Analysis Of Fitting Method On Plan Curve Based On Cubic Spline

A more perfect design and construction system has already been formed in the newly built highway engineering in our country, the relevant standard, the regulations and the construction technology become better and better. However, that, continued to use the mentality and the design method for a new road, cannot solve the actual problem of an old road. So far there's been no quite mature theory and technology of reconstruction for plan curve, according to survey data form an old road. In the track reconstruction engineering, plan curve parameters of existing highway have a significant effect on widening subgrade, theoretic analysis of highway existing circumstance, safety evaluating, and building route database of the highway and so on. According to distinctive feature of highway engineering, it's a theoretic discussion and complementarities for the reality question that curve reconstruction technology of mature reverse engineering is applied to highway engineering.It is pivotal for curve fitting to choose fitting methods and analyze plan curve parameters. There are some mature curve fitting methods in the reverse engineering, such as Lagrange interpolation, piecewise polynomial interpolation, least square method and spline interpolation. In this paper, after analyzed different characters, cubic spline interpolation is adopted and improved on the basis of fitting methods. There are eight combination style of the plan curve for highway. Plan elements are made up of line, circular curve and transition curve. This paper establishes cubic spline function, analyzes subsection curve function and curve slope and curvature, at last decides to place the curve especial points which can be obtain easement curve length and other line parameters, such as the ZH point (end of line and beginning of transition curve), the HY point (end of transition curve and beginning of circular curve), the QZ point (middle of curve), the YH point (end of circular curve and beginning of transition curve), the HZ point (end of transition curve and beginning of line).Design the Route Fitting Program based on Cubic Spline and, output viewdata, interface with AUTOCAD program, built up vary layers with different color, directly plot the fig of route ichnography, slope and curvature. Choose representative styles of basic type and "S" type, use the Route Fitting Program to fit the curve and find out the parameters while original design parameters were known, compare the two parameters to make sure whether the fitting method is accurate or effective, then apply to the arterial highway's rebuilding project from Daijia moutain to Huangpi in Wuhan.Further more, beginning with error analysis of curve reconstruction, compare with the statistical data of error with vary fitting nods' span, such as 100m, 60m, 50m and 40m. Then summarize that the error is usually abutting to the especial points; the error difference of curve is more outstanding than that of line. In order to minish the error, choose a bigger value of fitting nods' span at line and a smaller one at curve while measuring.Cubic spline fitting is a perfect plan curve fitting methods. However, this paper is founded on the planar curve, and in the future can apply to research dimensional curve of the highway engineering.