On a topographical map of civil engineering, there are various enclosed areas, for instance, rice fields, meadows, buildings, roads, walls, regional boundaries and so on. Before a software system such as road planer is run, it is necessary to extract these various regions and features, and to transform them to 3D data. The automatic extraction and classification of all of them on a screen are difficult and very time-consuming. It is better to combine the automatic recognition with interactive operation. It is obvious that interaction is easily done when vector date of maps is applied. On the other hand, the vector data is much less than the raster data of the same map. This paper proposes a practical solution for understanding of vector maps, including two major methoeds; ditching (DIrected Track stretCHING) method for open regions (e.g., roads, slopes and walls etc.) and inward tracing method for bounded regions (e.g., various fields).

Various calculations of derivatives, dealing with specific spaces, have been studied to define cubic splines. Some Modified 3-Point Methods have been proposed which would reduce the amount of calculations required. These methods enable us to preceive the result from a computer by lines. Some theorems that are useful for the discussion of local calculations are given and examples are executed to compare our methods with the original cubic spline functions. The results given in this paper have demonstrated a relation to the interactive computer graphics as well as the interpolation of data points.

Generation of line-drawing images in intelligent terminals seems to be an important theme in the area of computer graphics because of the recent architectures of computer systems. Required operations for the image generation should be local (or incremental), and each operation has to be carried out with limited amount of calculations and memories. The authors have reported the five-point method for this purpose. In this paper, the three-point method is newly investigated as a further study on this line. Traditional three-point methods cannot be applicable as their undulations" owing to the truncation of data points for local processing appear. Therefore, several types of estimations" are introduced in order to compensate the truncation; they are compared in view of derived results and required calculational steps, and one of the methods is recommended as the most useful local algorithm.