Geometric algorithms are a class of computational algorithms designed to solve problems related to geometric objects and their relationships in space. These algorithms are used in various fields such as computer graphics, computer-aided design, robotics, geographic information systems, and more. They deal with geometric primitives like points, lines, polygons, and shapes in 2D or 3D space.
Here are some common tasks and problems that geometric algorithms address:
Convex Hull: Finding the smallest convex polygon that encloses a set of points. This is useful in various applications like pattern recognition and image processing.
Point-in-Polygon: Determining whether a point is inside or outside a polygon.
Line Segment Intersection: Detecting if two line segments intersect in space.
Voronoi Diagrams: Dividing a space into regions based on the closest point from a set of input points. This has applications in facility location and mesh generation.
Delaunay Triangulation: Partitioning a set of points into non-overlapping triangles such that no point is inside the circumcircle of any triangle. This is often used in finite element analysis and mesh generation.
Collision Detection: Determining if two or more geometric objects (e.g., polygons, circles) intersect or collide.
Robot Motion Planning: Planning the path of a robot or object in a 2D or 3D space, avoiding obstacles.
Computational Geometry in 3D: Extending geometric algorithms to three-dimensional space for applications like 3D modeling, computer-aided design, and 3D gaming.
Geometric algorithms are fundamental in computer science and are essential in solving problems that involve spatial data and objects. They often require efficient data structures and mathematical techniques to perform their calculations accurately and quickly. These algorithms play a crucial role in various real-world applications, ranging from GPS navigation systems to video games and computer-aided manufacturing.