DEM generalization using polygonal simplification

Generalization methods and their quality is a very important element of geomorphometric research. Polygonal simplification methods in generalization can generally preserve the basic shapes well even at a higher level of generalization. The limited suitability for subsequent mathematical modeling is a major limitation of the use of TIN-based generalization (polygonal simplification) in geomorphometry. Our main goal was to build a method for generalizing the DEM of the land surface using polygonal simplification and to create a generalized model at any level of generalization suitable for further analysis. This involves converting the resulting coarse TIN to a smooth grid. We have created an algorithm that combines well-known algorithms for individual stages of the generalization process with a new method of anisotropic subdivision that increases the quality of the process. The algorithm consists of three main parts: generalization, skeletonization, and smoothing. The main generalization procedure uses Quadratic Error Metric Simplification (QEMS) on the polyhedral model. A smooth surface is created by Laplacian smoothing and Loop subdivision methods. With a greatly simplified model, the level of smoothing required to mitigate the triangular structure is high and thus has the undesirable effect of smoothing the actual edges. We improved the algorithm by using an additional step between generalization and smoothing. The algorithm creates a detailed triangular skeleton using our new anisotropic subdividing triangles based on QEMS quadrics at the vertices. The result shows that the algorithm can successfully progressively remove small features, but also preserve the basic shapes of the landscape surface. The output mesh is also sufficiently smooth without triangular artifacts from the polyhedral TIN model