal obstacles with a total ofn edges, so that a query can be answered inO(√ logn) time.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...