Shape simplification in map-like representations is used for two reasons: either to abstract from irrelevant detail to reduce a map user's cognitive load, or to simplify information when a map of a smaller scale is derived from a detailed reference map. In the talk a novel approach for abstracting simplified cartographic representations from more accurate spatial data is presented. First, the discrete curve evolution method developed for simplifying perceptual shape characteristics is explained. Specific problems of applying the method to cartographic data are elaborated. The algorithm is presented. The algorithm simplifies spatial data up to a degree of abstraction intended by the user and maintains spatial ordering between (elements of) cartographic entities. This is important since local arrangement of entities is crucial for spatial knowledge in maps.