COMPUTATIONAL GEOMETRY Meaning and
Definition
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Computational geometry is a branch of computer science and mathematics that deals with the study and design of efficient algorithms and methods for solving geometric problems. It focuses on solving problems related to geometry using computational power and algorithms.
In computational geometry, geometric objects such as points, lines, curves, polygons, and higher-dimensional shapes are represented in a discrete and digital form to facilitate their manipulation using computers. This field explores various algorithms and techniques to perform geometric computations and to efficiently solve problems like geometric intersection, triangulation, point location, convex hull computation, Voronoi diagrams, nearest neighbor searching, and many others.
The field of computational geometry extensively uses concepts and techniques from computational complexity theory, graph theory, discrete mathematics, and numerical analysis. It utilizes algorithms and data structures like divide-and-conquer, sweep lines, space partitioning trees, and random sampling to efficiently process and analyze geometric data.
The applications of computational geometry are wide-ranging and diverse. It finds applications in various fields like computer graphics, computer-aided design (CAD), robotics, geographic information systems (GIS), computer vision, scientific simulations, and pattern recognition, among others. By providing efficient algorithms and tools to solve complex geometric problems, computational geometry plays a crucial role in solving real-world problems and facilitating advanced technological applications.
Etymology of COMPUTATIONAL GEOMETRY
The word "computational geometry" is a combination of the term "computational" and "geometry".
The term "computational" derives from the Latin word "computare", which means "to calculate" or "to sum up". It refers to anything related to the process of using computers to solve problems or perform calculations.
The term "geometry" comes from the Greek word "geōmetria", which combines "geo" meaning "earth" and "metron" meaning "measure". It is the branch of mathematics that deals with the properties, relationships, and measurements of points, lines, shapes, and solids.
So, "computational geometry" is a field that combines geometry with computational methods and algorithms to solve problems related to the geometric representation, manipulation, and analysis of objects and their properties using computers.
