DouglasPeuckerVerfahren

The Douglas-Peucker algorithm is a method for reducing the number of points in a curve that is represented by a series of points. It is commonly used in computer graphics and geographic information systems (GIS) to simplify polygons and polylines. The algorithm works by recursively approximating the curve with a straight line segment.

The process begins by connecting the first and last points of the curve with a straight line. Then, the algorithm finds the point furthest from this line segment. If this distance is greater than a specified tolerance, the point is considered significant and the algorithm is applied recursively to the two sub-curves formed by this point. If the distance is within the tolerance, all points between the first and last are discarded, effectively simplifying the curve. This recursive process continues until all points have been evaluated against the tolerance. The result is a simplified version of the original curve with fewer points while preserving its general shape. The effectiveness of the algorithm is directly dependent on the chosen tolerance value; a larger tolerance leads to greater simplification and potentially more loss of detail, while a smaller tolerance results in less simplification and a more faithful representation of the original curve.