Deconstruction

Exercise 1

Figures 1a and 1b are examples of fractals and they consist of 32 points which link lines of equal length. This particular curve is a first generation Quadric Koch island.

		Figure 1a
		1. Please select 12 of the marked points in Figure 1a to provide a simpler representation of the line. Since the curves have no real world meanings, you may simplify them as you please and there is no single correct answer as such. Indeed, the aim of the exercise is to discover the variety of ways in which curves, such as this Koch curve, may be simplified. 2. Please note any problems you have had with this exercise and explain your choice of points.   Figure 1b Having selected 12 points in Figure 1a, you should now have some idea of the level of simplification required. 3. Use Figure 1b to indicate where you would place 12 points if you were not constrained to selecting points on the line. If you must draw a smooth curve, then please identify 12 critical points on your curve (i.e points through which curves must pass). 4. Please indicate your reasons for departing from your rendering in Figure 1a   and note any difficulties you have had with this exercise.

Exercise 2

			Figure 2a
			5. Please select between 20 to 40 points on Figure 2a. You may find it easier to focus on just half the curve and select between 10 to 20 points. 6. Please explain your choice of points on the reverse side. Were there any new problems?   Figure 2b 7. Use Figure 2b to indicate how you would provide a similar level of unconstrained generalisation of the same figure. 8. Please explain your approach.

Fractals to peek into the minds of cartographers

It is well known that manual generalisation of lines, such as coastlines, is somewhat subjective. Digital Cartography tries to eliminate such subjectivity through procedures for consistent generalisation. Having used fractals as test curves in the study of line generalisation algorithms, it seemed to me that they may be useful for noting some manifestations of subjectivity in cartographic generalisation.

So, at the 1996 BCS Symposium at Reading, members of the BCS Design and Teachers Groups were invited to do the above exercises. The curves which appear in Figures 1 and 2 are produced by repeated application of a ‘generator’ pattern to straight line sections of the curve to give an increasingly complex curve. Here only the first and second generations of the curve are considered. The study hoped that a comparison of manual and algorithmic outputs might indicate whether the former were engaging mainly in wholistic or algorithmic processing.

Quite understandably, most of those present became a little perplexed, even if not bored, by this seemingly meaningless exercise and did not give me their solutions. Fortunately, the variation in the returns was sufficiently striking and interesting to prompt further investigations. The results were quite interesting and led to the follwoing publications in:

• Computers & Graphics - which provides a Computer Science perspective
• Cartographic J - which examines the implications for Cartographic Education

Please feel free to send me your solutions and your comments on our papers.   Unfortunately, I do not have permission to put figures from the publications on the web. 

Mahes Visvalingam
Cartographic Information Systems Research Group
Department of Computer Science
University of Hull
HULL
HU6 7RX
United Kingdom

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