DEFORMATION MODELING SYSTEM BASED ON BEZIER CURVES

Abstract

The article presents the results of the work of a computer deformation modeling system for three-dimensional objects. The system is based on the apparatus for deforming objects based on using Bezier curves.

Due to the development of modern technologies and the increase of the computers’ power, the tasks associated with modeling the deformation of complex bodies and their behavior in real time are becoming increasingly important.

The deformation modeling functionality is implemented in a large number of 3D graphics packages, such as AutoDesk 3ds Max, Autodesk Maya, StechUp, Blender and others. These systems are examples of professional software designed for various purposes. In most cases, specific deformation modeling utilities are included in a paid toolbox that must be downloaded separately, and often do not use the full arsenal of capabilities of their environment. Some of these systems have free trial versions with clipped functionality, which are suitable only for educational purposes of a specific deformation modeling problem.

The purpose of creating the system was to automate the process of deformation of three-dimensional objects with the implementation of an algorithm based on using Bezier curves and surfaces, which would visually track the changes in these objects, and optimize the operation of this method.

As a result of the work, the properties of Bezier curves, Bernstein polynomials and Bezier surfaces were investigated on the basis of Bernstein polynomials in two variables. Based on the research, a software product using JavaScript programming language was developed to reproduce the geometric contour of a three-dimensional model of an object. The system is a cross-platform browser program that visualizes the deformation of 3D objects in real time.

Key words: deformation modeling, three-dimensional object, Bezier curve, Bezier surface, Bernstein polynomial.