Reduction of Systematic Length Error Involved by Polygonal Approximation of Curves using Polynomial Interpolation Methods
Résumé
In a geographical database, the geometry of polylines is usually constructed using a succession of vertices connected by linesegments. When the real world entities are curves (e.g. a sinuous road), their representation using polygonal lines induces a geometric simplification, called polygonal approximation of curves. The degree of curve approximation varies according to the level of details of the geographical database and its capture scale. As a consequence, the polygonal approximation of curves impacts the positional accuracy of the segments interpolated between two vertices, and also affects measurements computed from the polygonal line, by generating systematic underestimations of the curves lengths. So, in order to estimate the systematic error of lengths involved by the polygonal approximation of curves, this article proposes methods to re-construct realistic curve geometries from an original polygonal line using polynomial interpolation methods. To facilitate the re-construction of curve geometries using an original polygonal line, different methods of polynomial approximation are compared. Finally, the cubic Hermite splines polynomial interpolation method is selected, and more specifically the cardinal splines method, because of its low parameterization requirements. To preserve the realism of the re-constructed curves, a densification of the original polygonal line is performed previously, according to the level of detail of the geographical database, determined by data exploration, using the median inter-vertices distance. Finally, an experiment is performed on a sample of road network located in a mountainous area and presenting curve shapes. After a detection of sinuous roads, the experiments show that the use of cardinal splines with a tension parameter of 0.7 on a densified polyline is adapted for the re-construction of realistic curves. Results finally demonstrate thatthe proposed methods allow to reduce the systematic length error involved by the polygonal approximation of curves.