Mathematical models of the complex surfaces in simulation and visualization systems

Modeling, simulation and visualization of three-dimension complex bodies widely use mathematical model of curves and surfaces. The most important curves and surfaces for these purposes are curves and surfaces in Hermite and Bezier forms, splines and NURBS. Article is devoted to survey this way to use geometrical data in various computer graphics systems and adjacent fields. Simulation, modeling and visualization of 3D objects with complex form are receiving a lot of attention nowadays due to the practical and theoretical interest of 3D modeling, analysis and visualization. There are used in a wider and wider range of application, such as Computer Graphics, Computer-Assisted Design, Geographic Information System, Medicine, Science Experimental Results Viewer, Virtual Reality and so on. Actuality of investigation in area of modeling and visualization of 3D objects with complex form are rising. This relates to evolve complication of Computer Graphics System. Simulation, modeling and visualization of 3D objects with complex form attract some useful mathematical methods of the 3D surface representing. These methods provide with sufficient precision for solving problems. Spaces objects with complex form are commonly used for representing geometric models in a great variety of applications, which require vary large and high precision data computing. Usually the curve or graphic models represent surface and form of such objects. Also triangulations meshes are widely used for visualization complex 3D objects. Thus Computer Graphics