Polygon

In this paper the method of processing the concave polygon class is presented. This method is implemented as a part of the system of shape understanding (SUS) and tested on the broad classes of shapes. The system of shape understanding is able to perform different tasks of shape analysis and recognition based on the ability of the system to understand the different concepts of shape on the different levels of cognition, The system consist of different types of experts that perform different processing and reasoning tasks. The concave polygon class model and processing methods are also described.

The problem of constructing a tight isothetic outer (or inner) polygon covering an arbitrarily shaped 2D object on a background grid, is addressed in this paper, and a novel algorithm is proposed. Such covers have many applications to image mining, rough sets, computational geometry, and robotics. Designing efficient algorithms for these cover problems was an open problem in the literature.

El presente artículo tiene como propósito compartir una serie de fórmulas matemáticas, para el cálculo del área de ciertos casos especiales de polígonos irregulares a partir de sus lados. Los autores se basan en el método de triangulación y descomposición en cuadriláteros, y su investigación les permite encontrar fórmulas de fácil uso, para calcular el área de polígonos irregulares de cinco y seis lados. Así, el principio utilizado; posibilita hallar el área de otros polígonos irregulares especiales con otra cantidad de lados.

Polygons can conveniently represent real world objects. In automatic character recognition, shapes of individual letters are represented by polygons. In robotics, obstacles are represented using polygons. In computer graphics programming, solid objects are represented using polygons on the two dimensional screen. The polygons can be easily manipulated using known mathematical operations. That is the reason for representing real world objects using polygons. However, polygons can be in complicated shapes. Therefore, it is better if there is a way to partition a polygon into smaller pieces. Triangulation is a particular way of doing this from which polygons are partitioned into triangles. The basic triangulation algorithm is widely used in applications where 100% accuracy is necessary. Algorithms with better asymptotic order than the basic triangulation algorithm exist. However they are not 100% accurate and use advanced data structures causing higher memory consumption. This paper proposes a simple, efficient and 100% accurate algorithm which uses lowest amount of memory. The proposed algorithm is more suitable for embedded systems which do not possess large amount of memory. The proposed algorithm was experimentally compared with the basic triangulation algorithm. The experimental results prove that the proposed algorithm is faster than the basic triangulation algorithm.

Real-time surface rendering of large-scale molecular models such as a colon bacillus requires a great number of polygons to be displayed on a display device. Since a long latency of display and manipulation is fatal in maintaining presence in a virtual environment, high performance computing power and high quality graphical components are required to exercise real-time rendering of such a

Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define two classes of polyominoes which interpolate between column-convex polygons and 2-column polyominoes. We derive the area generating functions of those two classes, using extensions of existing algorithms. The growth constants of both classes are greater than the growth constant of column-convex polyominoes. Rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis.

The eccentricity transform associates to each point of a shape the distance to the point farthest away from it. The transform is defined in any dimension, for open and closed manyfolds, is robust to Salt & Pepper noise, and is quasi-invariant to articulated motion. This paper presents and algorithm to efficiently compute the eccentricity transform of a polygonal shape with or without holes. In particular, based on existing and new properties, we provide an algorithm to decompose a polygon using parallel steps, and use the result to derive the eccentricity value of any point.

S. Bressan, J. Küng, and R. Wagner (Eds.): DEXA 2006, LNCS 4080, pp. 728–737, 2006. © Springer-Verlag Berlin Heidelberg 2006 ... Relaxing Constraints on GeoPQL Operators to Improve ... Arianna D'Ulizia1, Fernando Ferri1, Patrizia Grifoni1, and Maurizio Rafanelli2