Computer Modeling of the Level Curves using Matrix Calculation and BSP Tree

Abstract

The update of topographic maps which thirty years ago was done manually is nowadays done interactively. The level curves of the topographic maps are originally obtained either by photogrammetric restitution or by a generalization of this restitution. Many research projects have been put forward with the aim to realize the topographic maps from topographic data base (Braun et al., 2007). These works imply the development of a new series of production of digital maps, by exploiting the vector database and various complementary sources of the cartographic level curves which offers the possibility of extracting other topographical elements, such as collars and peaks. Many papers focus on the production of the level curves such as (Riegler et al., 2006 and Wang, 2008). The scientific issues discussed in this paper focus on the generalization of the level curves by an interpolation method based on computer modeling, starting from one or more base lines with reference points allowing to generalize the set of level curves that have essential roles for the realization of a topographic map. The procedures and the computer objects that are put in the place integrate the cartographic constraints, and show the interest of object oriented modeling and the operations on sets (union, intersection, difference ...), and by manipulation of geometric transformations based on matrix operations. The data structures of the BSP tree have a crucial role for the conservations of geological constraints (Cheaito, and Cheaito, 2014), as well as the manipulation of set operations in two dimensions.