ON AUTOMATIC GENERALIZATION OF CONTOUR LINES 
Poul Frederiksen 
Institute of Surveying and Photogrammetry 
The Technical University of Denmark 
Landmálervej 7, DK-2800 Lyngby, Denmark 
and 
Kurt Kubik 
The Ohio State University 
Department of Geodetic Science and Surveying 
1958 Neil Avenue, Columbus, Ohio. 
ABSTRACT 
A new method of generalization of contour lines is proposed, based on 
a mathematical model for the terrain surface. 
INTRODUCTION 
though contours drawn at different scales differ in their specific de- 
tail, they still have the same generic features. In a rough approxi- 
mation, the small and large details of a contour line are geometri- 
cally identical except for scale. 
When each piece of a shape is geometrically similar to the whole, we 
call this shape selfsimilar (Mandelbrot, 1977). Let us illustrate this 
concept of selfsimilarity with an example of a regular curve (Koch 
curve) (Koch, 1904). The construction begins with an equilateral tri- 
angle A with sides of unit length. Then, one adds on the mid-third of 
each side a A with sides of length 1/3. This second shape ends with a 
star hexagon (Fig. 1). 
Figure 1. Triadic Koch Island, original construction by Helge von Koch. 
The same process of addition of the A is repeated with the star sides, 
and then repeated again and again. 
- 260 -