The CONVERSION of TERRAIN MODELS, or the HEADACHE of TERRAIN MODELING
Two areas of digital terrain models still offer challenges to developers: the conversion of one type of model into another, and the generalization of models. In these pages we address both types of problems.
BIRD'S EYE VIEW OF THE CONTOURS-TO-TIN CONVERSION PROCESS
We see "contours into triangulations (TINs)" as the most challenging conversion. Also as one of the highest significance. Just think of the hundred of thousands of top quality contour overlays in the world, waiting to be converted into models that faithfully verify the source contours. Another conversion, contours into uniform grids (or DEMs), is now used far more often. By numbers, the USGS is the heaviest user of that kind of conversion: 55,000 quad sheets have been converted. They are now under revision and correction. Completeness, however, is not the only measure of success. In our eyes, even more important is the faithfulness of the converted model to the source contours.
The definitive proof of that faithfulness is the linearity in the model between adjacent source contours. Several ways can be taken to test that linearity. The simplest is the contouring of the model at intervals equal to a fraction of that in the source data. If the model is a faithful representation of the source data, the derived contours, all across the project area, must spread themselves uniformly between pairs of source contours. With all generality, that condition is not seen throughout a grid or DEM unless a great deal of additional features have been created in interactive mode. On the other hand, there is a fully automated approach that verifies linearity without the least human intervention. Two pages in this series show a well spread distribution of derived contours, one in feet and one in meters. We earnestly recommend this test to all users of contour conversions.
To obtain these TINs, additional features are derived from the source contours in fully automated mode. Those features are the stems and branches of a network structure known as medial-axis. They provide systematic support to the TIN so that all its elements are supported by both the medial-axis and the source contours (every triangle has two vertices on a contour line and one on the medial-axis, or vice-versa). Reciprocal
links between triangles, contours and medial-axes ensure the easy accessibility that permitted, among other functions, the assignment of the proper elevations to the vertices and nodes of the medial-axis. In turn, those proper elevations ensure the linearity of the TIN and its faithfulness to the source data.
The conversion of TINs into uniform grids, for trivial, doesn't deserve much elaboration or remarks. On the contrary, the inverse conversion, from uniform grids to TINs, is nothing like that. It has really no place in a well designed production plan. It is much better to convert contours into TINs first, and from them to obtain the desired uniform grids, in a sequence that would yield the three sets of models representing accurately (within their own limitations) the same piece of ground.
THE LINKS BETWEEN CONTOURS, TIN AND MEDIAL-AXES
SMALL SAMPLE. VIEWS OF TIN BASED ON DLG CONTOURS AND MEDIAL-AXES
Our conversion runs on IBM RS6000 and eServers. We wrote these conversion programs in a mix of FORTRAN and "C" and compiled them under AIX, an IBM UNIX flavor. For the setting up of the data and the display of the results, some of which can be examined in these pages, we relied on EAGLE, a versatile CAD, and on the support of http://www.abodata.com, agents for EAGLE in Genoa, Italy.