: This paper presents the authentication method using the Delaunay triangulation incremental algorithm and the Catalan objects. The proposed method is a combination of computational geometry and cryptography. This method presents a new step towards encoding the triangle coordinates using the Catalan-key. We provided specific suggestions for the application of this method in the authentication for bank clients by the image encryption. Client authentication verification is performed by asking the client to enter the (x,y) coordinate values of randomly selected indices of an array. If the entered coordinates match the index values in the banking system array, then the transaction or other operation is approved. If the matching fails, it means that we have an unidentified person who has followed the whole process and wants to break into the banking system. There are many advantages arising from a scenario for the user authentication by the assigned Catalan object and the stack permutation method. Also, we provided concrete examples for the Delaunay encryption of image with an authentication scenario and experimental results for the proposed method.

To evaluate and promote ecologically responsible practices in the sintering business, conducting a sustainability evaluation of sintering flue gas is essential. An important step in making iron and steel, sintering releases flue gas emissions that, if not controlled, may harm the environment. Reducing emissions, improving energy efficiency, managing waste, using water, utilizing resources, monitoring community effects, complying with regulations, conducting a life cycle assessment, and continuously improving are all part of the assessment's extensive scope. When these aspects are considered, stakeholders may better understand the economic, social, and environmental effects of sintering flue gas management. This paper used the multi-criteria decision-making (MCDM) methodology to evaluate the criteria. We used the DEMATEL method as an MCDM method. The DEMATEL is used to build the relation between the criteria. We collect ten criteria in this study. We compute the criteria weights to show this study’s best and worst criterion. The DEMATEL method is used to draw the effect diagram between criteria.

This chapter presents the possibilities of applying cryptography and steganography in design advanced methods of medical software. The proposed solution has two modules: medical data encryption and medical data hiding. In the first module for the encryption of patient data a Catalan crypto-key is used combined with the LatticePath combinatorial problem. In the second module for hiding patient data, the Catalan stego-key and medical image is used. The objective of the second part is to explain and investigate the existing author's method to steganography based on the Catalan numbers in the design of medical software. The proposed solution is implemented in the Java programming language. In the experimental part, cryptanalysis and steganalysis of the proposed solution were given. Cryptanalysis is based on time and storage complexity, leaking information and machine learning-based identification of the encryption method. Also, steganalysis is based on the amount of information per pixel in stego image, approximate entropy and bit distribution in stego-images.

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.

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.

In this paper we implement Block method for convex polygon triangulation in web environment (PHP/MySQL). Our main aim is to show the advantages of usage of web technologies in performing complex algorithm from computer graphics. The basic assumption is that one obtained results we store in database and use it for other calculation. Databases are convenient and structured methods of sharing and retrieving data. We have performed a comparative analysis of developed program with respect to two criteria: CPU time in generating triangulation and CPU time in reading results from database.

This paper presents a new technique of generation of convex polygon triangulation based on planted trivalent binary tree and ballot notation. The properties of the Catalan numbers were examined and their decomposition and application in developing the hierarchy and triangulation trees were analyzed. The method of storage and processing of triangulation was constructed on the basis of movements through the polygon. This method was derived from vertices and leaves of the planted trivalent binary tree. The research subject of the paper is analysis and comparison of a constructed method for solving of convex polygon triangulation problem with other methods and generating graphical representation. The application code of the algorithms was done in the Java programming language.

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.

The aim of the article is to present the methodology, components, the benefits of introducing an electronic payment system in the specific case study. Through the case study, we attempt to prove the hypothesis, to show the system of electronic payments, required computer equipment, ICT infrastructure, information system and the benefits that such a system of electronic payments has made. The advantages are shown in economic, technical, social aspects regarding all the participants in the exploitation of this system.

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.