A Smoothing Algorithm for Contour Lines by Means of Triangulation

Contour lines are very important features in the representation of quantitative relief over a wide range of scales. As scale is reduced, contour lines should be generalized. One of the generalization routines involves smoothing lineal features. Nevertheless, contour lines are a special class of lineal feature, as they represent a three-dimensional object. Accordingly the generalization should be conducted while taking into account all the contour lines over the map, bearing in mind the three-dimensional object that they represent. The algorithm presented in this paper smoothes the contour line irregularities that generate flat and erroneous triangles in a Delaunay triangulation. Smoothing is achieved by moving only the sharp vertex toward the baricenter of the flat triangle; in an iterative algorithm, this produces a smooth line that does not generate flat triangles.