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Terrain Modelling from Contours

Good quality terrain models are becoming more and more important, as applications such as runoff modelling are being developed that demand better surface orientation information than is available from traditional interpolation techniques. A consequence is that poorquality elevation grids must be massaged before they provide useable runoff models. Rather than using direct data acquisition, this project concentrated on using available contour data, for two reasons. Firstly, despite modern techniques, contour maps are still the most available form of elevation information. Secondly, manual contour tracing has imposed a subjective interpretation of the form of the landscape that is lost with automation, yet which is of considerable value. The maximum slope of the terrain is perpendicular to the contour, and this permits us to visualize the relationships between pairs of contours. With care this may be modelled by triangulation methods, as the spatial relationships can be preserved, although standard grid interpolation methods based on "n nearest neighbours" often have problems. However, whenever we have relationships between portions of the same elevation contour, such as in peaks, pits or valley heads, our interpretation based on triangle slope is insufficient we get "flat triangles". In this case we need to re-examine our spatial model. The usual triangulation approach, the Delaunay triangulation, is effective because it is locally stable a property based on its dual, the Voronoi diagram. These two spatial structures have been much studied by workers in the field of computational geometry largely in terms of efficient calculation, but also in terms of their properties. In particular, recent work on the automatic reconstruction of curves from point samples, and the generation of medial axis transforms (skeletons) has greatly helped in the visualization of the relationships between sets of boundaries, and families of curves. This provides us with tools to enrich our original contour data for "flat triangles". The insertion of skeleton points in these cases guarantees the elimination of all flat triangles. Additional assumptions about the local uniformity of slopes, either along or across valleys and other features, give us enough information to assign elevation values to these skeleton points. If required, appropriate interpolation techniques may generate an elevation grid for visualization purposes that preserves reasonable slopes at all points on the model even at the data points themselves and that are faithful to the input data. In addition, the algorithms used are only moderately more complex than the underlying Voronoi diagram or Delaunay triangulation. The result provides us with a surprisingly realistic model of the surface that is, one that conforms well to our subjective interpretation of what a real landscape should look like.