From left to right are the operations of moving, rotating, and scaling, each coordinate axis corresponds to a color.

Editing such as cropping, enlarging, adding, subtracting… to create the desired object in the real world.

Figure 1.2. From left to right are the operations of moving, rotating, and scaling, each coordinate axis corresponds to a color.

The objects are then given bones (if any), surface properties (such as color, skin, hair, eyes, etc.) and movements that vividly simulate the object's real-world representations.

When working with software, we will operate on 4 different views of the object. These 4 views will allow us to see the object at different angles at the same time. The images below illustrate this very clearly:

Figure 1.3. Different views.

We have a 3-dimensional coordinate system XYZ, blue corresponds to the Y axis, red to the X axis and dark blue to the Z axis. The upper right corner is the working frame that allows us to work in 3 dimensions, the remaining 3 corners allow us to work in 3 cross-sections of the model. With the frames

This view makes it easier to work with, as a change in one view will have an effect on other views.

Besides the XYZ coordinate system, we also have the UV coordinate system, the UV coordinate system covers the surface in 2 directions: left to right and bottom to top. This coordinate system can be visualized as the longitude and latitude lines of the earth. This coordinate system is mainly used in the process of adding surface properties to the model.

1.2.1.3. Main 3D modeling techniques

Through research on different modeling software, it is shown that, in general, working in a 3D environment has the following main tasks:

- Modeling techniques : This is the part that uses modeling tools to create models and edit them as desired. From there, 3D objects are shaped;

- Character animation technique : includes operations to attach characters to a set of keys . Each key represents the position and shape of the character at different times. The movement of the character is the representation of the character at each of these key positions;

- Rendering : This is the part to assign materials to characters and create renderings;

So we can understand that modeling is the technique of creating frames for objects. We can imagine this stage as the process of creating a skeleton for a human body, then using rendering techniques to add flesh to that person, and then using animation techniques to create human movement. We can clearly understand the work of each stage through the illustrations in Figure 1.4 and Figure 1.5.

Figure 1.4. The construction frame of a ball, created after the creation step

model

Figure 1.5. The ball after the demonstration step.

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With this topic, the scope of exploitation stops at learning the techniques of creating objects and rendering. So the main work often used is modeling and rendering.

There are many different methods for describing 3D objects. Depending on the specific object, we use a method that is appropriate to the properties of those types of objects. For example, to represent simple Euclidean objects such as ellipses and polyhedra, we use polygonal and quadratic surfaces. To represent surfaces of revolution and objects used to design model airplanes, gears and other technological structures, we often represent them using curves. Procedural approaches such as Fractals allow us to accurately represent objects such as clouds, grass and other natural objects.

3D mesh representation:Using wireframe modeling allows us to visualize the internal structure of a 3D model by rotating the object and selectively removing hidden lines (lines that are often invisible through cross-sectional planes).

When represented by this model, these objects are not very realistic. Therefore, techniques for shading and removing hidden lines and faces are used. This model is usually fast, so it is often used to view sketches of objects, especially in CAD systems.

A common form of polygon mesh is a series of triangles. When a polygon is described by more than three vertices, its vertices may not be coplanar. This can

can lead to calculation errors. A simple method is to divide this polygon into triangles.

Parametric smooth surface representation:In the case of really complex objects, one or more smooth surfaces are often joined together. Each component used for joining is called a patch surface.

1.2.2. Simulation in virtual reality

1.2.2.1. Overview of simulation

Traditionally, interaction with computers is done through devices such as keyboards, mice or Joystick/Trackball/Keyboard/Styplus to provide input information and use visual display blocks to receive output information from the system. With the advent of virtual reality systems, new communication methods have been developed that allow users to actively interact with computers. VR technology is currently developing rapidly in the world. Currently, in Lao PDR, VR technology is gradually gaining attention due to its strengths such as allowing the creation and visualization of big data. This is very important for applications such as urban design, emergency response, tourism, entertainment, traffic management, large-scale construction projects, and education. In these fields, interactive visualization of the model is crucial for in-depth analysis of the data set. The purpose of the system is to simulate the visual and perceptual effects of a survey over a given area. The system combines simulation techniques using 3D graphics with hardware devices.

Simulation is the process of "imitating" a real system. Current computer programs can create Simulation Models such as Simulations of technical weapons, its technical and tactical features, the ability to exploit and use in the field, and even combat operations on the virtual battlefield in real time.

Simulation can be defined as a process of creating a model (such as to describe an abstract concept) of an existing system (such as a

The study program, training, training, technical and tactical features of equipment and their capabilities in combat operations on the battlefield, the activities of soldiers of different military branches on the battlefield, the combat operations of units on the battlefield in weather, climate, terrain conditions, etc.) to identify and understand the factors controlling the system, or predict/forecast the future behavior of the system. Most systems are described qualitatively and quantitatively on the basis of random algorithms, programmed according to the principles of teaching, learning, training, and simulated exercises.

