# Algorithmic geometry

As **computational geometry** ( English *Computational Geometry* ) refers to a branch of computer science that deals with the algorithmic solution geometrically busy formulated problems. A central problem is the storage and processing of geometric data. In contrast to image processing , the basic elements of which are image points ( pixels ), algorithmic geometry works with geometric structural elements such as points , lines , circles , polygons and bodies .

Areas of responsibility for algorithmic geometry include:

- Efficient storage and retrieval of geometric information using databases
- Problems of analytical geometry (e.g. sections of geometric objects)
- Calculation of connected curves and surfaces from point clouds
- Linear optimization
- Search in geometric spaces
- Segmentation of spaces and sorting of objects

The processes of algorithmic geometry are used in computer-aided design , in computer graphics and for geographic information systems. Robotics was added as the most recent field of application , especially in the planning of motion sequences for robotic systems.

## literature

- Franco Preparata, Michael Shamos:
*Computational Geometry: An Introduction.*Springer 1993, ISBN 0-387-96131-3 - Mark de Berg et al. a:
*Computational Geometry: Algorithms and Applications.*Springer 2000, ISBN 3-540-65620-0 - Rolf Klein:
*Algorithmic Geometry.*Springer 2005, ISBN 3-540-20956-5 - Hanan Samet:
*Foundations of Multidimensional and Metric Data Structures.*Elsevier, Amsterdam 2006, ISBN 0-12-369446-9 - Philip Schneider, David Eberly:
*Geometric Tools for Computer Graphics.*Morgan Kaufmann, Amsterdam 2006, ISBN 1-55860-594-0