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.
- 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