Convex Polygons relations applied in point distributions importance detection
ISBN 978-85-88783-11-9
Authors
1Firkowski, H.; 2Chiarani, E.; 3Farias, P.P.S.
1FEDERAL UNIVERSITY OF PARANÁ Email: firkowski@gmail.com
2FEDERAL UNIVERSITY OF PARANÁ Email: eduardoooc@gmail.com
3FEDERAL UNIVERSITY OF PARANÁ Email: pedrobfarias@gmail.com
Abstract
Point distributions are common in cartographic databases for representing any phenomenon or occurrence that can be perceived or sensed in the real world and have no (enough) size to be represented as area, although being important. This way its representation is achieved by means of two or three values (coordinates) including one or more attributes. Spatial point distributions can lead to questions about the relative importance of these points over a part of the real world. There are many ways for achieving a sense of importance for spatial data distribution. In the case of visual analyses, an inspection may determine the number of occurrences of a cartographic point symbol and how many occurrences there are and what is its relation to a defined initial condition, such as proximity or pertinence. That is, user performs its analyses using its own human sense resources, knowledge and history. Although possible in many cases, this approach may result in difficulties due to the amount of data one can find in different maps and due to other aspects related to the map itself. Relations among these representative data can be found by performing analysis of their spatial distribution. More than this, to reveal spatial relations between different occurrences it is necessary to manipulate or operate these representative data. Considering that it is natural to find different phenomenon representation coexisting in the same data set, is it also possible try to find relations among them by selecting pairs or other arrangements of phenomenon. In these experiments we implement tolls for performing these relations and then conclude in terms of importance order or rank of importance for these data sets according to a specific criteria. For producing these experiments a convex polygon algorithm has been computationally implemented in an application devoted to point in image digitalization as well as an algorithm for point in polygon detection was also implemented. Along with interactive tools, these two algorithms form the approach used to face point distributions exploitation. Are performed interactive operations to define a spatial region, for identifying points that appear inside that region, for defining subsets of points for different phenomenon occurrence in hat region, and then performing tasks for convex polygon construction and convex polygon mutual relations detection. These experiments were conducted in an own application developed in C++ Object Oriented Language using Borland Builder 6.0. This application allows for digitalizing point data, adding meaning to the digitalized points, and also manipulating and managing these data. As results for these experiments the relations are presented both graphically and textually in an interactive fashion. Textually one can see if the pairs of convex polygons overlap and what is the amount of this overlap, and graphically one can see relations that has been found.
Keywords
Point distribution; Convex polygon; Point in polygon