SIMULATION AND COMPUTER IMPLEMENTATION OF SURFACES ON THE BASIS OF CURVES OF THE 5TH DEGREE

Abstract

The paper considers the construction of the surface potion on the basis of the application of the fifth degree curve for given two points and the first and second derivatives in them.

This allows you to set the curvature at the boundaries of the surface portion. On the basis of this curve it is possible to construct a strip of a surface on the set two boundary curves and the set first and second derivatives in them.

It is also possible to construct a portion of the surface at given four points and the first and second derivatives in them in two directions - along and across the portion of the surface.A portion of the surface at four points allows you to build a smooth surface with a second order of smoothness on a given list of points in three-dimensional space.

In addition, specifying the first and second derivatives allows you to specify the curvature.In this case, you can first specify the first derivatives, and the second will be determined by the formula of curvature.

These strips and portions of surfaces are advantageous to use in the design of surfaces of machines and units operating in a moving environment (surfaces of aircraft, cars, ships), in which it is important to specify the law of curvature along the surface.

The law of curvature change is very important in this case, because the fracture of the curvature on the surface mimics the turbulent disruption of the flow of the moving medium, which increases the resistance of the unit to the moving medium.

Increasing resistance to the moving medium causes a decrease in speed.And when used in aircraft construction, the failure of the moving environment can lead to a peak and a plane crash.

It was proved in the work that on the basis of a curve of the 5th degree it is possible to construct strips and portions of surfaces with given curvatures at the boundaries. Also, a computer program in the AutoLISP language has been developed in the environment of the AutoCAD system, which implements the construction of this portion of the surface.

Keywords: surface strip, surface portions, fifth degree curve for given two points and the first and second derivatives in them.