Computational Geometry

Computational geometry is a branch of computer science that studies algorithms which can be expressed in other forms of geometry. Historically, it is considered one of the oldest fields in computing, although modern computational geometry is a recent development. The primary reason for the development of computational geometry has been due to progress made in computer graphics, as well as computer-aided design and manufacturing. However, several problems tend to be classical in nature and come from mathematical visualization. Applications of computational geometry can be found in robotics, integrated circuit design, computer vision (3-D reconstruction), computer-aided engineering and geographic information systems (GIS)

Computational geometry is largely classified into two major branches: combinatorial computational geometry and numerical computational geometry. The first deals with geometric objects as discrete entities. For example, it can be used to determine the smallest polyhedron or polygon that contains all points that are given, which is a convex hull problem. Another example is that of the nearest neighbor problem, where it is required to find the closest point to a query point from a set of points. The second, numerical computational geometry, is meant to represent real-world objects in ways that are apt for computations in CAD or CAM systems. Important portions here are parametric surfaces and curves, such as spline curves and Bezier curves.