Lecture 4, Aug 30: Lines and Line Simplification

"Everything is related to everything else, but near things are more related than distant things." Waldo Toblerís First Law of Geography


Generalization applied to cartographic lines

Today we encounter the simplest form of one of the recurring themes for dealing with large models: simplifications that preserve the essential features of the models. In cartography, the term for the process of replacing entities by readable symbols at a particular scale is generalization. We focus on line simplification.

Barbara Buttenfieldís paper lists five ways to think about a line

She also discusses corresponding generalization procedures; Iíve added some others.


Problem Set #2, Due Weds, Sept 15.

Do two of the following three problems, and hand in your solutions either in class or anytime before midnight at my office sn333. Collaboration is permitted; good scholarship requires that collaborations be acknowledged.

  1. For the recursive selection procedure of Douglas and Peucker, analyze the expected running time under the assumption that whenever a fragment of a polygonal line is split, the splitting vertex is chosen with equal probability from the interior points of the fragment.
  2. Design an algorithm and data structure for line simplification that, given a tolerance, will produce a polygonal line that meets that tolerance. Ideally, the data structure should have linear size and the algorithm should produce a line with k segments in O(k) time.
  3. Consider the problem of simplifying either a river represented by two lines for its two banks, or a set of contour lines. Design an algorithm (at least at the pseudocode level, but if you want to implement it, then Iíll provide data) that will simplify, but guarantee that the simplified curves do not intersect.



Preview for Weds lecture: Topology, from a GIS perspective: