The Application Of Head/Tail Breaks In The Simplification Of Vector Linear Feature

Map generalization is one of the important basic theories in cartography,which is mainly used to solve the problem of multi-scale representation of spatial data.The realization of map generalization relies on four types of generalization operators: selection operators,reduction operators,displacement operators,and merge operators.Among them,the simplification operators can be subdivided into simplification of point features,simplification of linear features,and simplification of areal features.Because vector linear features are ubiquitous on maps,its simplification is one of hot research issues in map generalization.Early vector linear feature simplification algorithms regarded vertices as the basic unit of linear features.Simplification of linear features was achieved by deleting vertices that did not meet the requirements.This type of algorithms is easy to implement and has high efficiency,but the simplification results of this type are not smooth enough and do not conform to the habit of human cognition.It is more like a compression algorithm instead of a map generalization algorithm.Therefore,some scholars have proposed that bends of the linear feature should be used as the basic unit of the linear feature in simplifying it,so as to obtain a smooth and consistent result that meets human cognitive habits.However,neither a vertex-based or a bend-based vector linear feature simplification algorithm relies on an artificial threshold.An appropriate threshold requires the cartographers to have enough professional cartographic knowledge and experiences.This inevitably leads to some general shortcomings in using vector linear feature simplification algorithms such as uneasily to use the algorithms and the algorithms are not automatic.With the theory of self-similarity between local and overall figures in fractal geometry,the heavy-tail distribution law commonly found in the nature and human societies,and the classification of head/tail breaks,this paper proposes two vector linear feature simplification algorithms based on vertex and bend,respectively.These two algorithms can iteratively obtain the simplification results of vector linear features at different levels of detail without artificial threshold selection,reducing the threshold for using the vector linear feature simplification algorithm,and increasing the degree of automation and intelligence of the algorithm.The vertex-based vector linear feature simplification algorithm is suitable for hand-drawn navigation linear features that only need a few feature points to transfer geographic information.The algorithm first calculates the weight factors of each vertex on the linear feature in the Douglas-Peucker algorithm;then,the arithmetic average value of the weight factors is used as the dividing line,and the vertex whose weight factors are greater than the arithmetic average value is regarded as the "head",and vertex whose weight factors are less than the arithmetic average value is regarded as the "tail".If the ratio of "head" vertices to the total is less than 40%,keep the "head" vertices to get the simplification result.Based on the current simplification results,classification can be performed again to obtain simplification results at different levels of detail.The vector linear feature simplification algorithm based on bend is suitable for closed curves such as contours and national boundaries.Such linear features require that the simplification results should keep the features as curved and smooth as possible.The algorithm uses the oblique-dividing-curve method to divide the vector linear feature into a set of continuous bends,and calculates the area of each bend.Similarly,a bend with an area larger than the arithmetic mean is referred to as a "head" bend,and a bend with an area less than the arithmetic mean is referred to as a "tail" bend.If the ratio of “head” to the total is less than 40%,the “head” bends is retained and the feature points in the “tail” curve are extracted.The feature curve and feature points are combined to obtain the first simplification result.Repeating the above operation can get the simplification results at different levels of detail.The experiments show that the algorithms in this study have the advantages of less time-consuming,easy to use,simplification results with different levels of detail,and high similarity between the simplification results and the original graphics.