Computational Geometry Applications

Computational geometry is an integral part of mathematics and computer science deals with the algorithmic solution of geometry problems. From the beginning to today, computer geometry links different areas of science and techniques, such as the theory of algorithms, combinatorial and Euclidean geometry, but including data structures and optimization. Today, computational geometry has a great deal of application in computer graphics, geometric modeling, computer vision, and geodesic path, motion planning and parallel computing. The complex calculations and theories in the field of geometry are long time studied and developed, but from the aspect of application in modern information technologies they still are in the beginning. In this research is given the applications of computational geometry in polygon triangulation, manufacturing of objects with molds, point location, and robot motion planning

Implementation example of the expert system for decision support on Android platform based on a specific dataset

This paper presents the method of creating Expert system for decision support on the Android platform. The system knowledge base for the given area of expertise is generated by inductive learning methods based on examples from the WEKA data research system. The system was realized using the Expert System shell for the e2gDroid lite mobile device, based on the application area and a set of training examples, specifically based on the Covertype Data Set qualification problem

Generation of Cryptographic Keys with Algorithm of Polygon Triangulation and Catalan Numbers

In this paper is presented a procedure for the application of one computational geometry algorithm in the process of generating hidden cryptographic keys from one segment of the 3D image. The presented procedure consists of three phases. In the first phase, is done the separation of one segment from the 3D image and determination of triangulation of the separated polygon. In the second phase, is done a conversion from the obtained triangulation of the polygon in the record which represent the Catalan key. In the third phase, the Catalan-key is applied in encryption of text based on the balanced parentheses combinatorial problem

Memoization method for storing of minimum-weight triangulation of a convex polygon

This study presents a practical view of dynamic programming, specifically in the context of the application of finding the optimal solutions for the polygon triangulation problem. The problem of the optimal triangulation of polygon is considered to be as a recursive substructure. The basic idea of the constructed method lies in finding to an adequate way for a rapid generation of optimal triangulations and storing - them in as small as possible memory space. The upgraded method is based on a memoization technique, and its emphasis is in storing the results of the calculated values and returning the cached result when the same values again occur. The significance of the method is in the generation of the optimal triangulation for a large number of n. All the calculated weights in the triangulation process are stored and performed in the same table. Results processing and implementation of the method was carried out in the Java environment and the experimental results were compared with the square matrix and Hurtado-Noy method

Algoritam računarske geometrije i njihova primena u linijskoj optimizaciji i dinamičkom programiranju

Računarska geometrija kao disciplina ima značajno mjesto i veliki značaj u tehnološkom razvoju inženjerstva i primjenjuje se u različitim područjima. Kao grana informatike posvećena je proučavanju algoritama koji se mogu izraziti u smislu geometrije. Neke od ovih studija su čisto geometrijski problemi, dok se drugi dobijaju kao posljedica ispitivanja računarskih geometrijskih algoritama. Algoritmi računarske geometrije danas se primjenjuju u numeričkom računanju, geometrijskom modeliranju, računarskom vidu, kompjuterskoj grafici, geodeziji, dinamičkom računanju, u izotetičkoj računarskoj geometriji i u paralelnom računanju. U ovom istraživanju dat je postupak za generisanje kriptografskih ključeva sa algoritmom jednostavne poligonske triangulacije i Katalonskih brojeva, konstruisan je algoritam za triangulaciju poligona zasnovan na zasađenom trivalentnom stablu, postavljen je algoritam za triangulaciju minimalne težine koji se temelji na proizvodu matričnog lanca i memoizaciji i analizirana je primjena računarske geometrije u linearnoj optimizaciji. Ovo istraživanje detaljno opisuje interakciju između Katalonskih brojeva, triangulacije konveksnog poligona i jednim delom kriptografije. Implementacije su izvršene u Java okruženju i dizajnirane su tako da budu efikasne i jednostavne za upotrebu

Algoritam računarske geometrije i njihova primena u linijskoj optimizaciji i dinamičkom programiranju

Računarska geometrija kao disciplina ima značajno mjesto i veliki značaj u tehnološkom razvoju inženjerstva i primjenjuje se u različitim područjima. Kao grana informatike posvećena je proučavanju algoritama koji se mogu izraziti u smislu geometrije. Neke od ovih studija su čisto geometrijski problemi, dok se drugi dobijaju kao posljedica ispitivanja računarskih geometrijskih algoritama. Algoritmi računarske geometrije danas se primjenjuju u numeričkom računanju, geometrijskom modeliranju, računarskom vidu, kompjuterskoj grafici, geodeziji, dinamičkom računanju, u izotetičkoj računarskoj geometriji i u paralelnom računanju. U ovom istraživanju dat je postupak za generisanje kriptografskih ključeva sa algoritmom jednostavne poligonske triangulacije i Katalonskih brojeva, konstruisan je algoritam za triangulaciju poligona zasnovan na zasađenom trivalentnom stablu, postavljen je algoritam za triangulaciju minimalne težine koji se temelji na proizvodu matričnog lanca i memoizaciji i analizirana je primjena računarske geometrije u linearnoj optimizaciji. Ovo istraživanje detaljno opisuje interakciju između Katalonskih brojeva, triangulacije konveksnog poligona i jednim delom kriptografije. Implementacije su izvršene u Java okruženju i dizajnirane su tako da budu efikasne i jednostavne za upotrebu