Combined approximation algorithms for interactive design of road routes in CAD

Objectives . The aim of the work is to create algorithms for approximating a sequence points on plane by arcs clothoids and circles. Such problem typically arises in design railroad highway routes. plan (projection onto horizontal plane) road route curve (spline) consisting repeating bundle elements “straight line + clothoid arc circle ...”. combination provides continuity not only its tangent, but also curvature. Since number spline known advance, their parameters are subject restrictions, there no mathematically consistent algorithm this problem. two-stage scheme solving developed at RTU MIREA with lines circles (i.e., without elements). At first stage, uses dynamic programming determine elements. second optimizes using nonlinear programming. This has yet be implemented due significantly more complicated nature Therefore, plans existing computer aided (CAD) systems carried out interactive mode iterative selection In regard, it makes sense develop element-by-element approximation. Methods approximation formalized as lowdimensional non-linear objective function sum squared deviations from original points. can represented Cartesian coordinates power series, difficulties calculating derivatives respect desired proposed these based integral representation functions length. Results A mathematical model have been method second-order calculation inversion matrix (Hesse matrix). Conclusions For programming, necessary an analytical expression terms required variables. make possible calculate first, absence such expressions.