Simulation is the process of "imitating" a real system. Current computer programs can create 2D & 3D Models such as Simulations of technical weapons, its technical and tactical features, the ability to exploit and use in the field, even combat operations on the virtual battlefield in real time.

Simulation is an effective and important tool because it helps users of design methods and options (or operational plans, force utilization options, and at the same time can choose to optimize proposed solutions, maximize the capacity of officers and soldiers) and accurately evaluate the results without having to experiment on a real system (which can be costly, time-consuming, dangerous and time-consuming for preparation). It allows officers and soldiers to answer the question "What would happen if…?" about a decision without actually experiencing the results of that decision.

1.2.2.2. Simulation technology

Simulation technology is not a technology that requires very modern equipment. Normally, when training and coaching in real conditions, we have used many simulation models, such as tools, training equipment such as cut-out models, which are the first simple simulation tools to help soldiers and students understand the features, structure and through the lectures of training officers, have a basic understanding of the issues that need to be conveyed.

Simulation technology is used frequently in various fields such as: drills, combat training at the squad level, from 3-person teams to squad, platoon and higher levels through sand tables, reliefs, tactical maps, and drills of unit command boards are carried out on these sand tables, diagrams, and simulation maps.

The strong development of military science and technology, with the widespread emergence of modern weapons, has led to modern combat methods, and future war models are becoming more and more complex. The battlefield space has become multi-dimensional, with many stealthy, secret, and unexpected attacks from space, air, ground, ocean, and underwater with great destructive power, high precision, and very serious target destruction.

Faced with the extremely complex changes of modern warfare, in addition to the task of gradually modernizing the armed forces according to mission requirements, students studying national defense work need to have a deep, broad and very thorough understanding of the means of war of countries with modern military industries, a firm grasp of the types of weapons and equipment in the establishment, need to have extensive knowledge, understand us and the enemy, the capabilities of each type of weapon and equipment that can be used on the battlefield, have a high level of technical and tactical skills to be able to use conventional weapons, currently in the establishment to defeat high-tech weapons, and have the ability to command and control combat operations accurately in the modern war environment. To fulfill the above requirements, countries with modern military industries have introduced 3D simulation technology as an application technology in battlefield control. In countries with developed industries, simulation technology has been gradually applied to training, teaching and education activities, gradually bringing 3D simulation technology into the reality of the task of protecting the Fatherland.

2D-3D simulation technology has a unique development, completely different from the development of other applied technology industries.

Like software technology or exploiting and using modern technology imported from abroad, like the development of society, 3D simulation technology must be suitable for the reality of the defense and military situation of an economic environment. It can be said that the development of 3D simulation technology must be suitable for the reality of the weapons and equipment establishment, the level of science and technology of the country, and the knowledge level of society.

Therefore, the development of 3D simulation technology often starts from modeling real objects in today's stage.

1.3. Overview of fiber objects and simulation

1.3.1. Overview of fibrous objects

Objects play an important role in creating a virtual reality environment, because virtual reality is essentially a 3D environment consisting of objects (3D) arranged and arranged in a logical order according to reality and can interact and move depending on each different type of object. Objects in virtual reality can be static, dynamic and a composite of both static and dynamic objects, objects exist in many different shapes suitable for real objects, there are block-shaped objects, fibers,... In this article, the group of authors focuses on researching and proposing techniques to improve the efficiency of simulating fiber-shaped objects such as: hair, mesh, fabric,...

In practice, depending on each different object or application, the modeling and simulation of fiber objects are required at different levels of fidelity. For applications that do not require high object fidelity but require computational speed, we can model and simulate fiber objects at a coarse level, that is, images, while for applications that require high fidelity and interactive motion of the resulting model, we need to model and simulate fiber objects at a fine level, that is, we need to use a mathematical model to represent the object. This paper focuses on the study of simulation of fiber objects at a fine level using a mathematical model.

Fiber objects are usually dynamic objects such as hair, mesh, fabric, etc. Therefore, to simulate these types of objects, we must represent the

their models by mathematical models. Only then can we represent the necessary variable components for the object to interact and move such as gravity, gravity, etc. To model and simulate fibrous objects in virtual reality, many domestic and international scientists have been interested in researching and proposing many different scientific works and many proposed methods. One of the methods used is mathematical models such as Spline, Be'zier curves, etc. In particular, the NURBS (Non-Uniform Rational B-Spline) model is more commonly used. Because fibrous objects such as mesh, hair or fabric, etc. are often dynamic and local, using NURBS to represent and simulate them is appropriate. For example, the groups described by Xu et al.; Noble et al.; Anna Sokol uses generic NURBS to simulate hair fibers and their interactions and movements.