METHOD OF INTERPOLATION OF POINT SET FOR THE FORMATION OF SMOOTH CONTOURS

The formation of complex functional surfaces given by an array of points is an actual task of geometric modeling. The geometric model of such a surface is formed on the basis of a discrete linear frame, the elements of which are contours consisting of sections of analytically determined curves lines. The paper solves the problem of modeling a smooth contour that represents the original curve with a given accuracy, interpolates the original point series and belongs to the line curve that does not contain special points. The contour is formed inside the area of the possible location of the parts of the interpolating curve, along which the values of the curvature monotonically increase or decrease. The method of determining the area of the location of the curve is based on the assignment of the positions of the tangent lines and the curvature values at the given points within the ranges, which guarantee the possibility of interpolation of the point series by a curve with the specified characteristics. All curved lines that meet the conditions of the problem cannot be located outside the specified area. The absolute error of the interpolation of the point set is estimated by the width of the area of the possible location of the curve. If the interpolation error of the original point set turns out to be greater than the specified value, then the width of the area of the curve is reduced due to the assignment of the corresponding intermediate points. As a result of assigning each intermediate point, we get the location areas of two new sections of the curve, which are inside the location area of the corresponding original section. After the interpolation error becomes smaller than the given value, the area of the curved line is considered to be formed, and the obtained point series is interpolated by the contour that is inside this area. The possibility of forming contours with given characteristics by sections of a circle and B-spline has been investigated.