The use of wavelets in computer-aided design

Аuthors

Bityukov Y. I.^*, Kalinin V. A.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: yib72@mail.ru
**e-mail: kalininmtak@gmail.com

Abstract

This article focuses on the application of wavelet theory in problems of geometric modeling of aircraft structures. Wavelets are the mathematical tool for layering functions. With their traditional applications in approximation theory, physics and signal processing, wavelets recently found applicaiton in many problems of geometric modeling, mainly in computer graphics. While apparent smoothness of curves and surfaces is enough for the computer graphics, CAD/CAM/CAE-systems require the surfaces belonging to different classes of smoothness. In this article we present the wavelet basiс set built on the interval, based on B-spline of arbitrary order. 2D wavelets are built based on this wavelet basiс set. on the ground of The famous Chaikin’s algorithm used for design of curves and surfaces of arbitrary smoothness class is generalized on the ground of these scheme.

Now, CAD/CAM/CAE/PDM-systems are widely used by the companies engaged in the design and manufacture of complex aircraft systems. This is stipulated by a number of reasons, among which the problems of product quality control are of utter importance, especially while its approach the world market.

Based on the principles of optimization and products parameters control at all stages of the design and manufacture such systems provide a comprehensive design work with sufficient reduction of terms together with simultaneous quality improvement. The main objective here is the steady decline in the cost of production and updating its product range, improved reliability, maintainability, cost, etc.

We can consider the development of methods for modeling curves and surfaces of arbitrary shape technology based on Bezier (Bezier) and NURBS, which has become the international industry standard for the design of complex curved surfaces one of the main achievements of the modern period. That is why the problems of improving current methods of geometrical modeling of 3D objects using mathematical apparatus standard for CAD/CAE/CAM-systems, as well as the adaptation of these methods for specific industrial applications are actual today.

Keywords:

wavelet, computer-aided design, spline, geometric modeling, algorithm Chaikin, filter analysis, synthesis filter, the filter unit

References

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