Abstract: The article presents an algorithm for modeling a composite curve of the first order smoothness. The necessary formulas for determining the bypass consisting of arcs of third degree polynomials are given. The first option describes the approximation of the entire array of points with the requirement of incidence of the first and last points of the contour. The second option considers the modeling of a curve, with the requirement of incidence of the first point and the free end at the last point, using the principle of drawing curves. In the third variant, the curve must pass through the last point of the array, and at the first point it must meet the requirement of the first order of smoothness tangentially obtained in the previous step. Special points are preliminarily defined on the object - the breakpoint of the contour and points with vertical and horizontal tangents that impose smoothness conditions on the modeled bypass. To model a curve, the least-squares approximation is performed by third-degree polynomials on the set of ordered points bounded by the break points that make up the edge. The advantage of the developed contour modeling method is, firstly, the possibility of processing a large array of points with the observance of a given accuracy. Secondly, it is much easier to ensure the smoothness of the first degree of bypass compared to other methods that use various functions of connecting arcs of the bypass, and it is also important to significantly reduce the amount of data being processed, while maintaining the required specified accuracy. Further works will present the remaining options and formulas for the calculation and their application in the field of reverse engineering, in solving problems of geometric modeling in image processing.