Robust line simplification on the plane

Abstract

Line simplification is an important task in map generalization, in traditional paper series as well as in geographic information systems and web map server services. Using the adequate method an accurate representation of the original elements should be obtained by suppression of redundant information while maintaining the shape of the original elements according to the new scale. To that effect one of the most widely used algorithms is the so-called Douglas–Peucker algorithm. It can lead to inconsistent results such as self-intersections or intersections with other elements, so the operator's supervision is necessary following the automatic treatment. In this piece of work a robust and easy-to-implement variation of the Douglas–Peucker algorithm for individual line simplification in two dimensions is presented. The robustness of the new algorithm is based on the concept of intersection of segments and it can be easily implemented in parallel. The new algorithm brings about correct results regardless of tolerance and morphology of the original line or polygon.The algorithm is coded in standard C99 and it can be compiled for serial or parallel execution via OpenMP. Both the algorithm itself and a program that implements it are distributed as free software. The validity of the solution was tested using the GSHHG geography database that can be obtained free through the Web. Results about accuracy of the output, execution speed and scalability of the parallel implementation are presented.