Phys. Dirk Burghardt

4
Abstract
With the help of highly advanced cartographic software programs it is possible to produce
topographic maps from digital data. In some cases, however, there exist graphical conflicts,
because symbol widths require more space than their real-size equivalents. Generalization of
such objects by manual editing is rather time-consuming. Therefore, automation of generalization
operations is desirable and should be possible in the age of information technology.
Automated cartographic displacement of vector data distinguishes between point, line and area
objects subject to processing. Modeling of line objects assumes a central position, because the
human eye is extremely sensitive to shape alterations caused by displacement. In many applications
splines are well-known tool for describing lines. It is especially the energy-minimizing
spline also called snakes model shape deformation as a result of external forces. The internal
energy is used to maintain the line shape which has been displaced due to conflicts. First and
second derivatives of the line coordinates with respect to the arc length are used as quality
measures. In cartographic displacement a minimal distance between adjacent objects should be
maintained. The external energy is used to describe the conflict situation if objects are too close
to each other.
To solve the graphic conflicts while maintaining the shape of the objects, the method of energy
minimization is employed. Minimizing the energy functional of internal and external energy
leads to two independent Euler equations. These are discretized by means of finite differences.
The equations can be solved iteratively using the Cholesky factorization. Parametrization of the
energy-minimizing splines by means of the tangent angle function (tafus) replaces the two eulerian
equations of the 4 th order with one equation of the 2 nd order. Simplification of the equation
system requires an additional amount of calculation for transforming the resulting changes of
line direction to attain cartesian coordinates. Verification of a desirably faster convergence has
yet to be achieved. The Greedy Algorithm is an alternative procedure to accomplish energy
minimization using the Variational Calculus. With the aid of this algorithm the energy of each
individual support point is minimized by way of minor displacements. As opposed to the Variational
Calculus the effects are more local. Therefore, the Greedy Algorithm is advantageous
used for the displacement of buildings or for the positioning of label boxes.
The integration of this displacement approach in a cartographic program provides evidence of
the fact that it can be used in practical applications. Cooperation with a software producer
will help to find additional fields of application, a case in point being the automated map edge
work which allows displacement and suppression of text and symbols at the map boundaries.
Experience has shown that the research effort required for developing new software tools is
estimated to amount to between 30 and 50 percent of the total effort.