Fractal Enhancement of Cartographic Line Detail

In plane geometry curves have a dimension of exactly 1 and no width. In nature, all curvilinear features have width, and most have dimension greater than 1, but less than 2. Many phenomena, such as coastlines, have the same "look," even when viewed at greatly varying scales. The former property is called "fractional dimensionality," and the latter is called "self similarity." Curves digitized from maps may be analyzed to obtain measures of these properties, and knowledge of them can be used to manipulate the shape of cartographic objects. An algorithm is described which enhances the detail of digitized curves by altering their dimensionality in parametrically controlled, self-similar fashion. Illustrations show boundaries processed by the algorithm.     

Complexity and Intractability: Limitations to Implementation in Analytical Cartography

The computational complexity of algorithms is an important consideration for all computer systems, including geographic information systems and mapping systems. Mathematical cartographers and GIS professionals need to understand and to take into account the limitations imposed on problem solving by the very nature of computation itself. We look at three active research sub-areas of analytical cartography to highlight the differences between traditional mathematical solutions and solutions with computationally tractable algorithms. The three sub-areas are map projections, map feature labeling, and map generalization.