Characteristics of space
Let's summarize the mentioned concepts and terms as follows:
- Homogeneous, isotropic space: Homogeneous surface, Euclidean distance, implicit path.
- Heterogeneous, isotropic space: Heterogeneous surface, distance weighting, no directional friction characteristics,
path related to the cumulative weighted distance.
- Heterogeneous, anisotropic space: Heterogeneous surface, distance weighting, directional friction characteristics, path
related to the cumulative weighted distance.
These three levels of modeling are illustrated below. At all levels, the distance is the basis of the measurement of
proximity, distance or accessibility. The distance is weighted by the characteristics of the elements. The directional
effect is
expressed by the variation of the weighting, depending on the orientation. Hence, the gravitational force, considered
as a friction
element, is considered to be neutral in the case of a transversal path. The moving element may be self driven or driven
by an external
force. Keep in mind that by modeling the space the 3D reality is reduced to two dimensions. In this example, the third
dimension
is translated into a thematic component: The friction properties.