The label placement problem is one of the most important problems in geographic information systems, cartography, graph drawing and graphical interface design. In this paper, we consider the problem of labeling points and curves in maps drawn from digital data. In digital maps, a curve is represented as a set of points and consists of many small segments. The label for each curve must be placed alongside the corresponding curve. We define a continuous labeling space for points and curves, and present an algorithm using this space for positioning labels. Computational results for subway and JR train maps in Tokyo are presented.