1,300 research outputs found
Multi-Step Processing of Spatial Joins
Spatial joins are one of the most important operations for combining spatial objects of several relations. In this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by
the following two steps. First of all, sophisticated approximations
are used to identify answers as well as to filter out false hits from
the set of candidates. For this purpose, we investigate various types
of conservative and progressive approximations. In the last step, the
exact geometry of the remaining candidates has to be tested against
the join predicate. The time required for computing spatial join
predicates can essentially be reduced when objects are adequately
organized in main memory. In our approach, objects are first decomposed
into simple components which are exclusively organized
by a main-memory resident spatial data structure. Overall, we
present a complete approach of spatial join processing on complex
spatial objects. The performance of the individual steps of our approach
is evaluated with data sets from real cartographic applications.
The results show that our approach reduces the total execution
time of the spatial join by factors
Set Estimation Under Biconvexity Restrictions
A set in the Euclidean plane is said to be biconvex if, for some angle
, all its sections along straight lines with inclination
angles and are convex sets (i.e, empty sets or
segments). Biconvexity is a natural notion with some useful applications in
optimization theory. It has also be independently used, under the name of
"rectilinear convexity", in computational geometry. We are concerned here with
the problem of asymptotically reconstructing (or estimating) a biconvex set
from a random sample of points drawn on . By analogy with the classical
convex case, one would like to define the "biconvex hull" of the sample points
as a natural estimator for . However, as previously pointed out by several
authors, the notion of "hull" for a given set (understood as the "minimal"
set including and having the required property) has no obvious, useful
translation to the biconvex case. This is in sharp contrast with the well-known
elementary definition of convex hull. Thus, we have selected the most commonly
accepted notion of "biconvex hull" (often called "rectilinear convex hull"): we
first provide additional motivations for this definition, proving some useful
relations with other convexity-related notions. Then, we prove some results
concerning the consistent approximation of a biconvex set and and the
corresponding biconvex hull. An analogous result is also provided for the
boundaries. A method to approximate, from a sample of points on , the
biconvexity angle is also given
On the Oß-hull of a planar point set
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We study the Oß-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle ß. Given a set P of n points in the plane, we show how to maintain the Oß-hull of P while ß runs from 0 to p in T(n log n) time and O(n) space. With the same complexity, we also find the values of ß that maximize the area and the perimeter of the Oß-hull and, furthermore, we find the value of ß achieving the best fitting of the point set P with a two-joint chain of alternate interior angle ß.Peer ReviewedPostprint (author's final draft
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