Important Fields in Computational Geometry and their Significance

 The field of Computational geometry emerged in order to tackle the challenges posed by geometric problems.Important applications of Computational Geometric algorithms includes robotics(motion planning and visibility problems)geographic information systems(geometrical location and search,route planning),integrated circuit design(IC geometry design and verification),computer-aided engineering(CAE) and computer vision.(3D reconstruction).

The two main branches of Computational Geometry are Computational computational geometry and numerical computational geometry. Computational computational geometry:-The work carried out in this field mainly consists of developing efficient algorithms and data structures for solving problems related to general geometric objects and concepts like polygon,lines points etc.Developing asymptotically faster algorithms when the dateset consists of millions of sample points is one of the important goals of researchers in this field.

Numerical Computational Geometry:-The work carried out in this field is mainly related to the representation of real world objects in a form which is suitable for computations in the CAD/CAM systems. Computational geometry is a growing field and the core problems in it can be distinguished into different classes.A few classes I would like to mention are:-

a)Static problems-In this category generally some input is given and the output needs to be constructed or found e.g.Convex Hull and  Line Segment intersection.

b)Geometric Search Problems-Here the input generally consists of search space part and the query part.In order to answer multiple queries efficiently the search space is generally prepossessed.

c)Dynamic Problems:-Here we have to develop an efficient algorithm for the solution as the input data is either added or deleted.e.g.The dynamic convex hull problem.

As the field continues to grow and more efficient algorithms are developed,it will definitely have a great positive impact on fields like Computer Graphics,Computer vision etc.