Improvement of Algorithm for Applicating Radial Basis Functions on 3 D Reconstruction of Complex Roadways

Abstract

Under the circumstances of insufficient sample data of road topography, in order to generate high-precision road digital models, it is necessary to apply the method of approximation by interpolation to reconstruct road geometrical shape. The radial interpolation functions represented by Multi-Quadric (MQ) are the most commonly used curved surface reconstruction method currently. MQ works satisfactorily when dealing with expressways and first class highways. But serious data divergence occurs for secondary, third and fourth class roadways which are characterized by complex alignment combination. This study found that non-injection of the complex alignment between range and independent variable is the real reason for MQ failure. In addition, if the range is too sensitive to the change in independent variable, ill-conditioned coefficient matrix may occur and consequently calculation instability may rise. Therefore swap of non-injection the range and independent variable range, as well as the method of decomposing complex alignment of bi-directional non-injection into “curve units” were put forward, which ensures injection of each “curve unit” in addition, swap of the range and independent variable range can also solve the problem of numerical divergence caused by sensitivity of the range to variation of the independent variable range, with the sensitivity after swap changed to 1/k from k, which can effectively eliminate calculation instability.