This paper describes a new method for constructing a visibility graph in 3D space. We use a method for predicting porosity of hardened specimens. We also use an intelligent system method to predict porosity of hardened specimens. Visibility graphs have many applications, one of which is the analysis of trend lines of market graphs. It is possible to use 2D visibility graphs for such analysis and the construction for 2D visibility graphs is well known; however, in this paper, we will present a new method for the construction of 3D visibility graphs. 3D visibility computations are central to any computer graphics application. Drawing graphs as nodes connected by links in 3D space is visually compelling but computationally difficult. Thus, the construction of 3D visibility graphs is highly complex and requires professional computers or supercomputers. This article describes a new method for analysing 3D visibility graphs. We develop new method for draws 3D visibility graphs for analysing microstructure pictures of robot laser-hardened specimens. The microstructure of robot laser-hardened specimens is very complex; however, we can present it using 3D visibility graphs. New method for the construction of 3D visibility graphs is very useful in many cases, including: illumination and rendering, motion planning, pattern recognition, computer graphics, computational geometry and sensor networks and the military and automotive industries. We use this new algorithm for determination complexity of porosity of the microstructure of robot laser-hardened specimens. For predicting surface porosity of hardened specimens we use neural network, genetic algorithm and multiple regression. With intelligent system we increase production of process of laser hardening, because we decrease time of process and increase topographical property of materials. Hybrid evolutionary computation is a generic, flexible, robust, and versatile method for solving complex global optimization problems and can also be used in practical applications. This paper explores the use of an intelligent system with such a hybrid method to improve existing hybrids. It describes a new hybrid method based on the cycle integration method. © 2017 Slovak Academy of Sciences. All rights reserved.